StackCards
Math & geometry formulas
The formulas you keep forgetting, grouped for quick review.
26 cardsBeginnerMath
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What is inside
Area of a circleRadius squared times pi.
A = πr²
Circumference of a circleTwice pi times the radius.
C = 2πr
Area of a triangleHalf the base times the height.
A = ½ · b · h
Area of a trapezoidAverage of the parallel sides times the height.
A = ½ (a + b) · h
Pythagorean theoremIn a right triangle, the squares of the legs add up to the square of the hypotenuse.
a² + b² = c²
Volume of a sphereFour thirds pi times the radius cubed.
V = (4/3)πr³
Surface area of a sphereFour pi times the radius squared.
S = 4πr²
Volume of a cylinderArea of the base times the height.
V = πr²h
Volume of a coneA third of the cylinder with the same base and height.
V = ⅓πr²h
Quadratic formulaSolves ax² + bx + c = 0.
x = (−b ± √(b² − 4ac)) / 2a
DiscriminantPositive: two real roots. Zero: one. Negative: none real.
Δ = b² − 4ac
Slope of a lineRise over run between two points.
m = (y₂ − y₁) / (x₂ − x₁)
Equation of a lineSlope-intercept form.
y = mx + b
Distance between two pointsThe Pythagorean theorem in the plane.
d = √((x₂ − x₁)² + (y₂ − y₁)²)
MidpointAverage the coordinates.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Difference of squaresA product that collapses.
a² − b² = (a + b)(a − b)
Square of a sumDon't forget the middle term.
(a + b)² = a² + 2ab + b²
Sine, cosine, tangentOpposite, adjacent and hypotenuse: SOH-CAH-TOA.
sin = opp/hyp, cos = adj/hyp, tan = opp/adj
Fundamental trig identityHolds for every angle.
sin²θ + cos²θ = 1
Law of sinesSides over the sine of their opposite angles are equal.
a / sin A = b / sin B = c / sin C
Law of cosinesThe Pythagorean theorem with a correction.
c² = a² + b² − 2ab cos C
Degrees to radiansMultiply by pi over 180.
rad = deg · π / 180
Sum of an arithmetic seriesNumber of terms times the average of first and last.
S = n(a₁ + aₙ) / 2
Sum of a geometric seriesWith ratio r not equal to 1.
S = a(1 − rⁿ) / (1 − r)
Compound interestAmount after t years at rate r, compounded n times a year.
A = P(1 + r/n)^(nt)
CombinationsWays to choose k from n when order doesn't matter.
C(n, k) = n! / (k!(n − k)!)