SAT Math Formula Sheet — Complete Reference for Test Day A complete reference of every math formula you need for the SAT. The College Board provides only 12 formulas on the test; this sheet adds the formulas you should memorize on top of those. Covers Heart of Algebra, Problem Solving & Data Analysis, Passport to Advanced Math, and Additional Topics in Math.
Formulas Given on the SAT Reference Sheet Area of a Triangle
A = 1 2 b h A = \tfrac{1}{2} b h A = 2 1 bh Pythagorean Theorem
a 2 + b 2 = c 2 a^2 + b^2 = c^2 a 2 + b 2 = c 2 Volume of a Cylinder
V = π r 2 h V = \pi r^2 h V = π r 2 h Volume of a Cone
V = 1 3 π r 2 h V = \tfrac{1}{3} \pi r^2 h V = 3 1 π r 2 h Volume of a Sphere
V = 4 3 π r 3 V = \tfrac{4}{3} \pi r^3 V = 3 4 π r 3 Volume of a Pyramid
V = 1 3 l w h V = \tfrac{1}{3} l w h V = 3 1 l w h Special Right Triangle 45-45-90
1 : 1 : 2 1 : 1 : \sqrt{2} 1 : 1 : 2 Special Right Triangle 30-60-90
1 : 3 : 2 1 : \sqrt{3} : 2 1 : 3 : 2 Linear Equations & Functions Slope
m = y 2 − y 1 x 2 − x 1 m = \frac{y_2 - y_1}{x_2 - x_1} m = x 2 − x 1 y 2 − y 1 Point-Slope Form
y − y 1 = m ( x − x 1 ) y - y_1 = m(x - x_1) y − y 1 = m ( x − x 1 ) Standard Form
A x + B y = C A x + B y = C A x + B y = C Perpendicular Lines
m 1 ⋅ m 2 = − 1 m_1 \cdot m_2 = -1 m 1 ⋅ m 2 = − 1 Quadratics & Polynomials Quadratic Formula
x = − b ± b 2 − 4 a c 2 a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} x = 2 a − b ± b 2 − 4 a c Discriminant
Δ = b 2 − 4 a c \Delta = b^2 - 4ac Δ = b 2 − 4 a c Vertex of a Parabola
x = − b 2 a x = -\frac{b}{2a} x = − 2 a b Difference of Squares
a 2 − b 2 = ( a + b ) ( a − b ) a^2 - b^2 = (a + b)(a - b) a 2 − b 2 = ( a + b ) ( a − b ) Perfect Square
( a + b ) 2 = a 2 + 2 a b + b 2 (a + b)^2 = a^2 + 2 a b + b^2 ( a + b ) 2 = a 2 + 2 ab + b 2 Exponents & Radicals Product of Powers
a m ⋅ a n = a m + n a^m \cdot a^n = a^{m+n} a m ⋅ a n = a m + n Power of a Power
( a m ) n = a m n (a^m)^n = a^{m n} ( a m ) n = a mn Negative Exponent
a − n = 1 a n a^{-n} = \tfrac{1}{a^n} a − n = a n 1 Fractional Exponent
a m / n = a m n a^{m/n} = \sqrt[n]{a^m} a m / n = n a m Coordinate Geometry Distance Between Points
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Midpoint
M = ( x 1 + x 2 2 , y 1 + y 2 2 ) M = \left(\tfrac{x_1 + x_2}{2},\ \tfrac{y_1 + y_2}{2}\right) M = ( 2 x 1 + x 2 , 2 y 1 + y 2 ) Equation of a Circle
( x − h ) 2 + ( y − k ) 2 = r 2 (x - h)^2 + (y - k)^2 = r^2 ( x − h ) 2 + ( y − k ) 2 = r 2 Geometry & Trigonometry Triangle Angle Sum
A + B + C = 180 ° A + B + C = 180° A + B + C = 180° Polygon Angle Sum
S = ( n − 2 ) ⋅ 180 ° S = (n - 2) \cdot 180° S = ( n − 2 ) ⋅ 180° Sum of Exterior Angles
360 ° for any convex polygon 360° \text{ for any convex polygon} 360° for any convex polygon Sin, Cos, Tan (SOHCAHTOA)
sin = opp hyp , cos = adj hyp , tan = opp adj \sin = \tfrac{\text{opp}}{\text{hyp}},\ \cos = \tfrac{\text{adj}}{\text{hyp}},\ \tan = \tfrac{\text{opp}}{\text{adj}} sin = hyp opp , cos = hyp adj , tan = adj opp Arc Length
s = r θ (radians) s = r \theta \text{ (radians)} s = r θ (radians) Sector Area
A = 1 2 r 2 θ A = \tfrac{1}{2} r^2 \theta A = 2 1 r 2 θ Statistics & Data Analysis Mean
x ˉ = 1 n ∑ x i \bar{x} = \frac{1}{n}\sum x_i x ˉ = n 1 ∑ x i Median
middle value of sorted data \text{middle value of sorted data} middle value of sorted data Range
max − min \text{max} - \text{min} max − min Percent Change
new − old old × 100 % \frac{\text{new} - \text{old}}{\text{old}} \times 100\% old new − old × 100% Probability
P ( A ) = favorable total P(A) = \frac{\text{favorable}}{\text{total}} P ( A ) = total favorable Complex Numbers Imaginary Unit
i = − 1 , i 2 = − 1 i = \sqrt{-1},\ i^2 = -1 i = − 1 , i 2 = − 1 Powers of i
i 4 = 1 , i 3 = − i , i 5 = i i^4 = 1,\ i^3 = -i,\ i^5 = i i 4 = 1 , i 3 = − i , i 5 = i Complex Conjugate
a + b i ‾ = a − b i \overline{a + bi} = a - bi a + bi = a − bi 