ACT Math formulas you actually have to memorize

Q: How many formulas do I really need to memorize?

The high-yield core is roughly 25 to 30 formulas. Beyond those, you mostly need fluency in applying them quickly rather than a longer list. Focus your energy on speed and recognition, not memorizing rare edge cases.

The ACT hands you no formula sheet on test day, so the formulas live in your head or they don't help you at all. Here is the full must-know list, organized by topic, plus how to lock each one in.

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45questions

50minutes

1–36score scale

0formulas given

Why memorizing formulas matters

Unlike some standardized tests, the Enhanced ACT Math section gives you zero reference material. You get 45 multiple-choice questions, 50 minutes, and four answer choices each. That works out to roughly 67 seconds per question, so there is no time to re-derive the area of a trapezoid mid-test. The students who score highest treat formula recall like reflex: they see a circle and the equation appears automatically. Below is every formula worth memorizing, grouped the way the ACT actually tests them.

The must-know ACT Math formulas by topic

Algebra and number

Slope: m = (y₂ − y₁) / (x₂ − x₁)

Slope-intercept line: y = mx + b

Point-slope line: y − y₁ = m(x − x₁)

Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a

Distance: d = √((x₂−x₁)² + (y₂−y₁)²)

Midpoint: ((x₁+x₂)/2 , (y₁+y₂)/2)

Average: mean = sum of terms / number of terms

Geometry: area and perimeter

Rectangle area: A = l × w

Triangle area: A = ½ b h

Circle area: A = π r²

Circle circumference: C = 2π r

Trapezoid area: A = ½(b₁ + b₂) h

Parallelogram area: A = b h

Geometry: solids and the right triangle

Pythagorean theorem: a² + b² = c²

Box volume: V = l w h

Cylinder volume: V = π r² h

Sphere volume: V = (4/3) π r³

Memorize two special right triangles too: the 45-45-90 has sides in ratio 1 : 1 : √2, and the 30-60-90 has sides 1 : √3 : 2. They turn slow problems into instant ones.

Trigonometry

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

Pythagorean identity: sin²θ + cos²θ = 1

Law of sines: a/sin A = b/sin B = c/sin C

Law of cosines: c² = a² + b² − 2ab·cos C

Probability, percent, and logarithms

Probability: P = favorable outcomes / total outcomes

Percent change: (new − old) / old × 100

Log rule: logₙ(M) = x means bₓ = M

How to actually memorize them

Group by trigger, not by chapter. Pair each formula with the cue that summons it ("circle in the problem → A = πr²") so recall is automatic under time pressure.
Write the whole list from memory daily. A blank-sheet brain dump every morning surfaces the one or two you keep blanking on far faster than re-reading.
Drill in real questions, not flashcards alone. A formula you can recite but cannot apply is worthless. Practicing inside exam-true problems welds recall to use.
Test under the clock. Knowing a formula and retrieving it in 60 seconds are different skills. Timed reps build the second one.

That last point is where VECTOR comes in. Our infinite bank of exam-true questions tags every problem by the formula it tests, so you can drill exactly the ones you keep forgetting and see step-by-step explanations the instant you miss one.

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Frequently asked questions

Does the ACT give you a formula sheet?

No. Unlike some exams, the ACT Math section provides no reference formulas at all. Every formula you use must be memorized beforehand, which is exactly why a clean topic-by-topic list like this one is worth drilling.

Which ACT Math formulas show up the most?

Slope, the Pythagorean theorem, area and circumference of a circle, the quadratic formula, and SOH-CAH-TOA appear on nearly every test. The special right-triangle ratios (45-45-90 and 30-60-90) save the most time when you know them cold.

How many formulas do I really need to memorize?

The high-yield core is roughly 25 to 30 formulas, all listed above. Beyond those, you mostly need fluency in applying them quickly rather than a longer list. Focus your energy on speed and recognition, not memorizing rare edge cases.

How long is the Enhanced ACT Math section?

The Enhanced ACT Math section is 45 questions in 50 minutes, with four answer choices per question, scored on a 1 to 36 scale. That pace leaves little room to derive formulas on the spot, so instant recall is a real scoring advantage.

What is the best way to practice these formulas?

Drill them inside timed, exam-true questions rather than on flashcards alone. VECTOR offers an infinite question bank, full-length timed tests, and step-by-step explanations completely free, so you can practice applying every formula until it is automatic.