ACT Math Formulas: What to Memorize (No Sheet Given)

The ACT gives you no formula sheet. Every formula you need for ACT Math, from the Pythagorean theorem to SOH-CAH-TOA, has to be in your head on test day, and this page is the complete list worth memorizing. If you searched for an "ACT math formula sheet PDF," here's the honest answer: there is no official one, because the test doesn't provide a sheet at all. The list below is the sheet. Bookmark it, print it, or copy it into your notes.

The good news: the list is short. The ACT tests a small set of formulas over and over. Master the ones below, drill each with a practice question, and you've covered the formula side of the test.

The full list (copy or print this block)

Geometry

Pythagorean theorem: a² + b² = c² · common triples: 3-4-5, 5-12-13, 8-15-17
Special right triangles: 45-45-90 → sides x, x, x√2 · 30-60-90 → x, x√3, 2x
Area: triangle ½bh · circle πr² · rectangle lw · trapezoid ½(b₁+b₂)h
Circle: circumference 2πr · arc or sector = (central angle ÷ 360) × the whole-circle value

Algebra & coordinate plane

Slope: m = (y₂−y₁)/(x₂−x₁) · line: y = mx + b
Distance: √((x₂−x₁)² + (y₂−y₁)²) · midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
Quadratic formula: x = (−b ± √(b²−4ac)) / (2a)
Exponents: xᵃ·xᵇ = xᵃ⁺ᵇ · (xᵃ)ᵇ = xᵃᵇ · x⁻ᵃ = 1/xᵃ

Trig

SOH-CAH-TOA: sin = opp/hyp · cos = adj/hyp · tan = opp/adj

Percent, average, probability

Percent change: (new − old)/old × 100
Average: sum / count · probability: favorable / total

Geometry: where the formula questions live

Right triangles are the backbone of ACT geometry. Know a² + b² = c² cold, and know the common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) so you can skip the arithmetic entirely. A triangle with legs 9 and 12 is a 3-4-5 scaled by three; the hypotenuse is 15, no squaring required.

The two special right triangles let you find sides from a single length:

Triangle	Side ratio	How to use it
45-45-90	x : x : x√2	Legs equal; hypotenuse = leg × √2. Shows up in squares cut by a diagonal.
30-60-90	x : x√3 : 2x	Short side opposite 30°; hypotenuse is double the short side. Shows up in equilateral triangles cut in half.

For circles, two formulas cover almost everything: area πr² and circumference 2πr. Arc and sector questions are just fractions: a 90° slice is 90/360, or one quarter, of the whole circle's circumference or area. That single idea replaces a formula you'd otherwise have to memorize.

Practice: A circle has radius 6. What is the area of a sector with a central angle of 60°? A. 3π B. 6π C. 12π D. 36π

Answer: B. The full circle's area is π(6)² = 36π. A 60° sector is 60/360 = 1/6 of the circle, so the sector area is 36π/6 = 6π. Rule: arc or sector = (central angle ÷ 360) × the whole-circle value.

Algebra and the coordinate plane

Slope is one of the most heavily used formulas on the test: m = (y₂−y₁)/(x₂−x₁), rise over run. Pair it with y = mx + b, where m is the slope and b is the y-intercept, and you can handle most line questions. Two extras worth knowing: parallel lines share a slope, and perpendicular lines have slopes that are negative reciprocals.

The distance formula is just the Pythagorean theorem in disguise: the horizontal and vertical changes are the legs, and the distance is the hypotenuse. The midpoint formula averages the x's and averages the y's. And when a quadratic won't factor cleanly, the quadratic formula always works: x = (−b ± √(b²−4ac)) / (2a).

Exponent rules cost easy points when they're shaky. Multiplying same bases adds exponents, a power raised to a power multiplies them, and a negative exponent flips the base into a fraction.

Practice: What is the slope of the line through (2, −3) and (6, 5)? A. −2 B. 1/2 C. 2 D. 8

Answer: C. Slope = (y₂−y₁)/(x₂−x₁) = (5 − (−3))/(6 − 2) = 8/4 = 2. Watch the double negative in the numerator; subtracting −3 means adding 3, and missing that is exactly how trap answers like 1/2 get built.

Trig: SOH-CAH-TOA is most of what you need

ACT trig looks scarier than it is. Right-triangle ratios carry most of the weight, and SOH-CAH-TOA covers all three: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Label the sides relative to the angle in question, then read off the ratio. If a third side is missing, the Pythagorean theorem (or a triple you recognize) fills it in.

Practice: In a right triangle, the side opposite angle θ is 8 and the hypotenuse is 17. What is sin θ? A. 8/17 B. 8/15 C. 15/17 D. 17/8

Answer: A. Sine = opposite/hypotenuse = 8/17. Done. (This is the 8-15-17 triple, so the missing leg is 15, which makes cos θ = 15/17 and tan θ = 8/15: the trap choices.)

Percent, average, and probability

Three one-line formulas close out the list. Percent change is (new − old)/old × 100, and the base is always the original value. Average is sum / count; on harder questions, flip it around to find a missing total (sum = average × count). Probability is favorable outcomes / total outcomes, and it always lands between 0 and 1.

Practice: A jacket priced at $80 is marked down to $60. By what percent was the price reduced? A. 20% B. 25% C. 33⅓% D. 75%

Answer: B. Change = 80 − 60 = 20, and the base is the original price: 20/80 = 0.25 = 25%. Using the new price as the base gives 20/60 = 33⅓%, which is the trap at choice C.

How to actually memorize them (practice, not flashcards)

Flashcards get you recognition. The test demands recall under time pressure, and that only comes from using each formula on real problems. The method:

Drill one formula at a time. After reading a formula, immediately solve two or three questions that need it. Retrieval is what locks it in, not rereading.
Say the setup out loud before computing. "Sector means fraction of 360" or "base is the original price." Naming the rule builds the trigger you'll need on test day.
Backsolve when it's faster. The enhanced ACT has only four answer choices per math question, down from five. That makes plugging answer choices back into the problem genuinely fast: for many equation questions, testing the choices beats doing the algebra. Start with a middle value when choices are ordered.
Re-test yourself cold. A formula you could recite yesterday but not today isn't memorized yet. Two short sessions beat one long one.

Drill every formula on this page for free. Our practice console has original ACT-style math questions with instant explanations, a pace timer set to the real ~67 seconds per question, and this formula list built in as a cheat sheet. No signup, no paywall.

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ACT Math in 2026: the format you're memorizing for

Quick context on the enhanced ACT, which rolled out nationally in 2025 and into spring 2026 for school-day testing:

45 questions in 50 minutes, about 67 seconds per question. Pacing matters as much as formulas; see our ACT pacing strategy guide.
Four answer choices per question, down from five. Better guessing odds and faster backsolving.
No formula sheet provided. That's the whole reason this page exists. (The SAT does include some reference formulas; see ACT vs SAT in 2026 for the full comparison.)
Math is a core section and counts toward your Composite score, which averages English, Math, and Reading.
The digital version includes a basic on-screen calculator. Useful, but it doesn't know any formulas. Simple arithmetic is often faster by hand.
No penalty for wrong answers. Never leave a question blank.

FAQ

Does the ACT provide a formula sheet?

No. The ACT Math section gives you no formula sheet. You must memorize the essentials: the Pythagorean theorem, special right triangles, area formulas, slope-intercept form, the quadratic formula, and SOH-CAH-TOA.

What are the most important ACT math formulas?

Pythagorean theorem, 45-45-90 and 30-60-90 triangle ratios, area of triangles, circles, and trapezoids, slope and y=mx+b, distance and midpoint, the quadratic formula, SOH-CAH-TOA, and percent change.

Can you use a calculator on ACT Math?

Yes. The digital enhanced ACT includes a basic on-screen calculator. Use it selectively; simple arithmetic is often faster by hand, and the calculator does not replace knowing your formulas.