Math Formulas Cheat Sheet: Algebra, Geometry, Trig, Stats

All the formulas students reach for most, on one searchable page. Type a word like “area” or “slope”, or pick a subject, and each card shows the formula and what its letters mean. Print it as a study sheet.

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Quadratic formula

\(x = \frac{-b \pm \sqrt{b^{2} – 4ac}}{2a}\)

Solves ax² + bx + c = 0.

Slope of a line

\(m = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}\)

Rise over run between two points.

Slope-intercept form

\(y = mx + b\)

m is the slope, b the y-intercept.

Point-slope form

\(y – y_{1} = m(x – x_{1})\)

Line through a point with slope m.

Distance formula

\(d = \sqrt{(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}}\)

Distance between two points.

Midpoint formula

\(M = \left(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}\right)\)

Middle of a segment.

Difference of squares

\(a^{2} – b^{2} = (a + b)(a – b)\)

Factoring pattern.

Square of a sum

\((a + b)^{2} = a^{2} + 2ab + b^{2}\)

Perfect square trinomial.

Exponent rules

\(a^{m}a^{n} = a^{m + n}, \quad (a^{m})^{n} = a^{mn}\)

Multiply powers by adding exponents.

Arithmetic sequence

\(a_{n} = a_{1} + (n – 1)d\)

nth term with common difference d.

Geometric sequence

\(a_{n} = a_{1}r^{n – 1}\)

nth term with common ratio r.

Compound interest

\(A = P\left(1 + \frac{r}{n}\right)^{nt}\)

P principal, r rate, n compounds per year, t years.

Area of a rectangle

\(A = lw\)

Length times width.

Area of a triangle

\(A = \frac{1}{2}bh\)

Half base times height.

Area of a trapezoid

\(A = \frac{1}{2}(b_{1} + b_{2})h\)

Average of the bases times height.

Area of a circle

\(A = \pi r^{2}\)

Pi times radius squared.

Circumference

\(C = 2\pi r = \pi d\)

Distance around a circle.

Pythagorean theorem

\(a^{2} + b^{2} = c^{2}\)

Right triangles; c is the hypotenuse.

Volume of a rectangular prism

\(V = lwh\)

Length × width × height.

Volume of a cylinder

\(V = \pi r^{2}h\)

Base area times height.

Volume of a cone

\(V = \frac{1}{3}\pi r^{2}h\)

One third of the cylinder.

Volume of a sphere

\(V = \frac{4}{3}\pi r^{3}\)

Ball.

Volume of a pyramid

\(V = \frac{1}{3}Bh\)

B is the base area.

Interior angle sum

\(S = (n – 2) \cdot 180^{\circ}\)

Polygon with n sides.

Sine, cosine, tangent

\(\sin\theta = \frac{\text{opp}}{\text{hyp}}, \ \cos\theta = \frac{\text{adj}}{\text{hyp}}, \ \tan\theta = \frac{\text{opp}}{\text{adj}}\)

SOH CAH TOA.

Pythagorean identity

\(\sin^{2}\theta + \cos^{2}\theta = 1\)

From the unit circle.

Law of sines

\(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)

Any triangle.

Law of cosines

\(c^{2} = a^{2} + b^{2} – 2ab\cos C\)

Any triangle.

Degrees to radians

\(\text{rad} = \text{deg} \times \frac{\pi}{180}\)

180° = π radians.

Mean

\(\bar{x} = \frac{\sum x}{n}\)

Average.

Standard deviation (sample)

\(s = \sqrt{\frac{\sum (x – \bar{x})^{2}}{n – 1}}\)

Spread of data.

z-score

\(z = \frac{x – \mu}{\sigma}\)

Standard deviations from the mean.

Probability

\(P(A) = \frac{\text{favorable outcomes}}{\text{total outcomes}}\)

Equally likely outcomes.

Addition rule

\(P(A \cup B) = P(A) + P(B) – P(A \cap B)\)

Or.

Combinations

\(\binom{n}{r} = \frac{n!}{r!\,(n – r)!}\)

Order does not matter.

Permutations

\(P(n, r) = \frac{n!}{(n – r)!}\)

Order matters.

Power rule

\(\frac{d}{dx}x^{n} = nx^{n – 1}\)

Derivative of a power.

Product rule

\((fg)^{\prime} = f^{\prime}g + fg^{\prime}\)

Derivative of a product.

Chain rule

\(\frac{d}{dx}f(g(x)) = f^{\prime}(g(x))\,g^{\prime}(x)\)

Composite functions.

Power rule for integrals

\(\int x^{n}\,dx = \frac{x^{n + 1}}{n + 1} + C\)

For n not equal to −1.

Fundamental theorem

\(\int_{a}^{b} f(x)\,dx = F(b) – F(a)\)

F is an antiderivative of f.

How to use this formula sheet

Search by keyword or filter by subject. Every formula is typeset properly so it is easy to read on a phone. Print the page for a quick study guide before a test.

Understanding beats memorizing

Most formulas come from a picture: a triangle’s area is half a rectangle’s, a cone holds one third of a cylinder, and the distance formula is the Pythagorean theorem on a grid. Knowing where a formula comes from makes it easier to recall and to rebuild under pressure.

Formula sheets on tests

Some tests, such as the SAT and many state exams, give students a reference sheet; others do not. Check your test’s rules, and practice with the same sheet you will have on test day.

Math Formula Sheet quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What are the most important math formulas?

For most students: the quadratic formula, slope, the Pythagorean theorem, area and volume formulas, and the mean.

Can I print this formula sheet?

Yes. Use your browser's print option; filter a subject first for a shorter sheet.

Is this the official SAT reference sheet?

No. It covers more formulas. Check the official reference for any test you are taking.

Do I need to memorize formulas?

Memorize the core few and understand where the rest come from, so you can rebuild them.

Where can I practice using these formulas?

Each subject has calculators and worksheets on our site; the related links below are a good start.

Math Formula Sheet