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SAT Math Formulas: Every Formula You Need

Updated 2026-10-24

How to use this page

The Digital SAT Math test has a reference sheet you can open in the Bluebook app. It has only a few geometry formulas. You need to remember the rest.

This page splits them into two groups. Formulas the test gives you have a "Given on the test" tag. All the others you must remember. Read the whole page once the night before. If a formula feels new, tap the lesson link to review it.

We are not affiliated with College Board, and the real sheet in the app may change. Open it in Bluebook before test day to check.

Given on the test (reference sheet)

Area of a rectangleA = ℓwℓ is the length, w is the widthGiven on the testLesson 27 →
Area of a triangleA = ½bhb is the base, h is the heightGiven on the testLesson 27 →
Area of a circleA = πr²r is the radiusGiven on the testLesson 28 →
Circumference of a circleC = 2πrr is the radius, d is the diameter. Also C = πdGiven on the testLesson 28 →
Pythagorean theorema² + b² = c²c is the hypotenuseGiven on the testLesson 25 →
30°-60°-90° trianglex : x√3 : 2xx is opposite 30°, x√3 is opposite 60°, 2x is opposite 90°Given on the testLesson 25 →
45°-45°-90° trianglex : x : x√2The legs are x. The hypotenuse is x√2Given on the testLesson 25 →
Volume of a rectangular prismV = ℓwhGiven on the testLesson 27 →
Volume of a cylinderV = πr²hGiven on the testLesson 27 →
Volume of a sphereV = (4/3)πr³Given on the testLesson 27 →
Volume of a coneV = (1/3)πr²hGiven on the testLesson 27 →
Volume of a pyramidV = (1/3)ℓwhThe base is a rectangleGiven on the testLesson 27 →
Degrees in a circle360°Given on the testLesson 28 →
Radians in a circle2π radiansSame as 360°Given on the testLesson 28 →
Angles in a triangle180° totalThe three angles add up to 180°Given on the testLesson 23 →

Lines and linear equations

Slopem = (y₂ − y₁) / (x₂ − x₁)How much y changes for 1 step rightLesson 7 →
Slope-intercept formy = mx + bm is the slope, b is the y-interceptLesson 7 →
Point-slope formy − y₁ = m(x − x₁)Use when you know the slope and one pointLesson 7 →
Standard formAx + By = CSlope = −A/BLesson 7 →
Parallel linesm₁ = m₂Same slopeLesson 7 →
Perpendicular linesm₁ × m₂ = −1Flip the fraction and change the signLesson 7 →
Midpoint((x₁ + x₂)/2, (y₁ + y₂)/2)Average the x values and the y valuesLesson 7 →
Distance between two pointsd = √((x₂ − x₁)² + (y₂ − y₁)²)Or draw a right triangle and use the Pythagorean theoremLesson 25 →

Systems and inequalities

Different slopes1 solutionThe lines cross onceLesson 9 →
Same slope, different y-interceptsno solutionParallel lines never meetLesson 9 →
Same slope, same y-interceptinfinitely many solutionsIt is the same lineLesson 9 →
Multiply or divide by a negativeflip the sign, e.g. −2x < 6 gives x > −3< becomes >, and ≤ becomes ≥Lesson 10 →

Exponents and radicals

Multiply, same basexᵃ × xᵇ = xᵃ⁺ᵇAdd the exponentsLesson 15 →
Divide, same basexᵃ / xᵇ = xᵃ⁻ᵇSubtract the exponentsLesson 15 →
Power of a power(xᵃ)ᵇ = xᵃᵇMultiply the exponentsLesson 15 →
Power of a product(xy)ᵃ = xᵃyᵃLesson 15 →
Zero exponentx⁰ = 1Works when x ≠ 0Lesson 15 →
Negative exponentx⁻ᵃ = 1 / xᵃx cannot be 0Lesson 15 →
Fractional exponentx^(1/2) = √x, x^(m/n) = (ⁿ√x)ᵐThe bottom number is the rootLesson 15 →

Quadratics

Standard formy = ax² + bx + cc is the y-interceptLesson 18 →
Vertex formy = a(x − h)² + kThe vertex is (h, k)Lesson 18 →
Factored formy = a(x − p)(x − q)p and q are the x-interceptsLesson 18 →
x-coordinate of the vertexx = −b / (2a)This line cuts the parabola in half (the axis of symmetry)Lesson 18 →
Quadratic formulax = (−b ± √(b² − 4ac)) / (2a)Solves ax² + bx + c = 0Lesson 17 →
Discriminantb² − 4acPositive: 2 real solutions. Zero: 1 solution. Negative: no real solutionsLesson 17 →
Sum of the roots−b / aFor ax² + bx + c = 0Lesson 17 →
Product of the rootsc / aFor ax² + bx + c = 0Lesson 17 →

Percents, ratios and growth

Percent of a numberpart = (percent / 100) × wholeLesson 6 →
Percent change(new − old) / old × 100%Always divide by the old valueLesson 6 →
Multiplying factorUp r%: × (1 + r/100). Down r%: × (1 − r/100)Up 20% means multiply by 1.2Lesson 6 →
Exponential growth and decayy = a(1 + r)ᵗ (decay: y = a(1 − r)ᵗ)a is the start value. r is the rate as a decimal (5% = 0.05). t is the number of periodsLesson 20 →
Simple interestI = PrtP is the start amount, r is the yearly rate as a decimal, t is yearsLesson 20 →
Compound interestA = P(1 + r/n)ⁿᵗP is the start amount, r is the yearly rate as a decimal, t is years. Interest is added n times a yearLesson 20 →

Statistics and probability

Meansum / countLesson 11 →
Medianthe middle value, in orderWith two middle values, average themLesson 11 →
Rangemax − minLesson 11 →
Standard deviationYou do not calculate itBigger means the data is more spread out. Just compare.Lesson 11 →
ProbabilityP = wanted / totalAlways between 0 and 1Lesson 13 →
Conditional probabilityP(A | B) = (both A and B) / (all B)In a two-way table, use that row or column totalLesson 13 →
Expected countprobability × totalLesson 13 →

More circle formulas

Arc length(θ/360) × 2πrθ is in degreesLesson 28 →
Sector area(θ/360) × πr²Lesson 28 →
Circle equation(x − h)² + (y − k)² = r²Center (h, k), radius rLesson 29 →
Degrees to radiansradians = degrees × π/180Lesson 28 →
Radians to degreesdegrees = radians × 180/πLesson 28 →
Inscribed angle= ½ × central angleBoth use the same arcLesson 28 →

Triangles and trigonometry

SOH CAH TOAsin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adjopp = opposite, adj = adjacent, hyp = hypotenuseLesson 26 →
Sine and cosine of complementary anglessin x = cos(90° − x)The two acute angles add up to 90°Lesson 26 →
Similar trianglesside ratio = kMatching sides have the same ratioLesson 24 →
Area ratio of similar shapesk²The square of the side ratioLesson 24 →
Angle sum of an n-sided polygon(n − 2) × 180°Lesson 23 →

The night before

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