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 - y? = m(x - x?)
Slope formula: m = (y? - y?) / (x? - x?)
Standard form: Ax + By = C
Quadratic Equations
Standard form: ax2 + bx + c = 0
Quadratic formula: x = (-b ¡À ¡Ì(b2 - 4ac)) / 2a
Vertex form: y = a(x - h)2 + k
Discriminant: ¦¤ = b2 - 4ac
Exponent Rules
a? ¡Á a? = a???
a? ¡Â a? = a???
(a?)? = a??
a?? = 1/a?
a? = 1 (where a ¡Ù 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
log?(xy) = log?x + log?y
log?(x/y) = log?x - log?y
log?(x?) = n¡¤log?x
log?a = 1
log?1 = 0
Fractions
a/b + c/d = (ad + bc)/bd
a/b - c/d = (ad - bc)/bd
a/b ¡Á c/d = ac/bd
a/b ¡Â c/d = ad/bc
Geometry Formulas
Triangles
Area: A = ? ¡Á base ¡Á height
Perimeter: P = a + b + c
Pythagorean theorem: a2 + b2 = c2
Sum of angles: 180¡ã
Circles
Area: A = ¦Ðr2
Circumference: C = 2¦Ðr
Diameter: d = 2r
Arc length: s = r¦È (¦È in radians)
Rectangles & Squares
Rectangle area: A = length ¡Á 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 ¡Á w ¡Á h
Sphere volume: V = (4/3)¦Ðr3
Sphere surface area: A = 4¦Ðr2
Cylinder volume: V = ¦Ðr2h
Trigonometry
sin(¦È) = opposite/hypotenuse
cos(¦È) = adjacent/hypotenuse
tan(¦È) = opposite/adjacent
sin2(¦È) + cos2(¦È) = 1
Coordinate Geometry
Distance formula: d = ¡Ì((x?-x?)2 + (y?-y?)2)
Midpoint: ((x?+x?)/2, (y?+y?)/2)
Circle equation: (x-h)2 + (y-k)2 = r2
Statistics Formulas
Central Tendency
Mean: x? = (¦²x?) / n
Median: Middle value when sorted
Mode: Most frequent value
Range: max - min
Variance & Standard Deviation
Population variance: ¦Ò2 = ¦²(x? - ¦Ì)2 / N
Sample variance: s2 = ¦²(x? - x?)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¡ÈB) = P(A) + P(B) - P(A¡ÉB)
Multiplication rule: P(A¡ÉB) = P(A) ¡Á P(B|A)
Combinations & Permutations
Permutations: nPr = n! / (n-r)!
Combinations: nCr = n! / (r!(n-r)!)
Factorial: n! = n ¡Á (n-1) ¡Á ... ¡Á 2 ¡Á 1
Linear Regression
Slope: b = ¦²((x-x?)(y-?)) / ¦²(x-x?)2
Intercept: a = ? - bx?
Equation: ? = a + bx
Percentiles
z-score: z = (x - ¦Ì) / ¦Ò
Percentile rank: (number of values below x / total) ¡Á 100
Financial Formulas
Simple Interest
Interest: I = P ¡Á r ¡Á 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)?] / [(1+r)? - 1]
where r = monthly rate, n = number of payments
Percentage Calculations
Percent change: ((new - old) / old) ¡Á 100
Percent of: (part / whole) ¡Á 100
Percent to decimal: divide by 100
GPA Calculation
Semester GPA: ¦²(grade points ¡Á credits) / ¦²credits
Cumulative GPA: ¦²(all grade points) / ¦²(all credits)
BMI Calculations
Metric: BMI = kg / m2
Imperial: BMI = 703 ¡Á lb / in2
Categories: Underweight (<18.5), Normal (18.5-24.9), Overweight (25-29.9), Obese (¡Ý30)