# Formulas

A collection of math formulas for lookup and reference. Each formula contains a series of steps to produce a desired result.

Slope

The slope formula gives the slope of a line. Slope is defined as the change in y over the change in x. Another way of thinking about slope is the rise over run.

Area of Circle

The area of a circle is given by π (pi) times the radius of the circle squared.

Area of Parallelogram

The area of any parallelogram is equal to the base multiplied by the height.

Area of Rectangle

The Area of a rectangle is given by its width multiplied by its height.

Area of Trapezoid

The area of a trapezoid is given by its height multiplied by the sum of its top length and bottom length divided by two.

Area of Triangle

The area of a triangle is given by one half multiplied by its width and height.

Circumference of Circle

The circumference of a circle is given by two multiplied by pi and the radius.

Distance Between Two Points 1D

The distance between two points, in one dimension, is given by the absolute value of the difference between the two values.

Distance Between Two Points 2D

The distance between two points, in two dimensions, is given by solving pythagorean's theorem for the length the hypotenuse of the right triangle formed by the two points.

Midpoint Formula

To find the midpoint between two points, average the two points x coordinate together to get the midpoint's x coordinate, then average the two points y coordinate together to get the midpoints y coordinate.

Volume of Cone

The volume of a cone is given by one third multiplied by PI, the radius of its base squared, and its height.

Volume of Cube

The volume of a cube is given by the length of the cube length raised to the third power.

Volume of Cylinder

The volume of a cylinder is equal to PI multiplied by its radius squared and its height.

Volume of Rectangular Prism

To calculate the volume of a rectangular prism multiply its height, width, and length together.

Volume of Sphere

The volume of a sphere is equal to four over three multiplied by PI and its radius cubed.

Combination

The combination formula describes the possible combinations of r elements out of a group of n elements where order does not matter.

Permutation

The permutation formula describes the possible permutations of r elements out of a group of n elements where order does matter.

Permutations of Set

The number of permutations of n distinct items is given by n factorial. A permutation is a unique ordering or arangment of the set of items.

Arithmetic Mean

The arithmetic mean, also called the sample mean, is the average of a sample space. To calculate the arithmetic mean sum all the data points in a sample space and then divide by the number of elements.

Conditional Probability

The conditional probility formula shows how to calculate the probability of a event B, given that another event A has already occured.

Expected Value Continuous Distribution

The expected value, describes the most likely value of a probability distribution. It also describes where a probability distribution is centered.

Expected Value Discrete Distribution

To calculate the expected value of a discrete distribution multiply all of the events of the distribution with the probability of the element occuring.

Standard Deviation

The sample standard deviation formula is denoted by the greek lower case sigma symbol in the case of the population and the latin letter s for the sample.

Angle Between Two Vectors

The angle between two vectors can be calculated using the arc-cosine of their dot product divided by the product of their magnitudes.

Area Between Two Vectors

The area between two vectors is given by the magnitude of their cross product.

Cross Product

The cross product of two vectors can be calculated using the formal determinant.

Determinant of Three by Three Matrix

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

Determinant of Two by Two Matrix

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

Dot Product

The dot prodcut of two vectors is calculated by summing together the product of corresponding elements.

Dot Product Geometric

The dot product can be geometrically interpretted as the magnitude of the two vectors multiplied by the cosine of the angle between them.

Magnitude of Cross Product

The magnitude of the cross product can be given as the magnitude of the two vectors multiplied by the sine of the angles between them.

Magnitude of Vector

The magnitude of a vector is given by the square root of the sum of its components squared.