The ACT does not provide a formula sheet. Unlike the digital SAT, which gives you a geometry reference page during the math section, the ACT expects you to walk in with every formula already memorized. That is one of the most important facts students miss when they first prepare for the ACT.
This guide covers every formula you need for ACT Math, organized by category. Memorize it, practice with it, and know it cold before test day.
What Math Is on the ACT?
The ACT Math section has 60 questions in 60 minutes. The content breaks down into six categories:
Pre-Algebra and Plane Geometry together make up nearly half the test, so mastering those formulas gives you the highest return on your prep time. Use ACT Math practice on Larry Learns to identify which categories cost you the most points before committing your memorization effort.
Algebra Formulas You Must Know
These formulas cover Pre-Algebra, Elementary Algebra, and Intermediate Algebra. They appear frequently and reward students who can apply them quickly under the one-minute-per-question pacing requirement.
Core Algebra and Coordinate Formulas
- Slope of a line: m = (y2 - y1) / (x2 - x1)
- Slope-intercept form: y = mx + b
- Point-slope form: y - y1 = m(x - x1)
- Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
- Vertex of a parabola (x-coordinate): x = -b / 2a
- Difference of squares: a² - b² = (a + b)(a - b)
- Perfect square trinomial: (a + b)² = a² + 2ab + b²
- Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
- Midpoint formula: M = ((x1 + x2) / 2, (y1 + y2) / 2)
Sequences, Probability, and Statistics
- Arithmetic sequence nth term: a(n) = a(1) + (n - 1)d
- Geometric sequence nth term: a(n) = a(1) × r^(n-1)
- Mean (average): sum of values divided by number of values
- Probability: P = favorable outcomes / total outcomes
- Percent change: ((new - old) / old) × 100
Geometry Formulas You Must Know
Plane geometry and coordinate geometry together account for 38% of ACT Math. None of these are provided on test day.
Area and Perimeter
- Rectangle area: A = l × w
- Triangle area: A = (1/2) × b × h
- Circle area: A = πr²
- Circle circumference: C = 2πr
- Trapezoid area: A = (1/2)(b1 + b2) × h
- Parallelogram area: A = b × h
Volume and Surface Area
- Rectangular prism volume: V = l × w × h
- Cylinder volume: V = πr²h
- Cone volume: V = (1/3)πr²h
- Sphere volume: V = (4/3)πr³
Right Triangles and Circles
- Pythagorean theorem: a² + b² = c²
- 30-60-90 triangle: sides in ratio 1 : √3 : 2
- 45-45-90 triangle: sides in ratio 1 : 1 : √2
- Arc length: L = (θ / 360) × 2πr
- Sector area: A = (θ / 360) × πr²
- Equation of a circle: (x - h)² + (y - k)² = r²
Trigonometry Formulas
Trig accounts for roughly 7% of ACT Math (about four questions). These questions are worth getting right because most students skip trig during prep, leaving easy points available for anyone who prepares for this category specifically.
SOH-CAH-TOA (Core Trig Ratios)
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
- csc(θ) = 1 / sin(θ)
- sec(θ) = 1 / cos(θ)
- cot(θ) = 1 / tan(θ)
Key Trig Identities
- Pythagorean identity: sin²(θ) + cos²(θ) = 1
- Law of sines: a / sin(A) = b / sin(B) = c / sin(C)
- Law of cosines: c² = a² + b² - 2ab cos(C)
How to Use These Formulas on Test Day
Memorizing formulas is only half the battle. Applying them correctly under the one-minute-per-question time pressure is the other half. Three habits that separate high scorers from average scorers:
- Sketch every geometry problem. A rough diagram takes 10 seconds and significantly reduces errors. It prevents misidentifying which measurement you need (radius vs. diameter, base vs. height).
- Write out your formula before calculating. Students who jump straight to mental arithmetic make far more careless errors than those who write the setup first.
- Check units before finalizing your answer. Many ACT geometry questions switch between radius and diameter, or between degrees and radians. A quick unit check catches the most common mistakes.
Use ACT Math practice on Larry Learns to build your formula recall and pacing simultaneously. The adaptive format adjusts to your level, so weaker categories get more focus automatically.
How to Memorize ACT Math Formulas Fast
Most students make the mistake of reading through formula lists passively. Active memorization works far better and produces more durable recall.
The most effective method: write each formula from memory, check it against this guide, then immediately apply it to one practice problem before moving to the next formula. This takes more time upfront but produces lasting retention that passive re-reading cannot match.
For trig specifically, the SOH-CAH-TOA mnemonic is worth drilling until it is completely automatic. Most trig questions on the ACT are straightforward applications of the three core ratios. If you know them cold, trig questions become among the fastest on the test.
Take a free diagnostic quiz to identify which formula categories are your weakest, then concentrate your memorization effort on those categories first.
Frequently Asked Questions About ACT Math Formulas
Does the ACT provide a formula sheet on test day?
No. Unlike the digital SAT, which provides a geometry reference sheet during the math section, the ACT provides no formulas at all. Every formula in this guide must be memorized before you walk into the exam. This is one of the key differences between ACT and SAT Math preparation.
What are the most important formulas to know for ACT Math?
Algebra formulas (slope, quadratic formula, distance and midpoint) and geometry formulas (area, volume, Pythagorean theorem, special right triangles) are the highest priority because they cover the most questions. Trig formulas cover fewer questions but are straightforward once you know SOH-CAH-TOA and the three key identities.
How long does it take to memorize ACT math formulas?
Most students can memorize the core formulas in five to seven focused sessions of 30 minutes each. The key is active recall practice: write each formula from memory, then immediately apply it to a problem. Passive re-reading takes longer and produces weaker recall under test conditions.
Are the same math formulas on the SAT and ACT?
There is significant overlap in geometry and algebra. The critical difference is that the SAT provides some geometry formulas on its reference sheet while the ACT provides none. ACT Math also covers topics like logarithms and matrices that do not appear on the SAT, and includes a dedicated trigonometry category with more questions than the SAT tests.
How can I practice ACT math formulas before my test?
Drill individual formula categories using ACT Math practice questions on Larry Learns. The adaptive format identifies which categories you struggle with and routes more questions to those areas until the concepts are solid. Combine formula memorization sessions with timed practice questions to build both recall and application speed before test day.