SAT Math Formulas: The Full Cheat Sheet for the Digital SAT
Key Takeaways
- The Digital SAT reference sheet gives 12 formulas and 3 facts, all on area, volume, right triangles and angles.
- Slope, line equations, the quadratic formula, the discriminant, exponent rules and growth formulas are not on the sheet, so learn them by heart.
- Percent change, successive percentages, mean and conditional probability carry most Problem-Solving and Data Analysis questions.
- The circle equation, arc length, radians and the trigonometric ratios are the geometry formulas you must bring with you.
- Learn each formula through a question that uses it, and write the full list from memory once a week until nothing is missing.
Table of Contents
- What formulas does the SAT give you?
- Which SAT math formulas do you have to memorise?
- Algebra formulas for the SAT
- Advanced Math formulas for the SAT
- Problem-Solving and Data Analysis formulas
- Geometry and trigonometry formulas not on the sheet
- How should you use the formula sheet on test day?
- How do you memorise SAT math formulas?
The Digital SAT gives you a reference sheet with 12 formulas and 3 geometry facts, all for area, volume, right triangles and angles. Everything else, including slope, the quadratic formula, percent change, the equation of a circle and the trigonometric ratios, you need to know from memory. That second list is where most marks are won or lost.
This cheat sheet sets out both lists by Math domain, with one worked example for each domain. Every example was written by Galvanize for this page, so none of them is a College Board question.
What formulas does the SAT give you?
The reference sheet sits at the start of each Math module. It holds these formulas and facts, word for word in meaning:
| Formula on the sheet | What it gives you |
|---|---|
| A = πr2 | Area of a circle with radius r |
| C = 2πr | Circumference of a circle |
| A = ℓw | Area of a rectangle |
| A = ½bh | Area of a triangle |
| c2 = a2 + b2 | Pythagorean theorem for a right triangle with hypotenuse c |
| 30°-60°-90° triangle: sides x, x√3, 2x | Special right triangle |
| 45°-45°-90° triangle: sides s, s, s√2 | Special right triangle |
| V = ℓwh | Volume of a rectangular prism |
| V = πr2h | Volume of a cylinder |
| V = 4⁄3πr3 | Volume of a sphere |
| V = 1⁄3πr2h | Volume of a cone |
| V = 1⁄3ℓwh | Volume of a rectangular pyramid |
| 360 | Degrees of arc in a circle |
| 2π | Radians of arc in a circle |
| 180 | Sum of the angles of a triangle, in degrees |
Source: the Math module directions and reference page in College Board’s SAT Practice Test 4, checked 28 October 2026. The same directions say a calculator is permitted for all Math questions. The Math section is 70 minutes in two 35-minute modules with 44 questions, according to How the SAT Is Structured.
Worked example (from the sheet). A cone has radius 3 cm and height 8 cm. What is its volume? V = 1⁄3 × π × 32 × 8 = 24π ≈ 75.4 cm3. Knowing the formula is on the sheet saves time, but you still need to recognise which one the question wants.
Which SAT math formulas do you have to memorise?
The Math section tests four content domains. College Board’s Math Section overview gives the question counts: Algebra 13–15, Advanced Math 13–15, Problem-Solving and Data Analysis 5–7, and Geometry and Trigonometry 5–7. The reference sheet covers only part of the last domain. The tables below are Galvanize’s list of the formulas the other questions rely on; College Board does not publish a must-memorise list.
Algebra formulas for the SAT
| Formula | Use it for |
|---|---|
| m = (y2 − y1) ÷ (x2 − x1) | Slope of the line through two points |
| y = mx + b | Slope-intercept form: slope m, y-intercept b |
| y − y1 = m(x − x1) | Point-slope form: a line through (x1, y1) with slope m |
| Ax + By = C, slope = −A ÷ B | Standard form, and reading its slope |
| Parallel: m1 = m2. Perpendicular: m1 × m2 = −1 | Comparing two lines |
| Same slope, different intercept: no solution. Same line: infinitely many solutions | Counting the solutions of a linear system |
| distance = rate × time | Rate problems written in words |
Worked example. Line L passes through (2, 5) and (6, 17). What is its equation, and what is the slope of a line perpendicular to it? The slope is (17 − 5) ÷ (6 − 2) = 12 ÷ 4 = 3. Substitute (2, 5) into y = 3x + b: 5 = 6 + b, so b = −1 and the line is y = 3x − 1. A perpendicular line has slope −1⁄3, because 3 × (−1⁄3) = −1.
Worked example. For what value of k does the system 2x + 3y = 12 and 4x + ky = 7 have no solution? No solution means parallel lines: the x and y coefficients are in the same ratio but the constants are not. 4 is 2 × 2, so k = 3 × 2 = 6. Check the constants: 12 × 2 = 24, which is not 7, so the lines are parallel and distinct. k = 6.
Advanced Math formulas for the SAT
| Formula | Use it for |
|---|---|
| x = (−b ± √(b2 − 4ac)) ÷ 2a | Quadratic formula for ax2 + bx + c = 0 |
| b2 − 4ac: positive, zero or negative | Discriminant: two, one or no real solutions |
| x = −b ÷ 2a | x-coordinate of a parabola’s vertex (and its axis of symmetry) |
| y = a(x − h)2 + k | Vertex form: vertex at (h, k) |
| Sum of roots = −b ÷ a. Product of roots = c ÷ a | Answering about the roots without finding them |
| a2 − b2 = (a + b)(a − b); (a + b)2 = a2 + 2ab + b2 | Factoring and expanding quickly |
| xa · xb = xa+b; xa ÷ xb = xa−b; (xa)b = xab | Exponent rules |
| x−a = 1 ÷ xa; xm/n = (n√x)m | Negative and fractional exponents |
| y = a(1 + r)t and y = a(1 − r)t | Exponential growth and decay at rate r per period |
Worked example. The graph of y = 2x2 − 12x + 11 is a parabola. Find its vertex and say how many x-intercepts it has. The vertex x-coordinate is −(−12) ÷ (2 × 2) = 3. Then y = 2(9) − 36 + 11 = −7, so the vertex is (3, −7). The discriminant is 144 − 4(2)(11) = 144 − 88 = 56, which is positive, so there are two x-intercepts. Their sum is −(−12) ÷ 2 = 6 and their product is 11 ÷ 2.
Worked example. For what value of k does kx2 + 6x + 3 = 0 have exactly one real solution? Exactly one solution means the discriminant is zero: 62 − 4(k)(3) = 0, so 36 = 12k and k = 3.
Problem-Solving and Data Analysis formulas
| Formula | Use it for |
|---|---|
| Percent change = (new − old) ÷ old × 100 | Increases and decreases |
| new = old × (1 ± r), applied once per change | Successive percent changes (multiply, never add) |
| a : b = c : d means ad = bc | Ratios and proportions |
| Mean = sum ÷ number of values | Averages, and finding a missing value from a mean |
| Median: the middle value once sorted. Range: highest − lowest | Centre and spread |
| Probability = favourable outcomes ÷ total outcomes | Simple probability |
| P(A given B) = count in both A and B ÷ count in B | Conditional probability from a two-way table |
| I = Prt; A = P(1 + r ÷ n)nt | Simple and compound interest |
Worked example. A jacket’s price rises from $80 to $92, then falls by 15%. What is the final price, and what was the first percent change? The first change is (92 − 80) ÷ 80 = 0.15, a 15% increase. The fall gives 92 × 0.85 = $78.20. A 15% rise followed by a 15% fall does not bring the price back to $80, because the second percentage is taken of a larger number.
Worked example. The mean of five numbers is 14. A sixth number is added and the mean becomes 15. What is the sixth number? The first total is 5 × 14 = 70. The new total is 6 × 15 = 90. The sixth number is 90 − 70 = 20.
Geometry and trigonometry formulas not on the sheet
| Formula | Use it for |
|---|---|
| (x − h)2 + (y − k)2 = r2 | Circle with centre (h, k) and radius r |
| Arc length = (θ ÷ 360) × 2πr; sector area = (θ ÷ 360) × πr2 | Parts of a circle, with θ in degrees |
| radians = degrees × π ÷ 180; arc length = rθ with θ in radians | Converting angle units |
| sin = opposite ÷ hypotenuse; cos = adjacent ÷ hypotenuse; tan = opposite ÷ adjacent | Right-triangle trigonometry |
| sin x° = cos(90 − x)° | Complementary angles |
| Similar figures with scale factor k: lengths × k, areas × k2, volumes × k3 | Scaling questions |
| Distance = √((x2 − x1)2 + (y2 − y1)2); midpoint = ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2) | Points on the coordinate plane |
| Sum of interior angles = (n − 2) × 180° | Polygons with n sides |
Worked example. What are the centre and radius of the circle x2 + y2 − 6x + 8y = 11? Complete the square for each variable: (x − 3)2 − 9 + (y + 4)2 − 16 = 11, so (x − 3)2 + (y + 4)2 = 36. The centre is (3, −4) and the radius is 6.
Worked example. In right triangle ABC, angle C is 90° and sin A = 5⁄13. What is cos B? A and B add up to 90°, so cos B = sin A = 5⁄13. No side lengths are needed.
How should you use the formula sheet on test day?
- Know what is on it before the test. Opening it to check a cone formula costs seconds; opening it to discover that the circle equation is not there costs more.
- Use it to confirm, not to learn. On average you have about 95 seconds per Math question (70 minutes for 44 questions), which leaves no time to work out what a formula means.
- Watch the units. Volume questions often mix centimetres and metres, and angle questions mix degrees and radians.
- Check the special triangles first. A 30° or 45° angle in a right triangle usually means you can skip the Pythagorean theorem.
- Let the calculator do the arithmetic, not the thinking. Graphing a quadratic or a system can confirm an answer quickly; our Desmos SAT calculator guide shows how. You still need the formula to know what to graph.
How do you memorise SAT math formulas?
Learn each formula with a question that uses it, not as a list. Write the formulas from the four tables above from memory once a week, and mark any you could not recall. Then do topic-wise practice on our free SAT Math practice questions and note, for every miss, whether the gap was the formula or the set-up.
For the topics behind these formulas, see the SAT Math study guide and the SAT exam pattern. To see which domain costs you the most marks today, take the free SAT diagnostic test, then estimate your score with the SAT score calculator.
Frequently Asked Questions
Does the SAT give you a formula sheet?
Yes. Each Math module opens with a reference sheet listing 12 formulas for area, circumference, the Pythagorean theorem, the two special right triangles and five volumes, plus three facts: 360 degrees and 2 pi radians in a circle, and 180 degrees in a triangle.
Which formulas are not on the SAT reference sheet?
Everything outside basic geometry: slope and line equations, the quadratic formula, the discriminant, vertex form, exponent rules, exponential growth and decay, percent change, mean, probability, the equation of a circle, arc length, radians and the trigonometric ratios.
Is the equation of a circle on the SAT formula sheet?
No. The sheet gives the area and circumference of a circle but not its equation. You need to know (x – h)^2 + (y – k)^2 = r^2 and how to complete the square to find the centre and radius.
Do I need to memorise the quadratic formula for the SAT?
Yes. It is not on the reference sheet, and quadratics are a large part of Advanced Math, which has 13 to 15 questions. Learn the discriminant with it, since many questions ask only how many solutions an equation has.
Which trigonometry formulas do I need for the SAT?
Sine, cosine and tangent as ratios of sides in a right triangle, the rule that sin x equals cos(90 – x) in degrees, and the conversion between degrees and radians. The special right triangles are on the reference sheet.
Can I use a calculator for every SAT Math question?
Yes. College Board’s practice test directions say a calculator is permitted for all Math questions. A calculator does the arithmetic, but you still need the right formula to set the question up.
How many questions are in the SAT Math section?
44 questions in 70 minutes, split into two 35-minute modules. Algebra and Advanced Math have 13 to 15 questions each, and Problem-Solving and Data Analysis and Geometry and Trigonometry have 5 to 7 each.
How do I calculate successive percent changes on the SAT?
Multiply by one factor per change. A 20% rise is times 1.20 and a 10% fall is times 0.90, so together they are times 1.08. Adding the percentages gives the wrong answer.
What is the fastest way to find the vertex of a parabola?
For y = ax^2 + bx + c, the x-coordinate of the vertex is -b divided by 2a. Substitute it back to get the y-coordinate. If the equation is already in vertex form, y = a(x – h)^2 + k, the vertex is (h, k).
Are the worked examples on this page real SAT questions?
No. Galvanize wrote every example for this page to show how each formula is used. For official questions, use the full-length practice tests in College Board’s Bluebook app.
How long does it take to learn the SAT math formulas?
Most students can learn the list in two or three weeks of short daily practice. Recall is the easy part; using the right formula under time pressure takes longer, which is why topic-wise practice matters more than the list itself.
