Algebra
Quadratic Formula
Finds the roots of a quadratic equation ax² + bx + c = 0 when a is nonzero.
Printable reference
Common Math Formulas Cheat Sheet
Review frequently used algebra, geometry, calculus, probability, statistics, finance, and vector formulas.
How to use this sheet
Use the compact formulas as a reminder, then open the full reference to check variables, assumptions, units, and worked examples.
Geometry
Pythagorean Theorem
Relates the side lengths of a right triangle.
Algebra
Slope-Intercept Form
Expresses a straight line using its slope and vertical intercept.
Algebra
Distance Formula
Calculates the straight-line distance between two points in a coordinate plane.
Geometry
Area of a Circle
Calculates the area enclosed by a circle of radius r.
Geometry
Circumference of a Circle
Calculates the distance around a circle from its radius or diameter.
Geometry
Area of a Triangle
Calculates triangle area from a base and its perpendicular height.
Geometry
Volume of a Sphere
Calculates the volume enclosed by a sphere.
Applied Math
Compound Interest Formula
Calculates a balance with interest compounded a fixed number of times per year.
Applied Math
Percentage Change Formula
Measures relative increase or decrease from an original nonzero value.
Algebra
Arithmetic Sequence Formula
Finds the nth term of a sequence with a constant difference.
Algebra
Geometric Sequence Formula
Finds the nth term of a sequence with a constant ratio.
Algebra
Binomial Theorem
Expands a nonnegative integer power of a binomial.
Calculus
Chain Rule
Differentiates a composite function by combining outer and inner derivatives.
Calculus
Product Rule
Differentiates the product of two differentiable functions.
Calculus
Integration by Parts
Transforms an integral of a product using the product rule in reverse.
Calculus
Derivative Definition
Defines the instantaneous rate of change of a function as a limit.
Probability
Bayes’ Theorem
Updates the probability of an event after observing evidence.
Probability
Conditional Probability
Calculates the probability of A when B is known to have occurred.
Statistics
Sample Mean
Calculates the arithmetic average of n observed values.
Statistics
Sample Variance
Measures sample spread using squared deviations and Bessel’s correction.
Statistics
Z-Score Formula
Expresses how many population standard deviations a value lies from the mean.
Linear Algebra
Vector Dot Product
Combines two vectors into a scalar and relates their components to the angle between them.
Linear Algebra
Cross Product Components
Calculates the three-dimensional vector cross product.
Linear Algebra
2×2 Matrix Determinant
Calculates the determinant of a two-by-two matrix.
Verification note
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