Formula Library
A quick-reference index. Search across math, finance, health, statistics, and physics.
Geometry
Pythagorean theorem
a² + b² = c²
Right-triangle side lengths.
Area of a circle
A = π r²
Radius squared, times π.
Circumference
C = 2π r
Length around a circle.
Sphere volume
V = (4/3) π r³
Volume from radius.
Algebra
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Roots of ax² + bx + c = 0.
Slope of a line
m = (y₂ − y₁) / (x₂ − x₁)
Rise over run.
Finance
Compound interest
A = P(1 + r/n)^(nt)
Future value of P.
Simple interest
I = P r t
Flat interest, no compounding.
Mortgage payment
M = P r / (1 − (1+r)⁻ⁿ)
Monthly fixed-rate payment.
Health
BMI
BMI = kg / m²
Body mass index.
BMR (Mifflin–St Jeor)
10·kg + 6.25·cm − 5·age (+5 / −161)
Basal metabolic rate.
Statistics
Standard deviation (sample)
s = √(Σ(xᵢ − x̄)² / (n − 1))
Spread of a sample.
Mean
x̄ = (1/n) Σ xᵢ
Arithmetic average.
Physics
Newton's second law
F = m a
Force from mass and acceleration.
Kinetic energy
E = ½ m v²
Energy of a moving object.
Ohm's law
V = I R
Voltage = current × resistance.
Ideal gas law
P V = n R T
State of an ideal gas.
Distance, speed, time
d = v t
Constant velocity.