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https://www.symbolab.com/solver/algebra-calculator

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Number Line

Graph

Frequently Asked Questions (FAQ)

How do you solve algebraic expressions?

To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.

What are the basics of algebra?

The basics of algebra are the commutative, associative, and distributive laws.

What are the 3 rules of algebra?

The basic rules of algebra are the commutative, associative, and distributive laws.

What is the golden rule of algebra?

The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.

What are the 5 basic laws of algebra?

The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.

algebra-calculator

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Graph How do you solve algebraic expressions? To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.

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https://www.symbolab.com/geometry/angles-calculator

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Angles Calculator - find angle, given angles

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https://www.mathway.com/Graph

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Free graphing calculator instantly graphs your math problems.

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https://www.allmath.com/slope-intercept-form.php

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Enter the values in the below calculator. Hit the button to get the slope intercept form of a line using equation.

Slope intercept form calculator is an online tool that is used to find slope intercept form (equation of line) using two points, y-intercept, or one point and slope.

What is slope intercept form?

Slope intercept is a form of linear equation that can be used to find the equation of a straight line with y intercept and slope of line.

Slope intercept formula

The slope intercept equation can be represented as:
y = mx + b
Where,

m is slope of line, and

b is y intercept.

The equation of slope intercept varies in USA and UK. In UK, variable c is used to represent y-intercept.

y = mx + c

How to find the slope intercept form (equation of a straight line)?

To find equation of a straight line with slope and y-intercept, follow the example below.

Find the Straight line equation if y-intercept is and slope is
Solution:
Step 1: Identify the values.
b = 6 m = 4
Step 2: Write the slope form equation and place the values.

If you need to calculate the slope using two points, use slope calculator.

References

1. Khan Academy. (n.d.). Intro to slope-intercept form (Y=mx+b) | algebra (video). Retrieved january 4, 2020 from Khan Academy.

2. Alamo.edu. (2020). Slope Intercept Formula. Retrieved 4 january 2020.

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Slope intercept form Calculator (y-intercept graph Calculator)

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Enter the values in the below calculator. Hit the button to get the slope intercept form of a line using equation. Slope intercept form calculator is an online tool that is used to find slope intercept form (equation of line) using two points, y-intercept, or one point and slope.

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https://www.calculator.net/triangle-calculator.html

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This free triangle calculator computes the edges, angles, area, height, perimeter, median, as well as other values and a diagram of the resulting triangle.

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https://www.mathway.com/Algebra

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Free math problem solver answers your algebra homework questions with step-by-step explanations.

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https://www.calculatorsoup.com/calculators/geometry-plane/slope-calculator.php

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Slope calculator finds slope of a line using the formula m equals change in y divided by change in x. Shows the work, graphs the line and gives line equations.

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https://dqydj.com/greatest-to-least-calculator/

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On this page is a greatest to least calculator and organizer, which will take a mixed input of numbers and return the numbers sorted from highest to lowest.

Enter decimals, fractions, whole numbers, and even percentages and the tool will sort your numbers in descending order for you.
Other similar tools:
Greatest to Least Value Calculator

Using the Greatest to Least Calculator

First, enter all of your numbers into the big text box at the top of the calculator. Separate them with any character that isn't a number, percentage sign, or slash ('/').

You can enter:

Skip the Order field, unless you'd instead like to order them another way.

When happy, hit the Calculate Order button, and we'll normalize and sort all the numbers that you entered in descending order.
Now, try our other calculators and tools.

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Greatest to Least Calculator: Sort in Descending Order - DQYDJ

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On this page is a greatest to least calculator and organizer, which will take a mixed input of numbers and return the numbers sorted from highest to lowest. Enter decimals, fractions, whole numbers, and even percentages and the tool will sort your numbers in descending order for you.

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https://www.symbolab.com/solver/solve-for-equation-calculator

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Solve For a Variable Calculator - Symbolab

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Free solve for a variable calculator - solve the equation for different variables step-by-step

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https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php

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Calculator Use

Convert a number to and from scientific notation, e notation, engineering notation, standard form, and real numbers. Enter a number or a decimal number or scientific notation and the calculator converts to scientific notation, e notation, engineering notation, standard form and word form formats.

To enter a number in scientific notation use a carat ^ to indicate the powers of 10. You can also enter numbers in e notation. Examples: 3.45 x 10^5 or 3.45e5.

Order of magnitude will also be identified for the calculated standard form. The order of magnitude when written in standard form, is the nth power of 10. For example, 3.4 x 10^5 has an order of magnitude of 5 since 10 is raised to the 5th power.

How to Convert a Number to Scientific Notation

The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ | a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

1. Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

2. Count how many places you moved the decimal point. This number is b.

3. If you moved the decimal to the left b is positive.
If you moved the decimal to the rightb is negative.
If you did not need to move the decimalb = 0.

4. Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."

5. Remove trailing 0's only if they were originally to the left of the decimal point.

Example: Convert 357,096 to Scientific Notation

Move the decimal 5 places to the left to get 3.57096

a = 3.57096

We moved the decimal to the left so b is positive

b = 5

The number 357,096 converted to scientific notation is 3.57096 x 10^5

Example: Convert 0.005600 to Scientific Notation

Move the decimal 3 places to the right and remove leading zeros to get 5.600

a = 5.600

We moved the decimal to the right so b is negative

b = -3

The number 0.005600 converted to scientific notation is 5.600 x 10^-3

Note that we do not remove the trailing 0's because they were originally to the right of the decimal and are therefore significant figures.

E notation is basically the same as scientific notation except that the letter e is substituted for "x 10^".

Convert Scientific Notation to a Real Number

Multiply the decimal number by 10 raised to the power indicated.

3.456 x 10^4 = 3.456 x 10,000 = 34560

3.456 x 10^-4 = 3.456 x .0001 = 0.0003456

Additional Resources

See the Scientific Notation Calculator to add, subtract, multiply and divide numbers in scientific notation or E notation.

To round significant figures use the Significant Figures Calculator.

To see how standard form is similar to scientific notation visit Standard Form Calculator.

If you need a scientific calculator see our resources on scientific calculators.

Last updated: October 13, 2021

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Convert numbers to scientific notation. Calculator for conversion of numbers into scientific notation and e notation. Converts to proper scientific notation format.

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Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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A beautiful, free online scientific calculator with advanced features for evaluating percentages, fractions, exponential functions, logarithms, trigonometry, statistics, and more.

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https://www.calculatorsoup.com/calculators/statistics/quartile-calculator.php

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Calculator Use

This quartile calculator and interquartile range calculator finds first quartile Q ₁, second quartile Q ₂ and third quartile Q ₃ of a data set. It also finds median, minimum, maximum, and interquartile range.

Enter data separated by commas or spaces.

You can also copy and paste lines of data from spreadsheets or text documents. See all allowable formats in the table below.

Quartiles

Quartiles mark each 25% of a set of data:

The first quartile Q₁ is the 25th percentile

The second quartile Q₂ is the 50th percentile

The third quartile Q₃ is the 75th percentile

The second quartile Q ₂ is easy to find. It is the median of any data set and it divides an ordered data set into upper and lower halves.

The first quartile Q ₁ is the median of the lower half not including the value of Q ₂. The third quartile Q ₃ is the median of the upper half not including the value of Q ₂.

How to Calculate Quartiles

1. Order your data set from lowest to highest values

2. Find the median. This is the second quartile Q₂.

3. At Q₂ split the ordered data set into two halves.

4. The lower quartile Q₁ is the median of the lower half of the data.

5. The upper quartile Q₃ is the median of the upper half of the data.

If the size of the data set is odd, do not include the median when finding the first and third quartiles.

If the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q ₂.

How to Find Interquartile Range

The interquartile range IQR is the range in values from the first quartile Q ₁ to the third quartile Q ₃. Find the IQR by subtracting Q ₁ from Q ₃.

How to Find the Minimum

The minimum is the smallest value in a sample data set.

Ordering a data set from lowest to highest value, , the minimum is the smallest value . The formula for minimum is:

\[ \text{Min} = x_1 = \text{min}(x_i)_{i=1}^{n} \]

How to Find the Maximum

The maximum is the largest value in a sample data set.

Ordering a data set from lowest to highest value, , the maximum is the largest value . The formula for maximum is:

\[ \text{Max} = x_n = \text{max}(x_i)_{i=1}^{n} \]

How to Find the Range of a Set of Data

The range of a data set is the difference between the minimum and maximum. To find the range, calculate x n minus x ₁.

\[ R = x_n - x_1 \]

or

or

References

[1] Wikipedia contributors. " Quartile." Wikipedia, The Free Encyclopedia. Last visited 10 April, 2020.

Last updated: September 19, 2023

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Quartile Calculator | Interquartile Range Calculator

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Calculate first, second and third quartiles, Q 1 Q 2 Q 3 , for a set of data. Find median, interquartile range IQR, dataset minimum and maximum for statistics data analysis.

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https://www.calculator.net/volume-calculator.html

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The following is a list of volume calculators for several common shapes. Please fill in the corresponding fields and click the "Calculate" button.

Sphere Volume Calculator

Cone Volume Calculator

Cube Volume Calculator

Cylinder Volume Calculator

Rectangular Tank Volume Calculator

Capsule Volume Calculator

Spherical Cap Volume Calculator

Please provide any two values below to calculate.

Conical Frustum Volume Calculator

Ellipsoid Volume Calculator

Square Pyramid Volume Calculator

Tube Volume Calculator

Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter, or m³. By convention, the volume of a container is typically its capacity, and how much fluid it is able to hold, rather than the amount of space that the actual container displaces. Volumes of many shapes can be calculated by using well-defined formulas. In some cases, more complicated shapes can be broken down into simpler aggregate shapes, and the sum of their volumes is used to determine total volume. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary. Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite element method. Alternatively, if the density of a substance is known, and is uniform, the volume can be calculated using its weight. This calculator computes volumes for some of the most common simple shapes.

Sphere

A sphere is the three-dimensional counterpart of a two-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the set of points that are equidistant from a given point at its center, where the distance between the center and any point on the sphere is the radius r. Likely the most commonly known spherical object is a perfectly round ball. Within mathematics, there is a distinction between a ball and a sphere, where a ball comprises the space bounded by a sphere. Regardless of this distinction, a ball and a sphere share the same radius, center, and diameter, and the calculation of their volumes is the same. As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter, d. The equation for calculating the volume of a sphere is provided below:

EX: Claire wants to fill a perfectly spherical water balloon with radius 0.15 ft with vinegar to use in the water balloon fight against her arch-nemesis Hilda this coming weekend. The volume of vinegar necessary can be calculated using the equation provided below:

volume = 4/3 × π × 0.15 ³ = 0.141 ft ³

Cone

A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a set of line segments connected to a common center point, except that the center point is not included in the plane that contains the circle (or some other base). Only the case of a finite right circular cone is considered on this page. Cones comprised of half-lines, non-circular bases, etc. that extend infinitely will not be addressed. The equation for calculating the volume of a cone is as follows:

where r is the radius and h is the height of the cone

EX: Bea is determined to walk out of the ice cream store with her hard-earned $5 well spent. While she has a preference for regular sugar cones, the waffle cones are indisputably larger. She determines that she has a 15% preference for regular sugar cones over waffle cones and needs to determine whether the potential volume of the waffle cone is ≥ 15% more than that of the sugar cone. The volume of the waffle cone with a circular base with radius 1.5 in and height 5 in can be computed using the equation below:

volume = 1/3 × π × 1.5 ² × 5 = 11.781 in ³

Bea also calculates the volume of the sugar cone and finds that the difference is < 15%, and decides to purchase a sugar cone. Now all she has to do is use her angelic, childlike appeal to manipulate the staff into emptying the containers of ice cream into her cone.

Cube

A cube is the three-dimensional analog of a square, and is an object bounded by six square faces, three of which meet at each of its vertices, and all of which are perpendicular to their respective adjacent faces. The cube is a special case of many classifications of shapes in geometry, including being a square parallelepiped, an equilateral cuboid, and a right rhombohedron. Below is the equation for calculating the volume of a cube:

volume = a ³
where a is the edge length of the cube

EX: Bob, who was born in Wyoming (and has never left the state), recently visited his ancestral homeland of Nebraska. Overwhelmed by the magnificence of Nebraska and the environment unlike any other he had previously experienced, Bob knew that he had to bring some of Nebraska home with him. Bob has a cubic suitcase with edge lengths of 2 feet, and calculates the volume of soil that he can carry home with him as follows:

Cylinder

A cylinder in its simplest form is defined as the surface formed by points at a fixed distance from a given straight line axis. In common use, however, "cylinder" refers to a right circular cylinder, where the bases of the cylinder are circles connected through their centers by an axis perpendicular to the planes of its bases, with given height h and radius r. The equation for calculating the volume of a cylinder is shown below:

volume = πr ²h
where r is the radius and h is the height of the tank

EX: Caelum wants to build a sandcastle in the living room of his house. Because he is a firm advocate of recycling, he has recovered three cylindrical barrels from an illegal dumping site and has cleaned the chemical waste from the barrels using dishwashing detergent and water. The barrels each have a radius of 3 ft and a height of 4 ft, and Caelum determines the volume of sand that each can hold using the equation below:

volume = π × 3 ² × 4 = 113.097 ft ³

He successfully builds a sandcastle in his house, and as an added bonus, manages to save electricity on nighttime lighting, since his sandcastle glows bright green in the dark.

Rectangular Tank

A rectangular tank is a generalized form of a cube, where the sides can have varying lengths. It is bounded by six faces, three of which meet at its vertices, and all of which are perpendicular to their respective adjacent faces. The equation for calculating the volume of a rectangle is shown below:

volume= length × width × height

EX: Darby likes cake. She goes to the gym for 4 hours a day, every day, to compensate for her love of cake. She plans to hike the Kalalau Trail in Kauai and though extremely fit, Darby worries about her ability to complete the trail due to her lack of cake. She decides to pack only the essentials and wants to stuff her perfectly rectangular pack of length, width, and height 4 ft, 3 ft and 2 ft respectively, with cake. The exact volume of cake she can fit into her pack is calculated below:

volume = 2 × 3 × 4 = 24 ft ³

Capsule

A capsule is a three-dimensional geometric shape comprised of a cylinder and two hemispherical ends, where a hemisphere is half a sphere. It follows that the volume of a capsule can be calculated by combining the volume equations for a sphere and a right circular cylinder:

where r is the radius and h is the height of the cylindrical portion

EX: Given a capsule with a radius of 1.5 ft and a height of 3 ft, determine the volume of melted milk chocolate m&m's that Joe can carry in the time capsule he wants to bury for future generations on his journey of self-discovery through the Himalayas:

Spherical Cap

A spherical cap is a portion of a sphere that is separated from the rest of the sphere by a plane. If the plane passes through the center of the sphere, the spherical cap is referred to as a hemisphere. Other distinctions exist, including a spherical segment, where a sphere is segmented with two parallel planes and two different radii where the planes pass through the sphere. The equation for calculating the volume of a spherical cap is derived from that of a spherical segment, where the second radius is 0. In reference to the spherical cap shown in the calculator:

Given two values, the calculator provided computes the third value and the volume. The equations for converting between the height and the radii are shown below:

Given R and h: r = √
where r is the radius of the base, R is the radius of the sphere, and h is the height of the spherical cap

EX: Jack really wants to beat his friend James in a game of golf to impress Jill, and rather than practicing, he decides to sabotage James' golf ball. He cuts off a perfect spherical cap from the top of James' golf ball, and needs to calculate the volume of the material necessary to replace the spherical cap and skew the weight of James' golf ball. Given James' golf ball has a radius of 1.68 inches, and the height of the spherical cap that Jack cut off is 0.3 inches, the volume can be calculated as follows:

volume = 1/3 × π × 0.3 ² (3 × 1.68 - 0.3) = 0.447 in ³

Unfortunately for Jack, James happened to receive a new shipment of balls the day before their game, and all of Jack's efforts were in vain.

Conical Frustum

A conical frustum is the portion of a solid that remains when a cone is cut by two parallel planes. This calculator calculates the volume for a right circular cone specifically. Typical conical frustums found in everyday life include lampshades, buckets, and some drinking glasses. The volume of a right conical frustum is calculated using the following equation:

where r and R are the radii of the bases, h is the height of the frustum

EX: Bea has successfully acquired some ice cream in a sugar cone, and has just eaten it in a way that leaves the ice cream packed within the cone, and the ice cream surface level and parallel to the plane of the cone's opening. She is about to start eating her cone and the remaining ice cream when her brother grabs her cone and bites off a section of the bottom of her cone that is perfectly parallel to the previously sole opening. Bea is now left with a right conical frustum leaking ice cream, and has to calculate the volume of ice cream she must quickly consume given a frustum height of 4 inches, with radii 1.5 inches and 0.2 inches:

volume=1/3 × π × 4(0.2 ² + 0.2 × 1.5 + 1.5 ²) = 10.849 in ³

Ellipsoid

An ellipsoid is the three-dimensional counterpart of an ellipse, and is a surface that can be described as the deformation of a sphere through scaling of directional elements. The center of an ellipsoid is the point at which three pairwise perpendicular axes of symmetry intersect, and the line segments delimiting these axes of symmetry are called the principal axes. If all three have different lengths, the ellipsoid is commonly described as tri-axial. The equation for calculating the volume of an ellipsoid is as follows:

where a, b, and c are the lengths of the axes

EX: Xabat only likes eating meat, but his mother insists that he consumes too much, and only allows him to eat as much meat as he can fit within an ellipsoid shaped bun. As such, Xabat hollows out the bun to maximize the volume of meat that he can fit in his sandwich. Given that his bun has axis lengths of 1.5 inches, 2 inches, and 5 inches, Xabat calculates the volume of meat he can fit in each hollowed bun as follows:

volume = 4/3 × π × 1.5 × 2 × 5 = 62.832 in ³

Square Pyramid

A pyramid in geometry is a three-dimensional solid formed by connecting a polygonal base to a point called its apex, where a polygon is a shape in a plane bounded by a finite number of straight line segments. There are many possible polygonal bases for a pyramid, but a square pyramid is a pyramid in which the base is a square. Another distinction involving pyramids involves the location of the apex. A right pyramid has an apex that is directly above the centroid of its base. Regardless of where the apex of the pyramid is, as long as its height is measured as the perpendicular distance from the plane containing the base to its apex, the volume of the pyramid can be written as:

Generalized pyramid volume:

where b is the area of the base and h is the height

Square pyramid volume:

where a is the length of the base's edge

EX: Wan is fascinated by ancient Egypt and particularly enjoys anything related to the pyramids. Being the eldest of his siblings Too, Tree and Fore, he is able to easily corral and deploy them at his will. Taking advantage of this, Wan decides to re-enact ancient Egyptian times and have his siblings act as workers building him a pyramid of mud with edge length 5 feet and height 12 feet, the volume of which can be calculated using the equation for a square pyramid:

volume = 1/3 × 5 ² × 12 = 100 ft ³

Tube Pyramid

A tube, often also referred to as a pipe, is a hollow cylinder that is often used to transfer fluids or gas. Calculating the volume of a tube essentially involves the same formula as a cylinder ( volume=pr²h), except that in this case, the diameter is used rather than the radius, and length is used rather than height. The formula, therefore, involves measuring the diameters of the inner and outer cylinder, as shown in the figure above, calculating each of their volumes, and subtracting the volume of the inner cylinder from that of the outer one. Considering the use of length and diameter mentioned above, the formula for calculating the volume of a tube is shown below:

where is the outer diameter, is the inner diameter, and l is the length of the tube

EX: Beulah is dedicated to environmental conservation. Her construction company uses only the most environmentally friendly of materials. She also prides herself on meeting customer needs. One of her customers has a vacation home built in the woods, across a creek. He wants easier access to his house, and requests that Beulah build him a road, while ensuring that the creek can flow freely so as not to disrupt his favorite fishing spot. She decides that the pesky beaver dams would be a good point to build a pipe through the creek. The volume of patented low-impact concrete required to build a pipe of outer diameter 3 feet, inner diameter 2.5 feet, and length of 10 feet, can be calculated as follows:

Common Volume Units

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The following is a list of volume calculators for several common shapes. Please fill in the corresponding fields and click the "Calculate" button. Please provide any two values below to calculate. Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter, or m3 .

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https://www.calculator.net/standard-deviation-calculator.html

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Please provide numbers separated by comma to calculate the standard deviation, variance, mean, sum, and margin of error.

Related
Probability Calculator | Sample Size Calculator | Statistics Calculator

Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ. Conversely, a higher standard deviation indicates a wider range of values. Similarly to other mathematical and statistical concepts, there are many different situations in which standard deviation can be used, and thus many different equations. In addition to expressing population variability, the standard deviation is also often used to measure statistical results such as the margin of error. When used in this manner, standard deviation is often called the standard error of the mean, or standard error of the estimate with regard to a mean. The calculator above computes population standard deviation and sample standard deviation, as well as confidence interval approximations.

Population Standard Deviation

The population standard deviation, the standard definition of σ, is used when an entire population can be measured, and is the square root of the variance of a given data set. In cases where every member of a population can be sampled, the following equation can be used to find the standard deviation of the entire population:

For those unfamiliar with summation notation, the equation above may seem daunting, but when addressed through its individual components, this summation is not particularly complicated. The i=1 in the summation indicates the starting index, i.e. for the data set 1, 3, 4, 7, 8, i=1 would be 1, i=2 would be 3, and so on. Hence the summation notation simply means to perform the operation of on each value through N, which in this case is 5 since there are 5 values in this data set.

Sample Standard Deviation

In many cases, it is not possible to sample every member within a population, requiring that the above equation be modified so that the standard deviation can be measured through a random sample of the population being studied. A common estimator for σ is the sample standard deviation, typically denoted by s. It is worth noting that there exist many different equations for calculating sample standard deviation since unlike sample mean, sample standard deviation does not have any single estimator that is unbiased, efficient, and has a maximum likelihood. The equation provided below is the "corrected sample standard deviation." It is a corrected version of the equation obtained from modifying the population standard deviation equation by using the sample size as the size of the population, which removes some of the bias in the equation. Unbiased estimation of standard deviation however, is highly involved and varies depending on distribution. As such, the "corrected sample standard deviation" is the most commonly used estimator for population standard deviation, and is generally referred to as simply the "sample standard deviation." It is a much better estimate than its uncorrected version, but still has significant bias for small sample sizes (N<10).

Refer to the "Population Standard Deviation" section for an example on how to work with summations. The equation is essentially the same excepting the N-1 term in the corrected sample deviation equation, and the use of sample values.

Applications of Standard Deviation

Standard deviation is widely used in experimental and industrial settings to test models against real-world data. An example of this in industrial applications is quality control for some product. Standard deviation can be used to calculate a minimum and maximum value within which some aspect of the product should fall some high percentage of the time. In cases where values fall outside the calculated range, it may be necessary to make changes to the production process to ensure quality control.

Standard deviation is also used in weather to determine differences in regional climate. Imagine two cities, one on the coast and one deep inland, that have the same mean temperature of 75°F. While this may prompt the belief that the temperatures of these two cities are virtually the same, the reality could be masked if only the mean is addressed and the standard deviation ignored. Coastal cities tend to have far more stable temperatures due to regulation by large bodies of water, since water has a higher heat capacity than land; essentially, this makes water far less susceptible to changes in temperature, and coastal areas remain warmer in winter, and cooler in summer due to the amount of energy required to change the temperature of water. Hence, while the coastal city may have temperature ranges between 60°F and 85°F over a given period of time to result in a mean of 75°F, an inland city could have temperatures ranging from 30°F to 110°F to result in the same mean.

Another area in which standard deviation is largely used is finance, where it is often used to measure the associated risk in price fluctuations of some asset or portfolio of assets. The use of standard deviation in these cases provides an estimate of the uncertainty of future returns on a given investment. For example, in comparing stock A that has an average return of 7% with a standard deviation of 10% against stock B, that has the same average return but a standard deviation of 50%, the first stock would clearly be the safer option, since standard deviation of stock B is significantly larger, for the exact same return. That is not to say that stock A is definitively a better investment option in this scenario, since standard deviation can skew the mean in either direction. While Stock A has a higher probability of an average return closer to 7%, Stock B can potentially provide a significantly larger return (or loss).

These are only a few examples of how one might use standard deviation, but many more exist. Generally, calculating standard deviation is valuable any time it is desired to know how far from the mean a typical value from a distribution can be.

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This free standard deviation calculator computes the standard deviation, variance, mean, sum, and error margin of a given data set. Learn more about various applications of standard deviation, or explore hundreds of other calculators addressing topics such as finance, math, health, and fitness, among others.

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https://www.calculatorsoup.com/calculators/statistics/mean-median-mode.php

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Mean, median and mode calculator for statistics. Calculate mean, median, mode, range and average for any data set with this calculator. Free online statistics calculators.

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https://www.calculator.net/surface-area-calculator.html

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Use the calculators below to calculate the surface area of several common shapes.

Ball Surface Area

Cone Surface Area

Cube Surface Area

Cylindrical Tank Surface Area

Rectangular Tank Surface Area

Capsule Surface Area

Cap Surface Area

Please provide any two values below to calculate.

Conical Frustum Surface Area

Ellipsoid Surface Area

Square Pyramid Surface Area

Related
Volume Calculator | Area Calculator | Body Surface Area Calculator

The surface area of a solid is a measure of the total area occupied by the surface of an object. All of the objects addressed in this calculator are described in more detail on the Volume Calculator and Area Calculator pages. As such, this calculator will focus on the equations for calculating the surface area of the objects and the use of these equations. Please refer to the aforementioned calculators for more detail on each individual object.

Sphere

The surface area (SA) of a sphere can be calculated using the equation:

Xael doesn't like sharing her chocolate truffles with anyone. When she receives a box of Lindt truffles, she proceeds to calculate the surface area of each truffle in order to determine the total surface area she has to lick to decrease the probability that anyone will try to eat her truffles. Given that each truffle has a radius of 0.325 inches:

Cone

The surface area of a circular cone can be calculated by summing the surface area of each of its individual components. The "base SA" refers to the circle that comprises the base in a closed circular cone, while the lateral SA refers to the rest of the area of the cone between the base and its apex. The equations to calculate each, as well as the total SA of a closed circular cone are shown below:

Athena has recently taken an interest in Southeast Asian culture, and is particularly fascinated by the conical hat, typically referred to as a "rice hat," which is commonly used in a number of southeast Asian countries. She decides to make one of her own, and being a very practical person not mired in sentimentality, retrieves her mother's wedding dress from the dark recesses of the wardrobe in which it resides. She determines the surface area of material she needs to create her hat with a radius of 1 foot and a height of 0.5 feet as follows:

Cube

The surface area of a cube can be calculated by summing the total areas of its six square faces:

Anne wants to give her younger brother a Rubik's cube for his birthday, but knows that her brother has a short attention span and is easily frustrated. She custom orders a Rubik's Cube in which all the faces are black, and has to pay for the customization based on the surface area of the cube with an edge length of 4 inches.

Cylindrical Tank

The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface:

base SA = 2πr ²
lateral SA = 2πrh
total SA = 2πr(r + h) where r is the radius and h is the height

Jeremy has a large cylindrical fish tank that he bathes in because he doesn't like showers or bathtubs. He is curious whether his heated water cools faster than when in a bathtub, and needs to calculate the surface area of his cylindrical tank of height 5.5 feet and radius of 3.5 feet.

total SA = 2π × 3.5(3.5 + 5.5) = 197.920 ft ²

Rectangular Tank

The surface area of a rectangular tank is the sum of the area of each of its faces:

SA = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height

Banana, the eldest daughter of a long line of banana farmers, wants to teach her spoiled rotten little sister, Banana-Bread, a lesson about hope and expectations. Banana-Bread has been clamoring all week long about wanting a new set of drawers to house her new Batman action figures. As such, Banana buys her a large Barbie doll house with limited edition kitchen utensils, oven, apron, and realistic rotting bananas for Batman. She packs these into a rectangular box of similar dimensions as the drawer that Banana-Bread wants, and needs to determine the amount of wrapping paper she needs to complete her presentation of the gift of the 3 ft × 4 ft × 5 ft surprise:

SA = (2 × 3 × 4) + (2 × 4 × 5) + (2 × 3 × 5) = 94 ft ²

Capsule

The surface area of a capsule can be determined by combining the surface area equations for a sphere and the lateral surface area of a cylinder. Note that the surface area of the bases of the cylinder is not included since it does not comprise part of the surface area of a capsule. The total surface area is calculated as follows:

SA = 4πr ² + 2πrh
where r is the radius and h is the height

Horatio is manufacturing a placebo that purports to hone a person's individuality, critical thinking, and ability to objectively and logically approach different situations. He has already tested the market and has found that a vast majority of the sample population exhibit none of these qualities, and are very ready to purchase his product, further entrenching themselves within the traits they so desperately seek to escape. Horatio needs to determine the surface area of each capsule so that he can coat them with an excessive layer of sugar and appeal to the sugar predisposed tongues of the population in preparation for his next placebo that "cures" all forms of diabetes mellitus. Given each capsule has r of 0.05 inches and h of 0.5 inches:

SA = 4π × 0.05 ² + 2π × 0.05 × 0.5 = 0.188 in ²

Spherical Cap

The surface area of a spherical cap is based on the height of the segment in question. The calculator provided assumes a solid sphere and includes the base of the cap in the calculation of surface area, where the total surface area is the sum of the area of the base and that of the lateral surface of the spherical cap. If using this calculator to compute the surface area of a hollow sphere, subtract the surface area of the base. Given two values of height, cap radius, or base radius, the third value can be calculated using the equations provided on the Volume Calculator. The surface area equations are as follows:

spherical cap SA = 2πRh
base SA = πr ²
Total solid sphere SA = 2πRh + πr ²
where R is the spherical cap radius, r is the base radius, and h is the height

Jennifer is jealous of the globe that her older brother Lawrence received for his birthday. Since Jennifer is two-thirds the age of her brother, she decides that she deserves one-third of her brother's globe. After returning her father's hand saw to the toolshed, she calculates the surface area of her hollow portion of the globe with R of 0.80 feet and h 0.53 feet as shown below:

SA = 2π × 0.80 × 0.53 = 2.664 ft ²

Conical Frustum

The surface area of a solid, right conical frustum is the sum of the areas of its two circular ends and that of its lateral face:

Paul is making a volcano in the shape of a conical frustum for his science fair project. Paul views volcanic eruptions as a violent phenomenon, and being against all forms of violence, decides to make his volcano in the form of a closed conical frustum that does not erupt. Although his volcano is unlikely to impress the science fair judges, Paul must still determine the surface area of material he needs to coat the outer wall of his volcano with R of 1 foot, r of 0.3 feet, and h of 1.5 feet:

Ellipsoid

Calculating the surface area of an ellipsoid does not have a simple, exact formula such as a cube or other simpler shape does. The calculator above uses an approximate formula that assumes a nearly spherical ellipsoid:

Coltaine has always enjoyed cooking and recently won a ceramic knife from a contest. Unfortunately for his family, who almost exclusively eat meat, Coltaine has been practicing his cutting technique on an excessive amount of vegetables. Rather than eating his vegetables, Coltaine's father stares dejectedly at his plate, and estimates the surface area of the elliptical cuts of zucchini with axes 0.1, 0.2, and 0.35 inches:

Square Pyramid

The surface area of a square pyramid is comprised of the area of its square base and the area of each of its four triangular faces. Given height h and edge length a, the surface area can be calculated using the following equations:

Vonquayla's classroom recently completed building a model of the Great Pyramid of Giza. However, she feels that the model does not exude the feeling of architectural wonder that the original does and decides that coating it with "snow" would at least impart an aspect of wonder. She calculates the surface area of melted sugar she would need to fully coat the pyramid with edge length a of 3 feet and height h of 5 feet:

Unlike the Great Pyramid of Giza that has stood for thousands of years, its model, made of graham crackers and coated in sugar, lasted only a matter of days.

Common Area Units

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Use the calculators below to calculate the surface area of several common shapes. Please provide any two values below to calculate. Related Volume Calculator | Area Calculator | Body Surface Area Calculator The surface area of a solid is a measure of the total area occupied by the surface of an object.

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https://www.calculator.net/average-calculator.html

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Please provide numbers separated by a comma to calculate the average of the numbers.

Related
Standard Deviation Calculator | Sample Size Calculator

What is an average?

The term average has a number of different meanings. Most generally, it is a single number that is used to represent a collection of numbers. In the context of mathematics, "average" refers to the mean, specifically, the arithmetic mean. It is a relatively simple statistical concept that is widely used in many areas.

The equation below is one of the more commonly understood definitions of the average:

where the sum is the result of adding all of the given numbers, and the count is the number of values being added. For example, given the 5 numbers, 2, 7, 19, 24, and 25, the average can be calculated as such:

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Free calculator to determine the average, or the arithmetic mean, of a given data set. It also returns the calculation steps, sum, count, and more.

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https://www.calculatorsoup.com/calculators/math/decimal-to-fraction-calculator.php

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Convert decimals to fractions or mixed number fractions. Calculator to change decimals to fractions showing the work with steps. Converts repeating decimals to fractions.

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https://www.calculatorsoup.com/calculators/math/mixednumbers.php

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Calculator Use

Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions.

Mixed Numbers Calculator (also referred to as Mixed Fractions):

This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.

Enter mixed numbers, whole numbers or fractions in the following formats:

Mixed numbers: Enter as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).

Whole numbers: Up to 3 digits in length.

Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths. You can enter up to 3 digits in length for each the numerators and denominators (e.g., 456/789).

Adding Mixed Numbers using the Adding Fractions Formula

1. Convert the mixed numbers to improper fractions

2. Use the algebraic formula for addition of fractions:
a/b + c/d = (ad + bc) / bd

3. Reduce fractions and simplify if possible

Adding Fractions Formula

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \times d) + (b \times c)}{b \times d} \)

Example

Add 1 2/6 and 2 1/4

\( 1 \dfrac{2}{6} + 2 \dfrac{1}{4} = \dfrac{8}{6} + \dfrac{9}{4} \)

\( = \dfrac{(8 \times 4) + (9 \times 6)}{6 \times 4} \)

\( = \dfrac{32 + 54}{24} = \dfrac{86}{24} = \dfrac{43}{12} \)

1 2/6 + 2 1/4 = 8/6 + 9/4 = (8*4 + 9*6) / 6*4 = 86 / 24

So we get 86/24 and simplify to 3 7/12

Subtracting Mixed Numbers using the Subtracting Fractions Formula

1. Convert the mixed numbers to improper fractions

2. Use the algebraic formula for subtraction of fractions: a/b - c/d = (ad - bc) / bd

3. Reduce fractions and simplify if possible

Subtracting Fractions Formula

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{(a \times d) - (b \times c)}{b \times d} \)

Example

Subtract 2 1/4 from 1 2/6

1 2/6 - 2 1/4 = 8/6 - 9/4 = (8*4 - 9*6) / 6*4 = -22 / 24

Reduce the fraction to get -11/12

Multiplying Mixed Numbers using the Multiplying Fractions Formula

1. Convert the mixed numbers to improper fractions

2. Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd

3. Reduce fractions and simplify if possible

Multiplying Fractions Formula

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \)

Example

multiply 1 2/6 by 2 1/4

1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24

Reduce the fraction to get 3/1 and simplify to 3

Dividing Mixed Numbers using the Dividing Fractions Formula

1. Convert the mixed numbers to improper fractions

2. Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc

3. Reduce fractions and simplify if possible

Dividing Fractions Formula

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \times d}{b \times c} \)

Example

divide 1 2/6 by 2 1/4

1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54

Reduce the fraction to get 16/27

Related Calculators

To perform math operations on simple proper or improper fractions use our Fractions Calculator. This calculator simplifies improper fraction answers into mixed numbers.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

Last updated: October 17, 2023

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Mixed numbers calculator to add, subtract, multiply and divide mixed numbers (mixed fractions), fractions and integers. Do math with mixed numbers and mixed fractions such as 1 1/2 or 3 5/8.

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https://www.calculatorsoup.com/calculators/math/fractions.php

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Calculator Use

Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 × 3/8.

To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator.

Math on Fractions with Unlike Denominators

There are 2 cases where you need to know if your fractions have different denominators:

if you are adding fractions

if you are subtracting fractions

How to Add or Subtract Fractions

1. Find the least common denominator

2. You can use the LCD Calculator to find the least common denominator for a set of fractions

3. For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator

4. Multiply the numerator and denominator of your first fraction by that number

5. Repeat Steps 3 and 4 for each fraction

6. For addition equations, add the fraction numerators

7. For subtraction equations, subtract the fraction numerators

8. Convert improper fractions to mixed numbers

9. Reduce the fraction to lowest terms

How to Multiply Fractions

1. Multiply all numerators together

2. Multiply all denominators together

3. Reduce the result to lowest terms

How to Divide Fractions

1. Rewrite the equation as in "Keep, Change, Flip"

2. Keep the first fraction

3. Change the division sign to multiplication

4. Flip the second fraction by switching the top and bottom numbers

5. Multiply all numerators together

6. Multiply all denominators together

7. Reduce the result to lowest terms

Fraction Formulas

There is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below.

You may find that it is easier to use these formulas than to do the math to find the least common denominator.

The formulas for multiplying and dividing fractions follow the same process as described above.

Adding Fractions

The formula for adding fractions is:

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd} \)

Example steps:

\( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \)

\( = \dfrac{14}{24} = \dfrac {7}{12} \)

Subtracting Fractions

The formula for subtracting fractions is:

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd} \)

Example steps:

\( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Multiplying Fractions

The formula for multiplying fractions is:

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd} \)

Example steps:

\( \dfrac{2}{6} \times \dfrac{1}{4} = \dfrac{2\times1}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Dividing Fractions

The formula for dividing fractions is:

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc} \)

Example steps:

\( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \)

\( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \)

Related Calculators

To perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

Notes

Last updated: March 18, 2019

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Use this fraction calculator to add, subtract, multiply and divide fractions. Shows the work and the steps to do math with fractions. Reduces fractions to lowest terms.

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https://www.percentagecal.com/answer/what-is-25-percent-of-%2052#:~:text=Percentage%20Calculator%3A%20What%20is%2025,%3D%2013

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Solution for What is 25 percent of 52: 25 percent * 52 = (25:100)* 52 = (25* 52):100 = 1300:100 = 13 Now we have: 25 percent of 52 = 13 Question: What is 25 percent of 52? Percentage solution with steps: Step 1: Our output value is 52.