Every SAT Math Formula You Need to Memorize (Organized by Topic)

The SAT provides 12 formulas. You need to know 40.

The Digital SAT gives you a reference sheet with 12 geometry formulas accessible via a button on every Math question. That sounds generous, but it covers only the most common shape formulas — area of a circle, volume of a sphere, that sort of thing. For everything else, you're on your own.

This post is the complete list. Every formula tested on the Digital SAT, organized by topic. We'll cover the when and how for each, not just the formula itself.

Algebra

Slope of a line through two points

m = (y₂ - y₁) / (x₂ - x₁)

Use whenever you have two points and need to describe the line through them. Common trap: the order of the points doesn't matter as long as you're consistent (both top and bottom).

Slope-intercept form

y = mx + b

m is the slope, b is the y-intercept (where the line crosses the y-axis when x = 0). To find the x-intercept, set y = 0 and solve.

Point-slope form

y - y₁ = m(x - x₁)

Use when you have a slope and one point on the line. Fastest way to write a line's equation given minimal info.

Standard form

Ax + By = C

Less common on the SAT but shows up. To convert to slope-intercept: solve for y. Slope in standard form is -A/B.

Distance between two points

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

This is the Pythagorean theorem dressed up. Memorize it; the SAT won't give it to you.

Midpoint

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Average the x-coordinates, average the y-coordinates.

Quadratic formula

x = [-b ± √(b² - 4ac)] / (2a)

For any quadratic ax² + bx + c = 0. The sign of the discriminant b² - 4ac tells you:

Positive → 2 real solutions
Zero → 1 real (repeated) solution
Negative → 0 real solutions (2 complex)

Sum and product of roots

For ax² + bx + c = 0:

Sum of roots = -b/a
Product of roots = c/a

These come up in questions like "what is the sum of the solutions to 2x² - 8x + 3 = 0?" Answer: -(-8)/2 = 4. No need to actually solve.

Vertex form

y = a(x - h)² + k, vertex at (h, k).

For a general quadratic ax² + bx + c, the x-coordinate of the vertex is x = -b/(2a). Substitute to find the y-coordinate.

Factored form

y = a(x - r₁)(x - r₂), x-intercepts at r₁ and r₂.

Fastest form when you know the roots. Use when a question gives you x-intercepts.

Exponent rules

xᵃ · xᵇ = xᵃ⁺ᵇ
xᵃ / xᵇ = xᵃ⁻ᵇ
(xᵃ)ᵇ = xᵃᵇ
x⁻ᵃ = 1/xᵃ
x^(1/n) = ⁿ√x
x⁰ = 1 (for any nonzero x)

Radical simplification

√(ab) = √a · √b

Use to simplify roots: √72 = √(36 · 2) = 6√2.

Functions

Function notation

If f(x) = 2x + 3, then f(4) = 2(4) + 3 = 11. The number in parentheses replaces x.

Composition

f(g(x)) means plug g(x) into f. Work from the inside out: first find g(x), then evaluate f at that value.

Inverse

To find the inverse of a function: (1) replace f(x) with y, (2) swap x and y, (3) solve for y, (4) rename as f⁻¹(x).

Even and odd functions

Even: f(-x) = f(x) (symmetric about y-axis, e.g., x²)
Odd: f(-x) = -f(x) (symmetric about origin, e.g., x³)

Exponential functions

f(x) = a · bˣ, where a is the initial value and b is the growth/decay factor.

b > 1 → growth
0 < b < 1 → decay
Percent growth rate: b = 1 + r (so 5% annual growth → b = 1.05)

Geometry (memorize beyond what's on the sheet)

Pythagorean theorem

a² + b² = c², where c is the hypotenuse of a right triangle.

The reference sheet has this, but you should know it cold.

Special right triangles

45-45-90: sides are x : x : x√2 (both legs equal, hypotenuse is leg × √2)
30-60-90: sides are x : x√3 : 2x (opposite 30° is short, opposite 60° is short × √3, hypotenuse is double the short)
3-4-5: legs 3 and 4, hypotenuse 5 (memorize)
5-12-13: another common Pythagorean triple

Circle equations

Standard form: (x - h)² + (y - k)² = r², center (h, k) and radius r.

To go from expanded form x² + y² + Dx + Ey + F = 0 to standard form, complete the square.

Arc length and sector area

Arc length = (θ/360) · 2πr (in degrees) or rθ (in radians)
Sector area = (θ/360) · πr² (in degrees) or ½r²θ (in radians)

Polygon angle sum

Sum of interior angles of an n-sided polygon: (n - 2) · 180°.

Each interior angle of a regular n-gon: [(n - 2) · 180°] / n.

Parallel lines cut by a transversal

Corresponding angles are equal
Alternate interior angles are equal
Co-interior (same-side interior) angles are supplementary (sum to 180°)

Trigonometry

SOH-CAH-TOA

sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent

Reciprocal identities

csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)

Pythagorean identity

sin²(θ) + cos²(θ) = 1

This is the most commonly tested trig identity. Also:

tan(θ) = sin(θ)/cos(θ)

Unit circle key values

Angle	sin	cos	tan
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	√2/2	√2/2	1
60°	√3/2	1/2	√3
90°	1	0	undefined

Degrees to radians

radians = degrees · (π / 180)

Complementary angle identities

sin(θ) = cos(90° - θ)
cos(θ) = sin(90° - θ)

These come up in "if sin(x) = 0.6, what is cos(90° - x)?" type questions. Answer: 0.6 by definition.

Statistics and Data Analysis

Mean

mean = (sum of values) / (count of values)

Median

The middle value when sorted. If even count, average the two middle values.

Mode

The most frequent value. Can have more than one mode, or none.

Range

Range = max - min.

Standard deviation (conceptual only)

The SAT rarely asks you to calculate standard deviation, but asks you to compare it across datasets. Rule: more spread = larger standard deviation. Two datasets with the same mean can have very different standard deviations.

Percent change

% change = (new - old) / old · 100

If the answer is negative, it's a decrease. If positive, an increase.

Probability

P(event) = favorable outcomes / total outcomes

Complement rule: P(not A) = 1 - P(A).

Independent events: P(A and B) = P(A) · P(B).

Mutually exclusive: P(A or B) = P(A) + P(B).

General addition: P(A or B) = P(A) + P(B) - P(A and B).

Conditional probability

P(A | B) = P(A and B) / P(B)

Read "probability of A given B." SAT sometimes calls these "given that" problems.

Provided on the SAT reference sheet (you don't need to memorize, but know they exist)

The SAT gives you these 12 formulas during the test:

Area of a circle: A = πr²
Circumference: C = 2πr
Area of a rectangle: A = lw
Area of a triangle: A = ½bh
Pythagorean theorem: c² = a² + b²
Special right triangles (30-60-90 and 45-45-90)
Volume of a rectangular solid: V = lwh
Volume of a cylinder: V = πr²h
Volume of a sphere: V = (4/3)πr³
Volume of a cone: V = (1/3)πr²h
Volume of a pyramid: V = (1/3)lwh
Arc measure of a circle = 360° / 2π radians

Know these exist on the sheet so you can click through to them, but using the sheet mid-problem costs time. Memorize the common ones anyway.

Formulas that aren't on the sheet — the critical list

If I had to pick the 10 non-provided formulas most likely to appear and most frequently missed:

Quadratic formula
Slope of a line
Distance between two points
Midpoint
Vertex of a parabola: x = -b/(2a)
Sum of roots (-b/a) and product of roots (c/a)
Circle equation: (x - h)² + (y - k)² = r²
30-60-90 and 45-45-90 ratios
Exponent rules
Percent change formula

Make flashcards. Drill these until they're automatic.

Sample application problems

Problem 1. What is the distance between the points (-3, 4) and (5, -2)?

Using the distance formula: d = √[(5 - (-3))² + (-2 - 4)²] = √[8² + (-6)²] = √[64 + 36] = √100 = 10

Answer: 10.

Problem 2. For the quadratic 2x² - 12x + k = 0, what value of k gives exactly one real solution?

Discriminant = 0: (-12)² - 4(2)(k) = 0 144 - 8k = 0 k = 18

Answer: k = 18.

Problem 3. If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

Using sin²(x) + cos²(x) = 1: (3/5)² + cos²(x) = 1 9/25 + cos²(x) = 1 cos²(x) = 16/25 cos(x) = 4/5 (positive since first quadrant)

Answer: 4/5. Or note that this is a 3-4-5 triangle.

Common mistakes

Memorizing formulas but not their use cases. You need to recognize when to apply each formula, not just recall it. Drill mixed problems, not just formula recitation.

Forgetting the quadratic formula needs = 0. If the equation is 2x² - 12x = 5, you must first move everything to one side: 2x² - 12x - 5 = 0.

Using degrees where radians are expected. The SAT uses both. Watch for π in the problem — that often signals radians.

Confusing slope and y-intercept. In y = mx + b, m is slope (multiplies x), b is y-intercept (standalone). The number in front of x is always slope.

Key takeaways

The reference sheet has 12 geometry formulas; you need about 40 total
Focus memorization on algebra, vertex form, and Pythagorean identities
Special right triangles (3-4-5, 30-60-90, 45-45-90) come up constantly
Flashcards are more effective than re-reading formula lists
Know the formulas and when to apply them — rote memorization isn't enough

Next steps

Practice SAT Math by formula category on UnlimitedTests. Our drill sets are organized by the exact topics in this post, so you can target the formulas you're shaky on. Every question shows the formula being tested and a step-by-step solution.