Math Formulas Reference

Algebra, geometry & calculus formulas

Algebra

Square of sum(a + b)² = a² + 2ab + b²

Square of difference(a − b)² = a² − 2ab + b²

Difference of squaresa² − b² = (a + b)(a − b)

Cube of sum(a + b)³ = a³ + 3a²b + 3ab² + b³

Cube of difference(a − b)³ = a³ − 3a²b + 3ab² − b³

Sum of cubesa³ + b³ = (a + b)(a² − ab + b²)

Difference of cubesa³ − b³ = (a − b)(a² + ab + b²)

Quadratic formulax = (−b ± √(b² − 4ac)) / 2a

Exponent rulesaᵐ·aⁿ = aᵐ⁺ⁿ (aᵐ)ⁿ = aᵐⁿ aᵐ/aⁿ = aᵐ⁻ⁿ

Logarithm ruleslog(xy) = log x + log y log(x/y) = log x − log y log xⁿ = n log x

Geometry

CircleArea = πr² Circumference = 2πr

TriangleArea = ½bh Heron: √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2

Pythagorean theorema² + b² = c²

SphereV = 4⁄3πr³ S = 4πr²

CylinderV = πr²h S = 2πr(r + h)

ConeV = ⅓πr²h S = πr(r + ℓ)

Distance between pointsd = √((x₂−x₁)² + (y₂−y₁)²)

Sum of interior angles(n − 2) × 180° for an n-sided polygon

Curves & Functions

Lineary = mx + c (slope m, intercept c)

Parabola (quadratic)y = ax² + bx + c vertex at x = −b/2a

Parabola (vertex form)y = a(x − h)² + k vertex (h, k)

Cubicy = ax³ + bx² + cx + d

Circle equation(x − h)² + (y − k)² = r²

Ellipsex²/a² + y²/b² = 1

Hyperbolax²/a² − y²/b² = 1

Exponential / decayy = a·eᵏˣ (growth k>0, decay k<0)

Trigonometry

Fundamental identitysin²θ + cos²θ = 1

Tangenttan θ = sin θ / cos θ

Law of sinesa/sin A = b/sin B = c/sin C

Law of cosinesc² = a² + b² − 2ab·cos C

Double anglesin 2θ = 2 sin θ cos θ cos 2θ = cos²θ − sin²θ

Sum formulassin(A±B) = sin A cos B ± cos A sin B

Degrees ↔ radiansrad = deg × π/180 deg = rad × 180/π

Calculus — Derivatives

Power ruled/dx xⁿ = n·xⁿ⁻¹

Constant & sumd/dx c = 0 (f ± g)′ = f′ ± g′

Product rule(fg)′ = f′g + fg′

Quotient rule(f/g)′ = (f′g − fg′) / g²

Chain ruled/dx f(g(x)) = f′(g(x)) · g′(x)

Common derivatives(sin x)′ = cos x (cos x)′ = −sin x (eˣ)′ = eˣ (ln x)′ = 1/x

Calculus — Integrals

Power rule∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)

Reciprocal∫1/x dx = ln|x| + C

Exponential∫eˣ dx = eˣ + C

Trig integrals∫sin x dx = −cos x + C ∫cos x dx = sin x + C

Integration by parts∫u dv = uv − ∫v du

Fundamental theorem∫ₐᵇ f(x) dx = F(b) − F(a)

Statistics & Probability

Meanx̄ = Σxᵢ / n

Varianceσ² = Σ(xᵢ − x̄)² / n

Standard deviationσ = √variance

CombinationsC(n, r) = n! / (r!(n−r)!)

PermutationsP(n, r) = n! / (n−r)!

Bayes' theoremP(A|B) = P(B|A)·P(A) / P(B)

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About the Math Formulas Reference

Searchable math formula reference covering algebra (square and cube expansions, quadratic formula, exponent and log rules), geometry (areas, volumes, Pythagorean theorem), curves (linear, parabolic, cubic, circle, ellipse, hyperbola equations), trigonometry identities, calculus derivative and integral rules, and statistics. One-click copy for every formula — a free cheat sheet for students.

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