Reference

Math formula reference

The formulas behind every calculator on the site, grouped by topic. Each group links to a tool where you can apply it and see the working.

Updated October 3, 2026

Algebra Exponents & logarithms Trigonometry Fractions, percent & number theory Geometry Statistics & probability

Algebra

Apply these in the Quadratic Equation Solver.

Perfect square (sum)

(a + b)² = a² + 2ab + b²

Perfect square (difference)

(a − b)² = a² − 2ab + b²

Difference of squares

a² − b² = (a + b)(a − b)

Quadratic formula

x = (−b ± √(b² − 4ac)) / 2a

Discriminant

D = b² − 4ac

Linear equation

ax + b = cx + d → x = (d − b) / (a − c)

Exponents & logarithms

Apply these in the Scientific Calculator.

Product rule

aˣ · aʸ = aˣ⁺ʸ

Quotient rule

aˣ / aʸ = aˣ⁻ʸ

Power of a power

(aˣ)ʸ = aˣʸ

Zero exponent

a⁰ = 1 (a ≠ 0)

Log of a product

logₐ(xy) = logₐx + logₐy

Log of a power

logₐ(xʸ) = y · logₐx

Change of base

logₐx = ln x / ln a

Trigonometry

Apply these in the Scientific Calculator.

Right-triangle ratios

sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent

Pythagorean identity

sin²θ + cos²θ = 1

Tangent

tan θ = sin θ / cos θ

Law of sines

a / sin A = b / sin B = c / sin C

Law of cosines

c² = a² + b² − 2ab cos C

Degrees ↔ radians

radians = degrees × π / 180

Fractions, percent & number theory

Apply these in the Fraction Calculator.

Add / subtract

a/b ± c/d = (ad ± bc) / bd

Multiply

a/b × c/d = ac / bd

Divide

a/b ÷ c/d = ad / bc

X% of Y

(X ÷ 100) × Y

Percent change

(new − old) ÷ |old| × 100

GCF and LCM

GCF(a, b) × LCM(a, b) = a × b

Geometry

Apply these in the Volume & Surface Area Calculator.

Rectangle

A = lw, P = 2(l + w)

Triangle

A = ½bh

Heron’s formula

A = √(s(s−a)(s−b)(s−c)), s = (a + b + c)/2

Circle

C = 2πr, A = πr²

Pythagorean theorem

a² + b² = c²

Cylinder

V = πr²h, A = 2πr(r + h)

Sphere

V = 4/3 πr³, A = 4πr²

Cone

V = 1/3 πr²h

Statistics & probability

Apply these in the Mean, Median & Mode Calculator.

Mean

x̄ = Σx / n

Population standard deviation

σ = √(Σ(x − μ)² / n)

Sample standard deviation

s = √(Σ(x − x̄)² / (n − 1))

Probability

P(E) = favourable / total

Independent events

P(A and B) = P(A)P(B)

Union

P(A or B) = P(A) + P(B) − P(A and B)

Permutations

nPr = n! / (n − r)!

Combinations

nCr = n! / (r!(n − r)!)