SAT Math Formula Sheet (Digital SAT 2026): Every Formula You Need

The Digital SAT gives you a built-in reference sheet on test day — but only 13 formulas. Everything else, you’re expected to know cold. This guide is your complete SAT math cheat sheet: the formulas the College Board gives you, the ones they don’t (but you absolutely need), and a quick example for each.

Bookmark this page. By test day, every formula here should be muscle memory.

Tip: practice using these formulas, don’t just memorize them. Plug them into a real Digital SAT practice question on Makon AI’s free Question Bank and see your scaled score on our Digital SAT score calculator.

Part 1 — The 13 formulas the SAT gives you (the official reference sheet)

These show up at the start of each Math module. You don’t need to memorize them, but you do need to know when to use each one.

Geometry — area & circumference

1. Area of a rectangle A = lw

2. Area of a triangle A = \tfrac{1}{2}bh

3. Pythagorean theorem a^2 + b^2 = c^2

4. Special right triangle (45-45-90) — sides in ratio 1 : 1 : \sqrt{2}

5. Special right triangle (30-60-90) — sides in ratio 1 : \sqrt{3} : 2

6. Circle: area A = \pi r^2 · circumference C = 2\pi r

7. Cylinder volume V = \pi r^2 h

8. Sphere volume V = \tfrac{4}{3}\pi r^3

9. Cone volume V = \tfrac{1}{3}\pi r^2 h

10. Pyramid volume V = \tfrac{1}{3}lwh

11. Rectangular prism volume V = lwh

12. Number of degrees in a circle = 360

13. Sum of angles in a triangle = 180°

That’s the entire reference sheet. If you’re relying on it for anything more complex, you’re wasting time.

Part 2 — Formulas you need to memorize (the SAT does NOT give you these)

This is where most of the points are won or lost. The SAT loves to test these because they’re “high school knowledge,” not lookup-able.

Algebra & linear equations

Slope of a line m = \frac{y_2 - y_1}{x_2 - x_1}

Slope-intercept form: y = mx + b

Point-slope form: y - y_1 = m(x - x_1)

Standard form: ax + by = c

Distance between two points d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Midpoint of a segment M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals: m_1 \cdot m_2 = -1.

Quadratics

Standard form: y = ax^2 + bx + c

Vertex form: y = a(x - h)^2 + k — vertex at (h, k)

Factored form: y = a(x - r_1)(x - r_2) — roots at r_1, r_2

Quadratic formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Discriminant: b^2 - 4ac

• > 0: two real roots
• = 0: one real root
• < 0: no real roots

Vertex from standard form: x = -\frac{b}{2a}

Sum of roots = -\frac{b}{a} · Product of roots = \frac{c}{a}

Exponents & radicals

x^a \cdot x^b = x^{a+b} \frac{x^a}{x^b} = x^{a-b} (x^a)^b = x^{ab} x^{-a} = \frac{1}{x^a} x^{1/n} = \sqrt[n]{x} x^0 = 1 (when x \neq 0)

Percentages, ratios & proportions

Percent change \text{percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Percent of a number: convert percent to decimal, multiply.

• 25% of 80 = 0.25 × 80 = 20

Direct proportion: y = kx — y goes up when x goes up. Inverse proportion: y = \frac{k}{x} — y goes down when x goes up.

Functions

Function notation: f(x) means “the value of f at x”

• f(g(x)) — plug g(x) in everywhere f has x.

Linear function: f(x) = mx + b Exponential growth: f(x) = a(1 + r)^x Exponential decay: f(x) = a(1 - r)^x

Statistics & data

Mean (average) = sum / count

Median = middle value when sorted

Mode = most frequent value

Range = max − min

Standard deviation — you don’t calculate it on the SAT, but you should know that higher SD = data more spread out.

Probability

Single event probability P = \frac{\text{favorable outcomes}}{\text{total outcomes}}

Independent events: P(A \text{ and } B) = P(A) \cdot P(B)

Mutually exclusive events: P(A \text{ or } B) = P(A) + P(B)

Geometry & trigonometry (extras the reference sheet skips)

Area of a trapezoid: A = \tfrac{1}{2}(b_1 + b_2)h

Area of a parallelogram: A = bh

Circle equation: (x - h)^2 + (y - k)^2 = r^2 — center (h,k), radius r

Arc length: \text{arc} = \frac{\theta}{360} \cdot 2\pi r

Sector area: A = \frac{\theta}{360} \cdot \pi r^2

Trig (right triangles):

• \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
• \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
• \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} (mnemonic: SOH-CAH-TOA)

Trig identity: \sin^2(\theta) + \cos^2(\theta) = 1

Complementary angles: \sin(\theta) = \cos(90° - \theta)

Sequences

Arithmetic sequence: a_n = a_1 + (n - 1)d

Geometric sequence: a_n = a_1 \cdot r^{n-1}

Part 3 — How to actually memorize these

Don’t print the sheet and stare at it. Memory works through retrieval, not rereading. Use this sequence:

1. Day 1: read each formula once, write a 1-line example for each.
2. Day 2: flashcards (front: name. back: formula). 10 minutes.
3. Day 3+: every time you do a math practice question, identify which formula applies before solving. That’s the skill the SAT tests.

Inside Makon AI, the AI tutor flags which formula a question relies on whenever you miss it — that single feedback loop is worth more than re-reading this sheet.

Quick reference: formulas by Digital SAT topic area

The Digital SAT Math section covers four content areas. Here’s which formulas cluster where:

• Algebra (~35% of questions): linear equations, slope, systems, point-slope/standard/slope-intercept forms
• Advanced Math (~35%): quadratics, exponents, function notation, polynomials
• Problem-Solving & Data Analysis (~15%): percent change, ratios, proportion, mean/median/mode, probability
• Geometry & Trigonometry (~15%): the reference-sheet formulas + circle equation, arc/sector, trig