SAT Math Formulas: Reference Sheet + What to Memorize

The digital SAT gives you a built-in reference sheet with the common geometry formulas: area, volume, the Pythagorean theorem and special right triangles. It doesn't include the algebra you'll use most, such as slope, the quadratic formula, circle equations, percent change and exponential growth. Memorize those; glance at the sheet for the rest.

What's on the SAT reference sheet

Shape or fact	Formula
Circle	A = πr² · C = 2πr
Rectangle	A = ℓw
Triangle	A = ½bh
Pythagorean theorem	c² = a² + b²
Special right triangles	30°-60°-90°: sides x, x√3, 2x · 45°-45°-90°: sides s, s, s√2
Rectangular prism	V = ℓwh
Cylinder	V = πr²h
Sphere	V = (4/3)πr³
Cone	V = (1/3)πr²h
Rectangular pyramid	V = (1/3)ℓwh
Arc and angle facts	A circle has 360° or 2π radians of arc · Angles in a triangle add up to 180°

Formulas to memorize (not on the sheet)

Lines

Slope:            m = (y₂ − y₁) / (x₂ − x₁)
Slope-intercept:  y = mx + b
Point-slope:      y − y₁ = m(x − x₁)
Standard form:    Ax + By = C   (slope = −A/B)
Parallel lines:   same slope · Perpendicular: slopes multiply to −1

Quadratics

Quadratic formula:  x = (−b ± √(b² − 4ac)) / 2a
Discriminant:       b² − 4ac  (> 0: two solutions, = 0: one, < 0: none)
Vertex form:        y = a(x − h)² + k   (vertex at (h, k))
Vertex x-value:     x = −b / 2a
Sum of roots:       −b/a · Product of roots: c/a

Exponents and growth

Exponent rules:     xᵃ · xᵇ = xᵃ⁺ᵇ · xᵃ / xᵇ = xᵃ⁻ᵇ · (xᵃ)ᵇ = xᵃᵇ · x^(1/n) = ⁿ√x
Exponential model:  y = a(1 + r)ᵗ   (growth)   y = a(1 − r)ᵗ   (decay)
Percent change:     (new − old) / old × 100%

Circles

Circle equation:    (x − h)² + (y − k)² = r²   (center (h, k), radius r)
Arc length:         (angle / 360°) × 2πr
Sector area:        (angle / 360°) × πr²

Right-triangle trigonometry

SOH-CAH-TOA:  sin = opposite/hypotenuse · cos = adjacent/hypotenuse · tan = opposite/adjacent
Complementary angles:  sin(x°) = cos(90° − x°)

Data and statistics

Mean = sum ÷ count · Median = middle value of ordered data
Probability = favorable outcomes ÷ total outcomes

Let Desmos do some of the work

You often don't need a formula at all. Graph a quadratic and Desmos shows its vertex and zeros; graph a circle's equation and it shows the center and radius. Our Desmos guide covers when that's faster than using the formula.

How to learn them

Write each formula from memory on a blank page; check and correct.
Do three practice questions that use each one, from the College Board question bank.
Repeat the blank-page test after two days and again after a week. Retrieval spaced over days beats rereading a formula list.

Then check where formulas actually matter on the test with our guide to SAT Math topics.

Common questions

Does the SAT give you a formula sheet?

Yes. The digital SAT has a built-in reference sheet with common geometry formulas, available on every Math question. It doesn't include algebra formulas like slope or the quadratic formula.

What formulas should I memorize for the SAT?

Slope and line equations, the quadratic formula and vertex form, the discriminant, the circle equation, exponent rules, percent change, exponential growth and decay, and SOH-CAH-TOA.

Do I need to memorize geometry formulas for the SAT?

Mostly no, because area, volume, the Pythagorean theorem and special right triangles are on the reference sheet. Knowing them by heart still saves time.

Sources

Dates, policies and test details change. Check the official source before you make a decision.