Math reference
SAT Math Formulas: Free Reference Sheet and Worked Examples
A printable SAT Math formula reference with Bluebook-supplied geometry formulas, additional algebra and data relationships, and checked examples.
Reviewed
The short answer
Bluebook supplies a geometry reference sheet during SAT Math. You still need to recognize when a formula applies and know other algebra, percent, data and trigonometry relationships. This reference separates the supplied formulas from additional relationships and gives original examples you can check. Download the printable PDF or use the tables below.
Downloads
On this page
Geometry relationships supplied in Bluebook
These relationships appear on the current official reference sheet. Symbols describe the dimensions shown in the corresponding figure.
| Figure or fact | Relationship |
|---|---|
| Circle | Area A = πr²; circumference C = 2πr |
| Rectangle | A = lw |
| Triangle | A = bh/2, with height perpendicular to the base |
| Right triangle | a² + b² = c², with hypotenuse c |
| 30°–60°–90° triangle | Side ratio 1 : √3 : 2, opposite those angles |
| 45°–45°–90° triangle | Side ratio 1 : 1 : √2 |
| Rectangular prism | V = lwh |
| Cylinder | V = πr²h |
| Sphere | V = 4πr³/3 |
| Cone | V = πr²h/3 |
| Rectangular pyramid | V = lwh/3 |
| Full circle | 360° or 2π radians |
| Triangle angle sum | 180° |
Match units before substituting. Areas use square units; volumes use cubic units. A triangle’s height is not automatically one of its slanted sides.
Additional algebra relationships to recall
| Task | Relationship and condition |
|---|---|
| Slope | m = (y₂ − y₁)/(x₂ − x₁), with x₂ ≠ x₁ |
| Nonvertical line | y = mx + b; point-slope form y − y₁ = m(x − x₁) |
| Quadratic roots | x = (−b ± √(b² − 4ac))/(2a), for ax² + bx + c = 0 and a ≠ 0 |
| Quadratic vertex | x = −b/(2a); substitute to find y |
| Discriminant | b² − 4ac: positive gives two real roots, zero one repeated real root, negative no real roots |
| Root sum and product | For a quadratic with roots r₁ and r₂: r₁ + r₂ = −b/a; r₁r₂ = c/a |
| Difference of squares | u² − v² = (u − v)(u + v) |
| Powers, same base | xᵃxᵇ = xᵃ⁺ᵇ; xᵃ/xᵇ = xᵃ⁻ᵇ where defined |
A formula may reveal a requested coefficient, root or maximum without expanding everything. A canceled denominator retains its original domain restriction.
Percents, data and probability
| Task | Relationship |
|---|---|
| Percent change | (new − original)/original × 100%, for a nonzero original value |
| Percent increase or decrease | Multiply by 1 + p/100 or 1 − p/100 |
| Repeated growth | A(t) = A₀(1 + r)ᵗ, with decimal rate r per period |
| Arithmetic mean | Sum of values / number of values |
| Weighted mean | Sum of (value × count) / total count |
| Probability in a finite equally likely group | Favorable outcomes / total outcomes |
| Conditional probability | Restrict the denominator to the stated condition first |
Successive percent changes multiply. A 20% increase followed by a 20% decrease gives 1.20 × 0.80 = 0.96, or 96% of the original, because the second change uses a different base.
Additional geometry and trigonometry relationships
| Task | Relationship and condition |
|---|---|
| Circle equation | (x − h)² + (y − k)² = r²; center (h,k), radius r > 0 |
| Distance between points | √((x₂ − x₁)² + (y₂ − y₁)²) |
| Midpoint | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Arc length | (θ/360) × 2πr for angle θ in degrees; rθ for θ in radians |
| Sector area | (θ/360) × πr² for angle θ in degrees |
| Sine, cosine, tangent | For an acute angle in a right triangle: opposite/hypotenuse, adjacent/hypotenuse, opposite/adjacent |
| Similar figures | Corresponding lengths scale by k, areas by k², volumes by k³ |
Identify sides relative to the named angle. The hypotenuse is always opposite the right angle. Check the calculator’s degree/radian setting before evaluating a trigonometric expression.
Three checked examples
Slope: Between (2,7) and (5,19), m = (19 − 7)/(5 − 2) = 12/3 = 4. The line is y = 4x − 1; both points satisfy it.
Quadratic maximum: h(t) = −2t² + 12t + 5 = −2(t − 3)² + 23. The maximum over 0 ≤ t ≤ 6 is 23 at t = 3. See the full solution.
Circle arc: A 90° arc of a circle with radius 6 is one quarter of its circumference: (90/360)(2π × 6) = 3π. Its sector area is (90/360)(π × 6²) = 9π. Do not interchange length and area.
Sources
- College Board: Fall 2026 Bluebook SAT test directions and reference sheetsatsuite.collegeboard.org
- College Board: SAT Math contentsatsuite.collegeboard.org
Sources are linked for reference; they do not endorse PeakSAT. How we prepare our guides