Unlike some tests, the ACT does not hand you a formula sheet, so the ACT math formulas you carry into the room are the ones already in your head. The good news: the list is short and predictable. The enhanced ACT Math section is 45 questions in 50 minutes with 4 answer choices each, and it rewards students who can recall a formula quickly and move on. This guide organizes the formulas worth knowing by topic, with a plain-English note on when each one shows up, so you spend your study time on what the test actually asks.
The ACT Math section does not provide reference formulas, which means recall speed is part of your score. With 50 minutes for 45 questions, you have a little over a minute per question. Any second spent trying to reconstruct the quadratic formula or the area of a circle is a second you are not spending on the actual problem.
Two things make this manageable. First, the list of tested formulas is finite and stable from year to year. Second, most questions test whether you can recognize which formula applies, not whether you can memorize something exotic. Learn the core set below, practice pulling each one up on demand, and the section becomes far more about reading carefully than about mathematical memory. A note on the section itself: Math is scored 1 to 36 and counts toward your composite, which is the average of your English, Math, and Reading scores.
Geometry questions lean heavily on a handful of shape formulas. Keep these ready:
A common trap: the problem gives you the diameter but the formula needs the radius. Always halve the diameter first. Another: mixing up circumference (the distance around) with area (the space inside). Read the question twice before you pick a formula.
For any right triangle, a squared plus b squared equals c squared, where c is the hypotenuse (the side opposite the right angle). This single relationship powers a surprising number of ACT questions, including ones that do not look like triangle problems at first, such as finding the distance between two points or the diagonal of a rectangle.
It helps to recognize the common Pythagorean triples so you can skip the arithmetic: 3-4-5, 5-12-13, and their multiples like 6-8-10. Two special triangles also show up often: the 45-45-90 triangle, where the legs are equal and the hypotenuse is a leg times the square root of 2, and the 30-60-90 triangle, with sides in the ratio 1 to the square root of 3 to 2. Memorizing these ratios saves real time.
Lines and points on the xy-plane come up throughout the section. The three formulas to know cold:
Because distance and Pythagoras are the same idea, learning one reinforces the other.
When a quadratic equation will not factor cleanly, the quadratic formula solves it every time: x equals negative b, plus or minus the square root of (b squared minus 4ac), all divided by 2a, for an equation in the form a x squared plus b x plus c equals 0. The part under the square root, b squared minus 4ac, is the discriminant, and its sign tells you how many real solutions exist.
Averages appear constantly, often dressed up in word problems. The mean is the sum of the values divided by how many values there are. Rearranging that, the sum equals the average times the count, which is the key to problems that ask for a missing value needed to reach a target average. Also keep straight the median (the middle value when numbers are ordered) and the mode (the value that appears most often).
Right-triangle trig on the ACT comes down to one mnemonic: SOH CAH TOA. Sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. Label the sides relative to the angle in question, then match the ratio the problem asks for. That covers the large majority of ACT trig questions.
For probability, the core formula is the number of favorable outcomes divided by the total number of possible outcomes. Probabilities always fall between 0 and 1. For independent events happening together, multiply their individual probabilities. These basics, combined with careful counting, handle most probability items you will see.
Reading a formula list is not the same as owning it. The formulas stick when you apply them to real problems under time pressure, so the last step is practice, not more memorizing. Make a one-page cheat sheet of every formula above, quiz yourself until you can reproduce it from a blank page, then immediately use each one on practice questions until recall becomes automatic.
Prep36 is built for exactly this. It has more than 1,000 original practice questions (these are original Prep36 questions, not real or official ACT questions; official practice tests live at act.org), 6 full timed tests, and instant explanations so you see not just the answer but which formula solved it. Word banks and a daily challenge keep the concepts fresh, and a study planner helps you space it out before your test date. The whole question bank is free, with optional Plus and Max plans if you want extra features. When you register, always confirm current test dates and fees at act.org. Ready to make these formulas automatic? Start practicing free on Prep36 today.