SAT math formulas
The formulas on the Digital SAT reference sheet, plus the ones it leaves out that come up again and again in Algebra, Advanced Math, data analysis and trigonometry. Tap any quick check to test yourself.
On the Digital SAT you can open a reference sheet during the Math section. It gives area and circumference of a circle, area of a rectangle and triangle, the Pythagorean theorem, special right triangles, and volumes of a rectangular prism, cylinder, sphere, cone and pyramid, plus three facts: a circle has 360 degrees (2π radians) and the angles in a triangle add up to 180 degrees. Everything else, such as slope, the quadratic formula and percent change, you need to know.
Given to you in the test
You do not need to memorise these, but knowing them saves time.
A = πr² · C = 2πrA = ℓwA = ½bhc² = a² + b²30°-60°-90°: x, x√3, 2x
45°-45°-90°: s, s, s√2V = ℓwhV = πr²hV = (4/3)πr³V = (1/3)πr²hV = (1/3)ℓwhCircle: 360° = 2π rad
Triangle: angles sum to 180°Algebra formulas to know
m = (y₂ − y₁) / (x₂ − x₁)Quick check: Line through (1, 3) and (4, 12): slope?
(12 − 3)/(4 − 1) = 3
y = mx + bQuick check: Slope 2, y-intercept −5: equation?
y = 2x − 5
Parallel: equal slopes · Perpendicular: m₁m₂ = −1Quick check: Slope perpendicular to y = 4x + 1?
−1/4
Same slope, different interceptsQuick check: For which k does 2x + ky = 7 have no solution with 4x + 6y = 1?
k = 3 (lines parallel, intercepts differ)
Advanced Math formulas to know
x = (−b ± √(b² − 4ac)) / (2a)Quick check: Solve x² − 6x + 5 = 0.
x = 1 or x = 5
b² − 4ac > 0: 2 real roots · = 0: 1 · < 0: noneQuick check: How many real solutions does x² + 4x + 7 = 0 have?
16 − 28 < 0, so none
y = a(x − h)² + k, vertex (h, k)Quick check: Vertex of y = 2(x − 3)² + 1?
(3, 1)
For ax² + bx + c: sum = −b/a, product = c/aQuick check: Sum of the roots of 2x² − 10x + 3 = 0?
5
aᵐ·aⁿ = aᵐ⁺ⁿ · (aᵐ)ⁿ = aᵐⁿ · a^(1/n) = ⁿ√aQuick check: Write 8^(2/3) as an integer.
4
y = a(1 ± r)ᵗQuick check: A $500 balance grows 4% a year. Value after t years?
500(1.04)ᵗ
Problem-Solving and Data Analysis formulas to know
(new − old) / old × 100%Quick check: Price rises from $40 to $50. Percent increase?
25%
sum of values ÷ number of valuesQuick check: Mean of 4, 7, 10, 15?
9
favourable outcomes ÷ total outcomesQuick check: 3 red and 5 blue counters: P(red)?
3/8
multiply by conversion factors so units cancelQuick check: 72 km/h in m/s?
20 m/s
Geometry and Trigonometry formulas to know
sin = opp/hyp · cos = adj/hyp · tan = opp/adjQuick check: Right triangle, opposite 3, hypotenuse 5: sin θ?
3/5
sin x° = cos(90° − x°)Quick check: If sin 25° = k, what is cos 65°?
k
(x − h)² + (y − k)² = r²Quick check: Centre and radius of (x − 2)² + (y + 1)² = 9?
Centre (2, −1), radius 3
arc = (θ/360)·2πr · sector = (θ/360)·πr²Quick check: Sector area for θ = 90°, r = 4?
4π
180° = π radiansQuick check: 60° in radians?
π/3
Practise the formulas
SAT math formulas FAQ
Do you get a formula sheet on the SAT?
Yes. The Digital SAT Math section includes a reference sheet with common geometry formulas and angle facts. It does not include algebra formulas such as slope or the quadratic formula.
Which SAT math formulas should I memorise?
Slope, slope-intercept and point-slope forms, the quadratic formula and discriminant, vertex form, exponent rules, exponential growth and decay, percent change, mean and median, basic probability, SOH CAH TOA and the equation of a circle.
Can I use a calculator on the Digital SAT?
Yes. A built-in Desmos graphing calculator is available for the entire Math section, and you can bring an approved calculator.