SAT Math Formula Sheet — Complete Reference
Every formula you need for the SAT Math section, organized by topic. Includes the formulas provided on the test and the ones you must memorize.
Updated for Digital SAT · Geometry · Algebra · Statistics · Exponentials
Formulas provided on test
At the start of every SAT Math module, ETS provides a reference sheet with basic geometry formulas. These are marked PROVIDED below. You should still know them — finding them on the reference sheet costs time.
Formulas you must memorize
Algebra, coordinate geometry, statistics, and exponential formulas are not on the provided sheet. You must memorize every formula marked MEMORIZE below.
Geometry — Provided on the SAT
PROVIDEDArea of a circle
A = πr²
r = radius
Circumference of a circle
C = 2πr
or C = πd where d = diameter
Area of a rectangle
A = lw
l = length, w = width
Area of a triangle
A = ½bh
b = base, h = perpendicular height
Pythagorean theorem
a² + b² = c²
c is the hypotenuse (side opposite the right angle)
30-60-90 triangle
sides: x : x√3 : 2x
Opposite angles: 30° : 60° : 90°
45-45-90 triangle
sides: x : x : x√2
Opposite angles: 45° : 45° : 90°
Volume of a rectangular prism
V = lwh
l = length, w = width, h = height
Volume of a cylinder
V = πr²h
r = radius, h = height
Volume of a sphere
V = (4/3)πr³
r = radius
Volume of a cone
V = (1/3)πr²h
r = base radius, h = height
Volume of a pyramid
V = (1/3)lwh
l = length, w = width, h = height of rectangular base
Algebra — Must Memorize
MEMORIZESlope formula
m = (y₂ − y₁) / (x₂ − x₁)
Rise over run between two points
Slope-intercept form
y = mx + b
m = slope, b = y-intercept
Point-slope form
y − y₁ = m(x − x₁)
Useful when you have a slope and one point
Standard form of a line
Ax + By = C
A, B, C are integers; A ≥ 0
Quadratic formula
x = [−b ± √(b² − 4ac)] / 2a
Solves ax² + bx + c = 0; discriminant = b² − 4ac
Vertex form of a quadratic
y = a(x − h)² + k
Vertex is at point (h, k)
Standard form of a quadratic
y = ax² + bx + c
Vertex x-coordinate = −b / 2a
FOIL (multiplying binomials)
(a + b)(c + d) = ac + ad + bc + bd
First, Outer, Inner, Last
Difference of squares
a² − b² = (a + b)(a − b)
Classic factoring identity
Perfect square trinomial
(a + b)² = a² + 2ab + b²
Also (a − b)² = a² − 2ab + b²
Coordinate Geometry — Must Memorize
MEMORIZEDistance formula
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Derived from Pythagorean theorem
Midpoint formula
M = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
Returns the midpoint coordinates
Equation of a circle
(x − h)² + (y − k)² = r²
Center (h, k), radius r
Exponentials & Growth — Must Memorize
MEMORIZEExponential growth
y = a(1 + r)ᵗ
a = initial value, r = growth rate, t = time
Exponential decay
y = a(1 − r)ᵗ
a = initial value, r = decay rate, t = time
Simple interest
I = Prt
P = principal, r = annual rate, t = time in years
Compound interest
A = P(1 + r/n)^(nt)
n = number of compounds per year
Statistics & Data — Must Memorize
MEMORIZEMean (average)
x̄ = Σx / n
Sum of all values divided by count
Percent change
% change = (new − old) / old × 100
Positive = increase, negative = decrease
Probability
P(event) = favorable outcomes / total outcomes
Assumes equally likely outcomes
Weighted average
x̄ = Σ(wᵢxᵢ) / Σwᵢ
Each value weighted by its frequency or weight
Ratios, Rates & Percents — Must Memorize
MEMORIZEPercent formula
Part = Percent × Whole / 100
Or: Percent = Part / Whole × 100
Unit rate
Rate = Distance / Time
Also: D = RT, T = D/R
Proportion
a/b = c/d → ad = bc
Cross-multiply to solve
Percent of a percent
x% of y% = (x · y) / 100 %
E.g., 20% of 30% = 6%
Key facts about SAT Math
2
Modules
Each module has 22 questions (44 total)
35 min
Time per module
~1.6 min per question
Allowed
Calculator
All questions in both modules
4 domains
Topics
Algebra, Advanced Math, Problem-Solving, Geometry
~15%
Geometry share
About 5-7 questions across both modules
200–800
Score range
Combined with R&W for 400–1600 composite
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