Math formula quick reference.
A curated collection of essential math formulas for algebra, geometry, statistics, and finance. Use this page as a quick reference or print it for your study sessions.
Algebra Formulas
Linear Equations
Slope-intercept form: y = mx + b
Point-slope form: y - y₁ = m(x - x₁)
Slope formula: m = (y₂ - y₁) / (x₂ - x₁)
Standard form: Ax + By = C
Quadratic Equations
Standard form: ax² + bx + c = 0
Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
Vertex form: y = a(x - h)² + k
Discriminant: Δ = b² - 4ac
Exponent Rules
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁻ⁿ = 1/aⁿ
a⁰ = 1 (where a ≠ 0)
Special Products
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)(a - b) = a² - b²
(a + b)³ = a³ + 3a²b + 3ab² + b³
Logarithms
logₐ(xy) = logₐx + logₐy
logₐ(x/y) = logₐx - logₐy
logₐ(xⁿ) = n·logₐx
logₐa = 1
logₐ1 = 0
Fractions
a/b + c/d = (ad + bc)/bd
a/b - c/d = (ad - bc)/bd
a/b × c/d = ac/bd
a/b ÷ c/d = ad/bc
Geometry Formulas
Triangles
Area: A = ½ × base × height
Perimeter: P = a + b + c
Pythagorean theorem: a² + b² = c²
Sum of angles: 180°
Circles
Area: A = πr²
Circumference: C = 2πr
Diameter: d = 2r
Arc length: s = rθ (θ in radians)
Rectangles & Squares
Rectangle area: A = length × width
Rectangle perimeter: P = 2(length + width)
Square area: A = s²
Square perimeter: P = 4s
3D Shapes
Cube volume: V = s³
Box volume: V = l × w × h
Sphere volume: V = (4/3)πr³
Sphere surface area: A = 4πr²
Cylinder volume: V = πr²h
Trigonometry
sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
sin²(θ) + cos²(θ) = 1
Coordinate Geometry
Distance formula: d = √((x₂-x₁)² + (y₂-y₁)²)
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
Circle equation: (x-h)² + (y-k)² = r²
Statistics Formulas
Central Tendency
Mean: x̄ = (Σxᵢ) / n
Median: Middle value when sorted
Mode: Most frequent value
Range: max - min
Variance & Standard Deviation
Population variance: σ² = Σ(xᵢ - μ)² / N
Sample variance: s² = Σ(xᵢ - x̄)² / (n-1)
Standard deviation: Square root of variance
Probability
Basic probability: P(A) = favorable outcomes / total outcomes
Complement: P(A') = 1 - P(A)
Addition rule: P(A∪B) = P(A) + P(B) - P(A∩B)
Multiplication rule: P(A∩B) = P(A) × P(B|A)
Combinations & Permutations
Permutations: nPr = n! / (n-r)!
Combinations: nCr = n! / (r!(n-r)!)
Factorial: n! = n × (n-1) × ... × 2 × 1
Linear Regression
Slope: b = Σ((x-x̄)(y-ȳ)) / Σ(x-x̄)²
Intercept: a = ȳ - bx̄
Equation: ŷ = a + bx
Percentiles
z-score: z = (x - μ) / σ
Percentile rank: (number of values below x / total) × 100
Financial Formulas
Simple Interest
Interest: I = P × r × t
Total amount: A = P(1 + rt)
where P = principal, r = rate, t = time
Compound Interest
Amount: A = P(1 + r/n)^(nt)
Continuous: A = Pe^(rt)
where n = compounding periods per year
Loan Payments
Monthly payment:
M = P[r(1+r)ⁿ] / [(1+r)ⁿ - 1]
where r = monthly rate, n = number of payments
Percentage Calculations
Percent change: ((new - old) / old) × 100
Percent of: (part / whole) × 100
Percent to decimal: divide by 100
GPA Calculation
Semester GPA: Σ(grade points × credits) / Σcredits
Cumulative GPA: Σ(all grade points) / Σ(all credits)
BMI Calculations
Metric: BMI = kg / m²
Imperial: BMI = 703 × lb / in²
Categories: Underweight (<18.5), Normal (18.5-24.9), Overweight (25-29.9), Obese (≥30)