# Math Formulas

A collection of math formulas for lookup and reference. Each formula contains an explanation of how the formula is used, what different variables represent within the formula and examples of the formula in action.

## Algebra

Midpoint Formula

Calculate the midpoint of a line defined by two points.

Solve for the x-intercepts of a quadratic equation.

Slope

Calculate the slope of a line using two points on the line.

## Geometry

Area of Circle

Calculate the area of a circle given the radius.

Area of Circle π (pi)

Calculate the area of a circle given the radius.

Area of Parallelogram

Calculate the area of a parallelogram given the base and height.

Area of Rectangle

Calculate the area of a rectangle given the width and height.

Area of Trapezoid

Calculate the area of a trapezoid given the bottom, top and height.

Area of Triangle

Calculate the area of a triangle given the width and height.

Circumference of Circle

Calculate the circumference of a circle given the radius.

Circumference of Circle π (pi)

Calculate the circumference of a circle given the radius.

Distance Between Two Points 1D

Calculate the distance between two points in one dimension.

Distance Between Two Points 2D

Calculate the distance between two points in two dimensions.

Midpoint Formula

Calculate the midpoint of a line defined by two points.

Slope

Calculate the slope of a line using two points on the line.

Volume of Cone

Calculate the volume of a cone given the radius and height.

Volume of Cube

Calculate the volume of a cube given the width.

Volume of Cylinder

Calculate the volume of a cylinder given the radius and height.

Volume of Rectangular Prism

Calculate the volume of a rectangular prism given the width, height and length.

Volume of Sphere

Calculate the volume of a sphere given the radius.

## Trigonometry

Angle Between Two Vectors 2D

Calculate the angle between two vectors.

Magnitude of Cross Product

Calculate the magnitude of the cross product of two vectors.

Polar to Cartesian Coordinates

Convert a point from the polar coordinate system to the cartesian coordinate system.

## Calculus

Euler's Formula

Calculate a point on the complex unit circle given an angle.

Population Growth

Calculate the population after time has elapsed.

## Linear Algebra

Angle Between Two Vectors

Calculate the angle between two vectors.

Angle Between Two Vectors 2D

Calculate the angle between two vectors.

Area Between Two Vectors 2D

Calculate the area between two vectors.

Cross Product (Determinant)

Calculate the cross product of two vectors using the formal determinant.

Determinant of 2 by 2 Matrix

Calculate the determinant of a 2 by 2 matrix.

Determinant of 3 by 3 Matrix

The formula for the determinant of a three by three matrix.

Dot Product

Calculate the dot product of two vectors.

Dot Product Geometric

Calculate the dot product of two vectors.

Magnitude of Cross Product

Calculate the magnitude of the cross product of two vectors.

Magnitude of Vector

Calculate the magnitude (length) of a vector.

## Probability

Combination

Calculate the possible combinations of a subset of a collection.

Compound Interest

Calculate the value of principle with compounding interest over time.

Conditional Probability

Calculate the probability of an event, given that another event has already occurred.

Expected Value Continuous Distribution

Calculate the expected value of a continuous distribution.

Expected Value Discrete Distribution

Calculate the expected value of a discrete distribution.

Permutation

Calculate the number of possible permutations of a subset of a collection.

Permutations of a Set

Calculate the possible permutations of a set.

Sample Mean

Calculate the sample mean of data.

Sample Standard Deviation

Calculate the standard deviation of a distribution from sample data.

Standard Deviation

Calculate the standard deviation of a distribution from population data.