Look up any common formula in seconds: type a word like "slope", "cone", "law of cosines" or "standard deviation", or browse by topic. Each formula is typeset clearly with a short note on what the letters mean, and you can copy its LaTeX or print a tidy two-column sheet.
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How to use the Math Formulas Cheat Sheet
Type in the search box a formula name or topic, for example "area", "quadratic", "chain rule" or "z-score".
Or pick a topic tab: Algebra, Geometry, Trigonometry, Calculus or Statistics & Probability.
Read the note under each formula to see what each letter stands for and any conditions.
Press Copy LaTeX to paste a formula into a document, LaTeX editor or notes app.
Press Print formula sheet to print or save as PDF exactly the formulas currently shown; untick Show notes for a more compact sheet.
Exact trig values worth memorizing
Angle
Radians
sin
cos
tan
0°
0
0
1
0
30°
π/6
1/2
√3/2
√3/3
45°
π/4
√2/2
√2/2
1
60°
π/3
√3/2
1/2
√3
90°
π/2
1
0
undefined
180°
π
0
−1
0
A memory aid: the sines of 0°, 30°, 45°, 60° and 90° are √0/2, √1/2, √2/2, √3/2 and √4/2, and the cosines run through the same list backwards.
Common symbols on the sheet
Symbol
Meaning
Σ
Sum of the terms that follow, over the index shown
x̄, μ
Sample mean, population mean
s, σ
Sample and population standard deviation
n!
Factorial: n × (n − 1) × … × 2 × 1, with 0! = 1
∫
Integral (antiderivative, or area when limits a and b are given)
f′(x), d/dx
Derivative of f with respect to x
∪, ∩, Ac
Or (union), and (intersection), not A (complement)
P(A | B)
Probability of A given that B has happened
±, ∓
Plus or minus; minus or plus (signs paired with ± in the same formula)
Tips for using a formula sheet well
Check the units first. Areas come out in square units and volumes in cubic units; mixing centimeters and meters is the most common source of wrong answers.
Know the conditions. The Pythagorean theorem needs a right angle, the power rule for integrals excludes n = −1, and the infinite geometric sum needs |r| < 1. The note under each formula lists these.
Derive instead of memorizing everything. The distance formula is the Pythagorean theorem on a grid, the 1 + tan²θ identity is sin²θ + cos²θ = 1 divided by cos²θ, and the cone volume is one third of a cylinder's.
Estimate before you calculate. A circle of radius 10 has an area a little over 300 (π × 100), so a result of 31.4 or 3,140 signals a slip.
Frequently asked questions
What is the quadratic formula?
For an equation ax² + bx + c = 0 with a ≠ 0, the solutions are x = (−b ± √(b² − 4ac)) / (2a). The expression under the square root, b² − 4ac, is the discriminant: if it is positive there are two real solutions, if it is zero there is one, and if it is negative the solutions are complex.
What are the most important geometry formulas to memorize?
The ones used most often are the Pythagorean theorem a² + b² = c², the triangle area ½bh, the circle area πr² and circumference 2πr, the rectangle area lw, and the volumes of a prism (Bh), cylinder (πr²h), cone (⅓πr²h) and sphere (4/3 πr³). All of them are in the Geometry tab.
What is the difference between sample and population standard deviation?
Population variance divides the sum of squared deviations by N, the number of values in the whole population. Sample variance divides by n − 1 instead (Bessel's correction), because a sample's spread around its own mean tends to underestimate the true spread. The standard deviation is the square root of the variance in either case.
Do trig formulas use degrees or radians?
The identities, the law of sines and the law of cosines work in either unit. Formulas from calculus, such as d/dx sin x = cos x, the limit of sin x / x, arc length s = rθ and the Maclaurin series, require the angle to be in radians. To convert, multiply degrees by π/180.
How do I print the formula sheet?
Choose a topic tab or type a search to narrow the list, then press Print formula sheet. A two-column sheet with only the visible formulas opens in your browser's print dialog, where you can print it or choose Save as PDF. Untick Show notes first if you want a shorter one-page reference.
Can I copy the formulas into Word or Google Docs?
Press Copy LaTeX to copy the LaTeX source of a formula. Recent versions of Microsoft Word (Equation, then LaTeX mode) and Google Docs add-ons, Overleaf, Notion, Obsidian and most note apps accept LaTeX math, so the formula is rebuilt with proper typesetting.
Are these formulas enough for exams like the SAT or ACT?
They cover the standard high school and first-year college formulas, including the area, volume and special-right-triangle formulas that appear on the SAT reference sheet. Exam rules about which formulas are provided can change, so check the current test guidelines, and practice applying the formulas rather than only memorizing them.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.