SAT Math Formulas: Every Formula You Need to Know (2026)
The SAT Math section provides a reference sheet with 12 geometry formulas at the start of every test. But those 12 formulas cover only a fraction of what you need. Algebra, quadratics, trigonometry, statistics, and sequences are all fair game, and none of those formulas are given to you.
This is the complete list. Every formula that appears on the SAT Math section, organized by topic, with notes on when and how each one is used.
SAT MATH AT A GLANCE
- ✓44 questions across 2 modules (22 per module)
- ✓70 minutes total (35 minutes per module)
- ✓Scored from 200 to 800
- ✓Calculator allowed for all questions
- ✓Adaptive: Module 2 difficulty adjusts based on Module 1 performance
- ✓4 content areas: Algebra, Advanced Math, Problem Solving and Data, Geometry and Trigonometry
Formulas Provided on the SAT Reference Sheet
These 12 formulas appear on every SAT. You do not need to memorize them, but you should know them well enough that you never have to look them up mid-test. Referencing the sheet costs time.
| Formula | What It Is |
|---|---|
| A = πr² | Area of a circle |
| C = 2πr | Circumference of a circle |
| A = lw | Area of a rectangle |
| A = ½bh | Area of a triangle |
| A = ½(b₁ + b₂)h | Area of a trapezoid |
| V = lwh | Volume of a rectangular prism |
| V = πr²h | Volume of a cylinder |
| V = ⅓πr²h | Volume of a cone |
| V = (4/3)πr³ | Volume of a sphere |
| a² + b² = c² | Pythagorean theorem |
| 30-60-90: sides 1, √3, 2 | Special right triangle |
| 45-45-90: sides 1, 1, √2 | Special right triangle |
Algebra Formulas (Must Memorize)
Algebra makes up the largest content area on the SAT Math section, roughly 35 percent of all questions. These formulas are not on the reference sheet.
Linear Equations
m is the slope, b is the y-intercept. This is the most common form you will see on the SAT.
Used when you know the slope and one point on the line. Useful for writing the equation of a line quickly.
The SAT sometimes presents lines in this form. To find the slope, rewrite as slope-intercept. Slope equals negative A divided by B.
Rise over run. Given any two points, you can find the slope. Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals of each other.
Quadratic Equations
This is the most important formula on the entire test that is not provided. Memorize it completely. It solves any quadratic equation.
The vertex of the parabola is at the point (h, k). If a is positive, the parabola opens upward and the vertex is the minimum. If a is negative, it opens downward and the vertex is the maximum.
r₁ and r₂ are the x-intercepts (roots) of the parabola. The SAT frequently asks you to identify roots from this form.
If the discriminant is positive, the quadratic has two real roots. If zero, it has one real root (a perfect square). If negative, it has no real roots. The SAT tests this concept frequently.
Systems of Equations
Systems of linear equations appear on almost every SAT. You need to know two solution methods:
Substitution: Solve one equation for a variable, then substitute into the other equation.
Elimination: Multiply one or both equations by constants so that adding or subtracting them eliminates a variable.
A system has one solution when the lines intersect, no solution when the lines are parallel (same slope, different intercept), and infinitely many solutions when the equations describe the same line.
Advanced Math Formulas (Must Memorize)
Exponent Rules
| Rule | Example |
|---|---|
| xᵃ · xᵇ = xᵃ⁺ᵇ | x³ · x⁴ = x⁷ |
| xᵃ / xᵇ = xᵃ⁻ᵇ | x⁵ / x² = x³ |
| (xᵃ)ᵇ = xᵃᵇ | (x²)³ = x⁶ |
| x⁰ = 1 | 5⁰ = 1 |
| x⁻ᵃ = 1/xᵃ | x⁻² = 1/x² |
| x^(1/n) = ⁿ√x | x^(1/2) = √x |
Sequences
a₁ is the first term, d is the common difference (the amount added each time), and n is the term number. Used when a sequence increases or decreases by a fixed amount.
r is the common ratio (the number multiplied each time). Used when each term is multiplied by the same factor.
Functions
The SAT tests function notation and transformations. Key concepts to know:
- f(x + c) shifts the graph left by c units (if c is positive)
- f(x - c) shifts the graph right by c units
- f(x) + c shifts the graph up by c units
- f(x) - c shifts the graph down by c units
- -f(x) reflects the graph across the x-axis
- f(-x) reflects the graph across the y-axis
Geometry Formulas (Beyond the Reference Sheet)
Coordinate Geometry
Gives the straight-line distance between two points. This is the Pythagorean theorem applied to a coordinate plane.
Gives the exact midpoint between two coordinates. Average the x-values and average the y-values.
The center of the circle is at (h, k) and the radius is r. The SAT frequently asks you to identify the center or radius from this equation or to complete the square to convert a general form equation into this form.
Angles and Lines
- Angles on a straight line sum to 180 degrees
- Angles in a triangle sum to 180 degrees
- Vertical angles are equal
- Corresponding angles formed by parallel lines cut by a transversal are equal
- Alternate interior angles formed by parallel lines cut by a transversal are equal
- Interior angles of a polygon with n sides sum to (n - 2) times 180 degrees
Trigonometry Formulas (Must Memorize)
Trigonometry makes up about 5 to 10 percent of the SAT Math section. The formulas are not provided.
| Function | Definition | Mnemonic |
|---|---|---|
| sin(θ) | Opposite / Hypotenuse | SOH |
| cos(θ) | Adjacent / Hypotenuse | CAH |
| tan(θ) | Opposite / Adjacent | TOA |
This identity appears on the SAT. If you know sin(θ), you can find cos(θ), and vice versa.
The sine of an angle equals the cosine of its complement. The SAT tests this regularly in a form like: if sin(x°) = cos(y°), then x + y = 90.
Statistics and Data Analysis Formulas
Descriptive Statistics
| Measure | How to Calculate |
|---|---|
| Mean | Sum of all values divided by the number of values |
| Median | Middle value when data is ordered from least to greatest |
| Mode | Most frequently occurring value |
| Range | Maximum value minus minimum value |
| Standard deviation | Measures spread around the mean. A larger standard deviation means more spread out data. |
Probability
Percent and Rates
P is principal, r is annual interest rate (as a decimal), t is time in years.
n is the number of times interest compounds per year. When interest compounds continuously, A = Pe^(rt), but this rarely appears on the SAT.
a is the initial value, r is the growth or decay rate (as a decimal), and t is time. The SAT tests this in word problems about population growth, radioactive decay, and investment returns.
How to Use This Formula List Effectively
Having a list of formulas is not the same as knowing them. Here is how to actually internalize this material before test day.
Prioritize by Frequency
Not every formula appears on every test with the same frequency. The quadratic formula, slope formula, and basic trig ratios appear on almost every test. Arc length and compound interest appear less often. Focus your memorization time on the high-frequency formulas first.
The highest-frequency formulas to memorize, in order of importance: quadratic formula, slope formula, distance formula, vertex form, exponent rules, SOH CAH TOA, Pythagorean identity, and percent change.
Practice Applying, Not Just Reciting
You need to be able to use a formula under time pressure, not just recite it. For each formula, solve at least 5 to 10 practice problems that require applying it in different contexts. The quadratic formula, for example, might be used to find roots, the number of solutions, or the vertex, depending on how the question is framed.
Know What the Variables Mean
One of the most common formula errors on the SAT is plugging the wrong value into the wrong variable. For the compound interest formula A = P(1 + r/n)^(nt), students regularly mix up r and n, or forget to convert the percentage to a decimal. Understand what each variable represents before you memorize the formula.
Practice every formula in context.
AuraMint lets you practice SAT Math questions by topic, so you can drill quadratics, trigonometry, or statistics specifically until each formula is automatic. Scan any practice problem and get a step-by-step solution showing exactly which formula was used and why.
SAT Math Formulas: Frequently Asked Questions
Does the SAT give you a formula sheet?
Yes. The SAT provides a reference sheet at the beginning of the Math section with 12 geometry formulas. These include area and circumference of a circle, area of a triangle, the Pythagorean theorem, special right triangle ratios, and volume formulas for cones, cylinders, spheres, and rectangular prisms. However, algebra, statistics, and trigonometry formulas are not provided, so you must memorize those.
What is the quadratic formula on the SAT?
The quadratic formula is x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a. It solves any equation in the form ax squared plus bx plus c equals zero. The SAT does not provide this formula, so you need to memorize it.
What math formulas do I need to memorize for the SAT?
The formulas you must memorize for the SAT include the quadratic formula, slope formula, slope-intercept form, point-slope form, distance formula, midpoint formula, vertex form of a quadratic, arithmetic and geometric sequence formulas, simple and compound interest, trigonometric ratios (SOH CAH TOA), and the Pythagorean identity. Geometry formulas are provided on the test but you should know them too for speed.
What are special right triangles on the SAT?
The two special right triangles on the SAT are the 30-60-90 triangle and the 45-45-90 triangle. In a 30-60-90 triangle, the sides are in the ratio 1 to square root of 3 to 2. In a 45-45-90 triangle, the sides are in the ratio 1 to 1 to square root of 2. These ratios are provided on the SAT reference sheet but you should know them without looking.
How many math questions are on the SAT?
The SAT Math section has 44 questions total across two modules of 22 questions each. You have 35 minutes per module, for a total of 70 minutes. Most questions are multiple choice with 4 options, but some are student-produced responses where you fill in your own answer.