SAT Math Formula Sheet 2026-2027: The Complete List
Although Bluebook provides an official SAT Math formula sheet, it is a limited reference rather than a complete formula toolkit. To score well, you need to know the key formulas and mathematical relationships across all four SAT Math domains, including important ones that are not included on the official sheet. This guide fills that gap by covering what’s on the formula sheet, what’s missing, and when to use each formula.
What’s Actually on the Official SAT Reference Sheet
The official reference sheet covers key geometry, triangle, circle, and volume formulas — but it’s not a complete SAT math cheat sheet. Math also covers Algebra, Advanced Math, and Problem-Solving & Data Analysis, so you’ll need more than what’s given on test day.
See a full breakdown of what math is on the SAT for the full picture.
Official Geometry and Measurement Formulas
| Formula Name | Formula |
| Circle Area | A = πr² |
| Circle Circumference | C = 2πr |
| Rectangle Area | A = lw |
| Triangle Area | A = ½bh |
| Pythagorean Theorem | a² + b² = c² |
| 30-60-90 Triangle | x, x√3, 2x |
| 45-45-90 Triangle | x, x, x√2 |
| Rectangular Prism Volume | V = lwh |
| Cylinder Volume | V = πr²h |
| Sphere Volume | V = ⁴⁄₃πr³ |
| Cone Volume | V = ⅓πr²h |
| Pyramid Volume | V = ⅓lwh |
| Triangle Angle Sum | A + B + C = 180° |
| Full Rotation | 360° = 2π radians |
Key point: You do not need to spend valuable memorization time learning the formulas that are already supplied in the official reference information. You should, however, know what each formula means and recognize when a problem calls for it.
Algebra Formulas
Algebra represents the largest SAT Math domain, so your formula preparation should start here. Many questions can be solved without memorizing a complicated equation, but several relationships should become automatic because they appear across linear equations, functions, systems, and word problems.
Linear Equations and Rates
| Formula Name | Formula |
| Slope | m = (y₂ − y₁) / (x₂ − x₁) |
| Slope-Intercept Form | y = mx + b |
| Point-Slope Form | y − y₁ = m(x − x₁) |
| Standard Form | Ax + By = C |
| Average Rate of Change | [f(b) − f(a)] / (b − a) |
| Distance-Rate-Time | d = rt |
| Direct Variation | y = kx |
Systems and Proportions
| Formula Name | Formula |
| Proportion | a / b = c / d |
| Cross Multiplication | ad = bc |
| Unit Rate | quantity / number of units |
| System of Two Linear Equations | a₁x + b₁y = c₁; a₂x + b₂y = c₂ |
Inequalities
| Formula Name | Formula |
| Addition/Subtraction Rule | a < b ⇒ a + c < b + c |
| Multiplication/Division by Positive | a < b ⇒ ac < bc, c > 0 |
| Multiplication/Division by Negative | a < b ⇒ ac > bc, c < 0 |
| Compound Inequality | a < x < b |
A Quick Algebra Example
Suppose a SAT question gives two points, (2, 5) and (6, 13), and asks for the rate at which y changes as x increases.
Use the slope formula:
m = (13 − 5) / (6 − 2) = 8 / 4 = 2
The key is not simply remembering the formula. The phrase “rate at which y changes as x increases” is the signal that you should think about slope.
For many students, especially when solving SAT questions in a second language, recognizing these wording signals can be more useful than translating every sentence word for word.
Advanced Math Formulas
Advanced Math also accounts for a major portion of SAT Math and includes nonlinear equations, quadratics, exponentials, polynomials, and functions. These questions often look more complicated than they actually are because the same small group of relationships appears repeatedly.
For difficult questions, knowing the hardest SAT math problems students face can also help you understand which concepts deserve more practice.
Quadratics
| Formula Name | Formula |
| Quadratic Formula | x = (−b ± √(b² − 4ac)) / 2a |
| Discriminant | b² − 4ac |
| Vertex x-Coordinate | x = −b / 2a |
| Vertex Form | y = a(x − h)² + k |
| Standard Quadratic Form | y = ax² + bx + c |
| Factored Form | y = a(x − r₁)(x − r₂) |
| Difference of Squares | a² − b² = (a − b)(a + b) |
Exponents and Radicals
| Formula Name | Formula |
| Product of Powers | aᵐ · aⁿ = aᵐ⁺ⁿ |
| Quotient of Powers | aᵐ / aⁿ = aᵐ⁻ⁿ |
| Power of a Power | (aᵐ)ⁿ = aᵐⁿ |
| Power of a Product | (ab)ⁿ = aⁿbⁿ |
| Negative Exponent | a⁻ⁿ = 1 / aⁿ |
| Fractional Exponent | a¹⁄ⁿ = ⁿ√a |
| General Fractional Exponent | aᵐ⁄ⁿ = ⁿ√(aᵐ) |
Exponential Growth and Decay
| Formula Name | Formula |
| Exponential Growth | A = P(1 + r)ᵗ |
| Exponential Decay | A = P(1 − r)ᵗ |
| General Exponential Model | y = abˣ |
Function Relationships
| Formula Name | Formula |
| Function Notation | y = f(x) |
| Composition | f(g(x)) |
| Horizontal Shift | f(x − h) |
| Vertical Shift | f(x) + k |
| Reflection Across x-Axis | −f(x) |
| Reflection Across y-Axis | f(−x) |
A Quick Advanced Math Example
Suppose a quantity starts at 500 and increases by 8% every year. After 3 years, the model is:
A = 500(1.08)³
The important clue is “increases by 8% every year.” That indicates repeated percentage growth, so an exponential model is more appropriate than a linear equation.
You do not need to calculate the expression immediately. First identify the structure: initial value × repeated growth factor.
Problem-Solving & Data Analysis Formulas
Problem-Solving and Data Analysis questions focus on ratios, percentages, probability, statistics, units, and interpreting real-world data. The formulas themselves are usually manageable; the difficulty often comes from identifying exactly what the question is asking.
Ratios, Rates, and Percentages
| Formula Name | Formula |
| Percent | (part / whole) × 100% |
| Percent Change | [(new − original) / original] × 100% |
| Percent Increase | New = Original(1 + r) |
| Percent Decrease | New = Original(1 − r) |
| Unit Rate | quantity / units |
| Proportional Relationship | y = kx |
Statistics
| Formula Name | Formula |
| Mean | sum of values / number of values |
| Weighted Mean | Σwx / Σw |
| Range | maximum − minimum |
| Median | Middle value after ordering |
| Mean from a Known Sum | Mean = Total / n |
Probability
| Formula Name | Formula |
| Basic Probability | P(A) = favorable outcomes / total outcomes |
| Complement | P(not A) = 1 − P(A) |
| Addition Rule | P(A or B) = P(A) + P(B) − P(A and B) |
| Conditional Probability | P(A | B) = P(A ∩ B) / P(B) |
| Independent Events | P(A ∩ B) = P(A)P(B) |
Data Interpretation
| Formula Name | Formula |
| Relative Frequency | frequency / total |
| Percentile Interpretation | Percentage of observations at or below a value |
| Margin of Change | new value − old value |
SAT wording trap: “increase by 20%” means multiply the original value by 1.20. “Decrease by 20%” means multiply it by 0.80. These are not the same as simply adding or subtracting 20.
This distinction is particularly useful if you are solving SAT Math in English and are tempted to translate every sentence literally. Focus on the mathematical operation signaled by phrases such as “by,” “to,” “of,” “per,” “given that,” and “compared with.”
Geometry & Trigonometry Formulas
Geometry and Trigonometry make up a smaller share of SAT Math than Algebra and Advanced Math, but they contain many formulas that are easy to confuse. The most important distinction is whether the relationship appears on the official reference information.
The formulas marked Yes below are supplied on the test. The formulas marked No are relationships you should know before test day.
Geometry: Area, Volume, and Triangles
| Formula Name | Formula |
| Circle Area | A = πr² |
| Circle Circumference | C = 2πr |
| Rectangle Area | A = lw |
| Triangle Area | A = ½bh |
| Pythagorean Theorem | a² + b² = c² |
| 30-60-90 Triangle | x, x√3, 2x |
| 45-45-90 Triangle | x, x, x√2 |
| Rectangular Prism Volume | V = lwh |
| Cylinder Volume | V = πr²h |
| Sphere Volume | V = ⁴⁄₃πr³ |
| Cone Volume | V = ⅓πr²h |
| Pyramid Volume | V = ⅓lwh |
| Triangle Angle Sum | A + B + C = 180° |
Trigonometry and Coordinate Geometry
| Formula Name | Formula |
| Sine | sin θ = opposite / hypotenuse |
| Cosine | cos θ = adjacent / hypotenuse |
| Tangent | tan θ = opposite / adjacent |
| Distance Formula | d = √[(x₂ − x₁)² + (y₂ − y₁)²] |
| Midpoint Formula | ((x₁ + x₂) / 2, (y₁ + y₂) / 2) |
| Circle Equation | (x − h)² + (y − k)² = r² |
| Slope-Perpendicular Relationship | m₁m₂ = −1 |
he practical rule is simple: do not spend most of your memorization time memorizing formulas the test already provides. Instead, make sure you can recognize those formulas immediately and devote more study time to useful relationships that are not supplied.
How to Memorize and Use These Formulas Efficiently
Formula memorization is most effective when you connect each formula to a recognizable question pattern. Do not try to memorize every equation with equal priority. Build automatic recall for high-frequency relationships, then practice identifying which formula a question is signaling.
Priority 1: Know These Cold
| Formula | Why It Matters |
| Slope | Appears in lines, rates of change, tables, graphs, and word problems. |
| Quadratic Formula | Provides a reliable method for solving general quadratic equations. |
| Exponent Rules | Apply across many Advanced Math expressions. |
| Percent Change | Common in real-world data and comparison questions. |
| Exponential Growth/Decay | Important for repeated percentage-change models. |
| Probability Rules | Useful for multi-step probability and “given that” questions. |
| Basic Trigonometric Ratios | Useful for right-triangle problems when trig relationships are required. |
Priority 2: Recognize the Trigger Words
| If the Question Says… | Think… |
| “rate of change” | Slope |
| “per” | Unit rate |
| “increase by 15%” | Multiply by 1.15 |
| “decrease by 15%” | Multiply by 0.85 |
| “maximum” or “minimum” | Vertex / quadratic |
| “given that” | Conditional probability |
| “hypotenuse” | Pythagorean theorem or trigonometry |
| “growth factor” | Exponential model |
| “average” | Mean |
| “middle value” | Median |
| “distance between two points” | Distance formula |
Priority 3: Practice Formula Selection
The biggest mistake is treating formula memorization as the final goal. On the SAT, you need to identify the mathematical structure first.
For example:
A population increases by 5% every year.
The important information is not merely the number 5%. The phrase “every year” tells you the percentage change is repeated, which points toward an exponential model.
Similarly:
A line passes through two points. What is its rate of change?
The phrase “rate of change” points directly to slope.
For students who are preparing in English as a second language, this formula-to-word connection is especially useful. Instead of translating the entire problem into Chinese first, learn a small set of high-value mathematical phrases and connect each phrase to an operation.
- Alt Text：SAT math formulas decision guide connecting question wording with the correct formula
Summary
The official SAT reference sheet gives you important geometry and measurement formulas, but it is not a complete SAT math formula sheet. You should know which formulas are provided, which SAT formulas to memorize, and—most importantly—when each relationship applies. If you want to identify weak areas and practice the formulas most relevant to your target score, [a personalized SAT math prep course] can provide a more targeted approach than memorizing a generic SAT math cheat sheet.
FAQ
Does the Digital SAT still provide a formula sheet?
Yes. The Digital SAT provides reference information during the Math section, including key geometry, triangle, circle, and volume formulas. However, the official reference information does not contain every formula or relationship that may be useful for solving SAT Math questions.
Do I need to memorize the formulas already on the SAT reference sheet?
No. You can access the supplied reference information during the test. You should still understand what those formulas mean and recognize when to use them, because spending time searching for a basic formula can slow down your solution.
What formulas are NOT given on the SAT and should I memorize?
High-value relationships to know include slope, average rate of change, exponent rules, the quadratic formula, percent change, exponential growth and decay, probability rules, distance and midpoint formulas, and basic trigonometric ratios. Prioritize formulas that appear frequently and are not provided in the official reference information.
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Nathan, a graduate of the University of New South Wales, brings over 9 years of expertise in teaching Mathematics and Science across primary and secondary levels. Known for his rigorous yet steady instructional style, Nathan has earned high acclaim from students in grades 1-12. He is widely recognized for his unique ability to blend academic rigor with engaging, interactive lessons, making complex concepts accessible and fun for every student. Nathan also has extensive experience helping students prepare for the AMC 8 and Math Kangaroo competitions, guiding them to achieve outstanding results in international math contests.
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