SAT Formula Sheet: Every Formula You Need (+ How to Actually Memorize Them)
The College Board gives you a reference sheet at the start of every SAT Math section — but it only covers 12 geometric formulas. The rest of the formulas you need for SAT Math (algebra, statistics, trigonometry, advanced topics) you must know from memory. Most students don't realize how many formulas aren't on the sheet until they're sitting in the exam room.
This guide gives you the complete SAT formula picture: what the College Board provides, what you must memorize yourself, and exactly how to drill them so they're automatic on test day.
Part 1: Formulas the College Board Gives You
The official SAT Math reference sheet is provided at the beginning of every Math module. It contains the following geometric formulas:
Area Formulas
| Shape | Formula |
|---|---|
| Circle | A = πr² |
| Rectangle | A = lw |
| Triangle | A = ½bh |
Volume Formulas
| Shape | Formula |
|---|---|
| Rectangular prism | V = lwh |
| Cylinder | V = πr²h |
| Pyramid | V = ⅓lwh |
| Cone | V = ⅓πr²h |
| Sphere | V = (4/3)πr³ |
Special Right Triangles
- 30–60–90 triangle: sides in ratio 1 : √3 : 2
- 45–45–90 triangle: sides in ratio 1 : 1 : √2
Other Provided Facts
- The number of degrees of arc in a circle = 360
- The number of radians of arc in a circle = 2π
- The sum of the measures of the angles in a triangle = 180°
Important: Even though these formulas are provided, you should know them cold. Flipping back to the reference sheet repeatedly wastes time and breaks concentration. Treat the sheet as a backup, not a primary resource.
Part 2: Formulas You Must Memorize
The College Board reference sheet does not include algebra, statistics, coordinate geometry, or trigonometry formulas. These you must bring to the exam in your head.
Algebra
| Formula | What It's For |
|---|---|
| Quadratic formula: x = [−b ± √(b²−4ac)] / 2a | Solving quadratic equations |
| Discriminant: b² − 4ac | Number of real solutions (>0 = two, =0 = one, <0 = none) |
| Slope formula: m = (y₂−y₁)/(x₂−x₁) | Slope between two points |
| Slope-intercept form: y = mx + b | Line equation |
| Point-slope form: y−y₁ = m(x−x₁) | Line equation from point + slope |
| Standard form: Ax + By = C | Line equation |
| Midpoint formula: ((x₁+x₂)/2, (y₁+y₂)/2) | Midpoint between two points |
| Distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²] | Distance between two points |
Percent and Statistics
| Formula | What It's For |
|---|---|
| Percent change: [(new − old)/old] × 100 | % increase or decrease |
| Mean: sum of values / number of values | Average |
| Simple interest: I = Prt | Interest calculation |
| Compound interest: A = P(1 + r/n)^(nt) | Compound growth |
Geometry (Not on Reference Sheet)
| Formula | What It's For |
|---|---|
| Circle circumference: C = 2πr | Circumference |
| Arc length: (central angle/360) × 2πr | Length of an arc |
| Sector area: (central angle/360) × πr² | Area of a pie slice |
| Pythagorean theorem: a² + b² = c² | Right triangle sides |
Trigonometry (for SAT Math, Module 2)
| Formula | What It's For |
|---|---|
| sin θ = opposite/hypotenuse | SOHCAHTOA |
| cos θ = adjacent/hypotenuse | SOHCAHTOA |
| tan θ = opposite/adjacent | SOHCAHTOA |
| sin²θ + cos²θ = 1 | Pythagorean identity |
| sin(θ) = cos(90° − θ) | Complementary angles |
Exponents and Radicals
| Rule | Example |
|---|---|
| xᵃ × xᵇ = x^(a+b) | Same base → add exponents |
| (xᵃ)ᵇ = x^(ab) | Power to a power → multiply |
| x^(a/b) = ᵇ√(xᵃ) | Rational exponents |
| x⁰ = 1 | Zero exponent |
| x⁻¹ = 1/x | Negative exponent |
Part 3: How to Actually Memorize These Formulas
Knowing the formulas exist is not the same as retrieving them instantly under time pressure. Here's the fastest approach:
Tier 1: Drill the Non-Sheet Formulas First
The College Board-provided formulas can be checked if needed. The memorize-yourself formulas cannot. Build your flashcard deck around Part 2 above — these are your priority.
Create a card for each formula:
- Front: What does this formula calculate? (e.g., "Distance between two points")
- Back: The formula (e.g., "d = √[(x₂−x₁)² + (y₂−y₁)²]")
Drill with spaced repetition — card you miss → comes back the next day. Card you know → comes back in 3–4 days.
See: How to Make Flashcards That Actually Work
Tier 2: Practice Formulas in Context, Not Just Isolation
Knowing the quadratic formula on a flashcard doesn't mean you can use it under time pressure in a word problem. For each formula, do at least 5 practice problems that require applying it.
Common SAT applications to practice:
- Quadratic formula → applied to profit/loss word problems
- Percent change → price increase/decrease scenarios
- Circle formulas → arc length and sector area
- Distance formula → coordinate geometry
Tier 3: Write the Full Formula Sheet From Memory Weekly
Once a week leading up to your SAT, take a blank piece of paper and write out every memorize-yourself formula from scratch — no notes, no looking. Score yourself. Any formula you couldn't write goes back into daily flashcard rotation.
See: How to Study for Finals in 7 Days
The Most Commonly Missed SAT Formulas
Based on which formulas appear most on practice SATs and which students most commonly miss:
- Arc length and sector area — students use the full circumference/area instead of the fraction
- Compound interest — forgetting the n (number of compounding periods)
- Percent change direction — confusing (new−old)/old with (old−new)/old
- Discriminant — knowing the formula but forgetting what each case means
- Complementary trig — sin(θ) = cos(90°−θ) appears more often than students expect
Make sure these five are on your priority flashcard list.
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Frequently Asked Questions
Does the SAT give you a formula sheet?
Yes. The College Board provides a 12-formula reference sheet at the beginning of each SAT Math module, covering basic area, volume, and special right triangle facts. However, algebra formulas, statistics formulas, and trigonometry identities are not provided — you must memorize those yourself.
What formulas do I need to memorize for the SAT?
The most important formulas to memorize for the SAT (not provided on the reference sheet) are: the quadratic formula, slope and line equations, the distance and midpoint formulas, percent change, arc length, sector area, compound interest, SOHCAHTOA, and the Pythagorean identity (sin²θ + cos²θ = 1).
Is there a formula sheet for the digital SAT (Bluebook)?
Yes. The digital SAT (Bluebook platform) provides the same reference formulas as the paper SAT — 12 geometric formulas accessible during the Math section. The digital format doesn't add any new provided formulas; the memorize-yourself list is the same as for the paper exam.
How many formulas are on the SAT reference sheet?
The official SAT reference sheet contains 12 formulas/facts: area of circle, rectangle, and triangle; volume of rectangular prism, cylinder, pyramid, cone, and sphere; 30-60-90 and 45-45-90 triangle side ratios; degrees in a circle (360); and radians in a circle (2π).
Should I memorize the formulas on the SAT reference sheet too?
Yes — even though they're provided. Flipping back to the reference sheet takes time and interrupts your problem-solving flow. On a timed exam where every 30 seconds matters, having those 12 formulas in memory means you never need to look them up.
The Bottom Line
The SAT Math section tests two types of formula knowledge: the 12 the College Board gives you (which you should still memorize for speed) and the algebra, statistics, and trig formulas you must bring in your head. Both sets are drillable with flashcards and practice problems.
Action step today: Download this article's formula tables, cover the right column, and see how many formulas you can reproduce from memory. Every blank is a flashcard to make.
Also read: How to Raise Your SAT Score: A 4-Week Study Plan and Best Flashcard App for Students
Written by TikoNote Team
AI learning researchers & cognitive science enthusiasts building tools that help students study smarter with evidence-based methods like active recall, spaced repetition, and the Feynman Technique.
