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ACT math formula sheet

44 formulas across 8 topics, including the trigonometry identities and logarithm rules the SAT skips. The ACT prints no reference sheet, so every one of these has to be in your head on test day.

This is the same sheet Premium members see on their dashboard. Practise each group in the ACT Math drills — tiered easy, medium and hard — or start with a lesson.

Math formulas by topic

Linear equations & lines

Slope
m = (y₂ − y₁) / (x₂ − x₁)
Slope-intercept form
y = mx + b, where b is the y-intercept
Point-slope form
y − y₁ = m(x − x₁)
Parallel lines
same slope (m₁ = m₂)
Perpendicular lines
slopes are negative reciprocals (m₁ · m₂ = −1)

Quadratics

Standard form
y = ax² + bx + c
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Vertex x-coordinate
x = −b / 2a
Vertex form
y = a(x − h)² + k, vertex at (h, k)
Discriminant
b² − 4ac: positive → 2 real roots, zero → 1, negative → 0
Factoring a difference of squares
a² − b² = (a − b)(a + b)

Exponents & radicals

Product of powers
aᵐ · aⁿ = aᵐ⁺ⁿ
Quotient of powers
aᵐ / aⁿ = aᵐ⁻ⁿ
Power of a power
(aᵐ)ⁿ = aᵐⁿ
Negative exponent
a⁻ⁿ = 1 / aⁿ
Fractional exponent
a^(m/n) = ⁿ√(aᵐ)
Zero exponent
a⁰ = 1 (a ≠ 0)

Geometry — area & volume

Triangle area
A = ½ · base · height
Circle area
A = πr²
Circle circumference
C = 2πr
Rectangle area
A = length · width
Trapezoid area
A = ½(b₁ + b₂) · height
Rectangular prism volume
V = length · width · height
Cylinder volume
V = πr²h
Sphere volume
V = (4/3)πr³
Cone volume
V = (1/3)πr²h

Geometry — triangles & circles

Pythagorean theorem
a² + b² = c² (right triangles)
Special right triangle — 45-45-90
legs : legs : hypotenuse = x : x : x√2
Special right triangle — 30-60-90
sides = x : x√3 : 2x
Sum of interior angles
(n − 2) · 180°, for an n-sided polygon
Triangle angle sum
the three interior angles sum to 180°
Arc length
s = r θ (θ in radians), or (angle/360°) · 2πr

Statistics & probability

Mean
sum of values ÷ number of values
Median
the middle value once sorted (average the two middles if even count)
Probability
P(event) = favorable outcomes ÷ total outcomes
Independent events
P(A and B) = P(A) · P(B)

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

Logarithms

Definition
logₐ(b) = c means aᶜ = b
Product rule
logₐ(xy) = logₐ(x) + logₐ(y)
Quotient rule
logₐ(x/y) = logₐ(x) − logₐ(y)
Power rule
logₐ(xⁿ) = n · logₐ(x)

Sixty questions in sixty minutes leaves no time to reconstruct a formula. The free full-length ACT practice test shows which ones cost you, by topic and by pace.

Take the free practice testGrammar rules sheet

ACT formula questions, answered

Does the ACT give you a formula sheet?

No. Unlike the SAT, the ACT Math section prints no reference formulas at all — not even the area of a circle. Every formula on this page has to come from memory, which is why the sheet is worth printing and why the ACT rewards drilling the geometry formulas until they are automatic.

What math is on the ACT that is not on the SAT?

Trigonometry beyond right-triangle ratios — the Pythagorean identity, the laws of sines and cosines, radians — and logarithms. Both groups are on this sheet and left off the SAT one. The ACT also reaches into matrices, complex numbers and sequences occasionally, usually for one question each.

How many questions are on the ACT Math section?

Sixty questions in sixty minutes — one minute per question, with a calculator allowed throughout. That is the format of every full-length ACT practice test on this site. The questions climb in difficulty, so the formulas near the top of this sheet cover the first half and the trigonometry and logarithm groups near the bottom appear in the last fifteen or so.

Which ACT math formulas should I memorise first?

Slope and the forms of a line, the quadratic formula, the exponent rules, and the area and volume formulas — in that order, by how often they appear. SOH-CAH-TOA comes next; the laws of sines and cosines and the logarithm rules are worth learning last, once the rest is automatic.

How should I use this formula sheet?

Print it, take a timed practice test without it, then drill whatever you had to look up. The ACT math drills here are tiered easy, medium and hard by topic, so a formula you are shaky on gets practised in the shape the test uses.