{"id":558,"date":"2026-08-28T09:00:00","date_gmt":"2026-08-28T16:00:00","guid":{"rendered":"https:\/\/magoosh.com\/act\/?p=558"},"modified":"2026-08-28T11:18:53","modified_gmt":"2026-08-28T18:18:53","slug":"math-formulas-on-the-act","status":"publish","type":"post","link":"https:\/\/magoosh.com\/act\/math-formulas-on-the-act\/","title":{"rendered":"32 ACT Math Formulas &#8211; What to Absolutely Study [PDF]"},"content":{"rendered":"<style>\n@media (max-width: 768px) {\n  .table-responsive {\n    display: block;\n    width: calc(100vw - 50px);\n    max-width: calc(100vw - 50px);\n    overflow-x: auto;\n    -webkit-overflow-scrolling: touch;\n    margin-left: auto;\n    margin-right: auto;\n  }\n  .table-responsive table {\n    min-width: 500px;\n  }\n}\n<\/style>\n<p>The ACT does not give you a formula sheet. Unlike the digital SAT, which provides a reference sheet of geometry formulas during the math section, the ACT expects you to walk in with every formula memorized. That makes knowing your ACT math formulas cold one of the easiest ways to protect your score.<\/p>\n<p>The good news: you don&#8217;t need to memorize hundreds of formulas. As of 2026, the ACT Math section has 45 questions in 50 minutes, and the underlying math content is the same as it&#8217;s always been. The 32 ACT math formulas below cover the concepts the test uses most, sorted into three tiers: &#8220;Must-Know&#8221; formulas, &#8220;Good to Know&#8221; formulas, and &#8220;Bonus&#8221; formulas. Start at the top and work down.<\/p>\n<p>Prefer a printable version? Grab the free <a href=\"https:\/\/act.magoosh.com\/math-formulas\">Magoosh ACT Math Formulas PDF<\/a> and study a few formulas a day.<\/p>\n<div class=\"toc\">\n<p style=\"color: #4D2079; font-size:larger\"><strong>Table of Contents<\/strong><\/p>\n<ul>\n<li><a href=\"#act-formula-sheet\">Does the ACT Give You a Formula Sheet?<\/a><\/li>\n<li><a href=\"#must-know\">Must-Know ACT Math Formulas<\/a><\/li>\n<li><a href=\"#good-to-know\">ACT Formulas That Are Good to Know<\/a><\/li>\n<li><a href=\"#bonus\">Bonus ACT Math Formulas<\/a><\/li>\n<li><a href=\"#pdf\">Printable ACT Math Formula Sheet (Free PDF)<\/a><\/li>\n<li><a href=\"#memorize\">How to Memorize ACT Math Formulas<\/a><\/li>\n<li><a href=\"#faqs\">Frequently Asked Questions<\/a><\/li>\n<\/ul>\n<\/div>\n<h2 id=\"act-formula-sheet\" style=\"color: #4D2079; padding: 0;\">Does the ACT Give You a Formula Sheet?<\/h2>\n<p>No. The ACT provides no formula sheet or reference page on the Math section. Every formula you need has to come from memory. This is a real difference from the digital SAT, which displays a geometry reference sheet during its math section. (Comparing the two tests? See our <a href=\"https:\/\/magoosh.com\/act\/act-vs-sat\/\">ACT vs SAT guide<\/a>.)<\/p>\n<p>There is one helpful exception. When a problem depends on a genuinely advanced or unusual formula, such as the surface area of a sphere, the question itself will typically provide that formula. So you don&#8217;t need to memorize everything in your math textbook. Your job is to memorize the <em>common<\/em> formulas, and the list below covers exactly those.<\/p>\n<p>One more reason formulas matter now: the current version of the test (the <a href=\"https:\/\/magoosh.com\/act\/enhanced-act\/\">Enhanced ACT<\/a>) gives you 45 math questions in 50 minutes, and Math is one of just three sections (English, Math, and Reading) that make up your Composite score. With just over a minute per question, stopping to re-derive the slope formula is time you don&#8217;t have. Formulas you know cold turn into quick points.<\/p>\n<blockquote style=\"border-left: 4px solid #4d2079; background: #F9FAFB; padding: 1em 1.2em; margin: 1em 0; border-radius: 6px; box-shadow: 0 1px 2px rgba(0,0,0,0.05);\">\n<p><strong>Pro tip:<\/strong> Enhanced ACT Math questions have 4 answer choices instead of the old 5. That makes elimination and backsolving faster, but only if you know the relevant formula well enough to test answer choices quickly.<\/p>\n<\/blockquote>\n<h2 id=\"must-know\" style=\"color: #4D2079; padding: 0;\">Must-Know ACT Math Formulas<\/h2>\n<p>Though the ACT tests different concepts on each exam, some topics come up again and again. These 18 formulas are the ones to learn first. Each is listed as a name followed by the formula, so you can quiz yourself straight down the list.<\/p>\n<h3 style=\"color: #C5168C;\">Average<\/h3>\n<ol>\n<li><strong>Average (arithmetic mean):<\/strong> Average = (sum of the items) \/ (number of items)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Lines<\/h3>\n<ol start=\"2\">\n<li><strong>Slope-intercept form of a line:<\/strong> y = mx + b, where <em>m<\/em> is the slope and <em>b<\/em> is the y-intercept<\/li>\n<li><strong>Slope:<\/strong> m = (y\u2082 \u2212 y\u2081) \/ (x\u2082 \u2212 x\u2081)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Triangles<\/h3>\n<ol start=\"4\">\n<li><strong>Area of a triangle:<\/strong> A = (1\/2)bh (one-half base times height)<\/li>\n<li><strong>Pythagorean theorem:<\/strong> a\u00b2 + b\u00b2 = c\u00b2, where <em>c<\/em> is the hypotenuse of a right triangle<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Quadrilaterals and Solids<\/h3>\n<ol start=\"6\">\n<li><strong>Perimeter of a rectangle:<\/strong> P = 2l + 2w, where <em>l<\/em> is the length and <em>w<\/em> is the width<\/li>\n<li><strong>Area of a rectangle:<\/strong> A = lw (length times width)<\/li>\n<li><strong>Volume of a box:<\/strong> V = lwh (length times width times height)<\/li>\n<li><strong>Surface area of a rectangular solid:<\/strong> SA = 2lw + 2wh + 2lh<\/li>\n<li><strong>Diagonal of a rectangular solid:<\/strong> d\u00b2 = l\u00b2 + w\u00b2 + h\u00b2 (or apply the Pythagorean theorem twice)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Circles and Spheres<\/h3>\n<ol start=\"11\">\n<li><strong>Area of a circle:<\/strong> A = \u03c0r\u00b2<\/li>\n<li><strong>Circumference of a circle:<\/strong> C = 2\u03c0r<\/li>\n<li><strong>Volume of a sphere:<\/strong> V = (4\/3)\u03c0r\u00b3<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Cylinders<\/h3>\n<ol start=\"14\">\n<li><strong>Volume of a cylinder:<\/strong> V = \u03c0r\u00b2h<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Trigonometry<\/h3>\n<ol start=\"15\">\n<li><strong>SOHCAHTOA:<\/strong> sin x = opposite\/hypotenuse; cos x = adjacent\/hypotenuse; tan x = opposite\/adjacent<\/li>\n<li><strong>Trig signs by quadrant:<\/strong> In Quadrant I, sine, cosine, and tangent are all positive. In Quadrant II, only sine is positive. In Quadrant III, only tangent is positive. In Quadrant IV, only cosine is positive. (Memory aid: &#8220;All Students Take Calculus.&#8221;)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Probability and Counting<\/h3>\n<ol start=\"17\">\n<li><strong>Probability:<\/strong> P = (number of desired outcomes) \/ (number of total outcomes)<\/li>\n<li><strong>Factorials (e.g., 8!):<\/strong> Multiply the integer by every positive integer below it: 8! = 8 \u00d7 7 \u00d7 6 \u00d7 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1<\/li>\n<\/ol>\n<p>Bonus: these &#8220;Must-Know&#8221; ACT math formulas also show up in your high school math classes, so you&#8217;re really studying for two things at once. Nice.<\/p>\n<p>Want to hear these explained? In the video below, ACT expert Kristin walks through 6 of the must-know ACT math formulas in more detail:<\/p>\n<p><center><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/yWiFdbcVAdU\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<h2 id=\"good-to-know\" style=\"color: #4D2079; padding: 0;\">ACT Formulas That Are Good to Know<\/h2>\n<p>Once the must-know list is solid, add these 11. They appear less often, but each one can turn a hard question into an easy one.<\/p>\n<h3 style=\"color: #C5168C;\">Volume and Area<\/h3>\n<ol start=\"19\">\n<li><strong>Volume of a cone:<\/strong> V = (1\/3)\u03c0r\u00b2h<\/li>\n<li><strong>Volume of a pyramid:<\/strong> V = (1\/3) \u00d7 (area of the base) \u00d7 height<\/li>\n<li><strong>Area of a trapezoid:<\/strong> A = ((b\u2081 + b\u2082) \/ 2) \u00d7 h (add the bases, divide by two, then multiply by the height)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Logarithms<\/h3>\n<ol start=\"22\">\n<li><strong>Definition of a logarithm:<\/strong> If log\u2090b = c, then a\u1d9c = b<\/li>\n<li><strong>Change of base rule:<\/strong> log\u2090b = (log b) \/ (log a)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Special Right Triangles<\/h3>\n<ol start=\"24\">\n<li><strong>30-60-90 triangle ratio:<\/strong> the sides are in the ratio 1 : \u221a3 : 2 (the shortest side is opposite the 30\u00b0 angle; the hypotenuse is twice the shortest side)<\/li>\n<li><strong>45-45-90 triangle ratio:<\/strong> the sides are in the ratio 1 : 1 : \u221a2 (the two legs are equal; the hypotenuse is a leg times \u221a2)<\/li>\n<\/ol>\n<h3 style=\"color: #C5168C;\">Additional Formulas<\/h3>\n<ol start=\"26\">\n<li><strong>Equation of a circle:<\/strong> (x \u2212 h)\u00b2 + (y \u2212 k)\u00b2 = r\u00b2, where the center of the circle is (h, k) and <em>r<\/em> is the radius<\/li>\n<li><strong>Arithmetic sequences:<\/strong> t\u2099 = t\u2081 + d(n \u2212 1), where <em>d<\/em> is the common difference<\/li>\n<li><strong>Geometric sequences:<\/strong> t\u2099 = t\u2081 \u00d7 r\u207d\u207f\u207b\u00b9\u207e, where <em>r<\/em> is the common ratio<\/li>\n<li><strong>Compound growth (exponential growth):<\/strong> A = P(1 + r\/n)\u207f\u1d57, where <em>P<\/em> is the starting value (principal), <em>r<\/em> is the growth rate, <em>n<\/em> is the number of times growth compounds per year, <em>t<\/em> is the time in years, and <em>A<\/em> is the new amount<\/li>\n<\/ol>\n<h2 id=\"bonus\" style=\"color: #4D2079; padding: 0;\">Bonus ACT Math Formulas<\/h2>\n<p>These three are the least likely to be essential, but if you&#8217;re aiming for a top Math score, know them too.<\/p>\n<ol start=\"30\">\n<li><strong>Quadratic formula:<\/strong> x = (\u2212b \u00b1 \u221a(b\u00b2 \u2212 4ac)) \/ (2a), for equations in the form ax\u00b2 + bx + c = 0. Often you&#8217;ll be better off backsolving (plugging the answer choices into the equation), but keep the formula in the back of your mind.<\/li>\n<li><strong>Permutations:<\/strong> \u2099P\u1d63 = n! \/ (n \u2212 r)! (ordered arrangements of <em>r<\/em> items chosen from <em>n<\/em>)<\/li>\n<li><strong>Combinations:<\/strong> \u2099C\u1d63 = n! \/ (r!(n \u2212 r)!) (unordered groups of <em>r<\/em> items chosen from <em>n<\/em>)<\/li>\n<\/ol>\n<p>Curious what Math score these formulas could help you reach? Try our <a href=\"https:\/\/magoosh.com\/act\/act-score-calculator\/\">ACT score calculator<\/a> to see how correct answers translate to section and Composite scores.<\/p>\n<h2 id=\"pdf\" style=\"color: #4D2079; padding: 0;\">Printable ACT Math Formula Sheet (Free PDF)<\/h2>\n<p>Since the ACT won&#8217;t hand you a formula sheet, make your own part of your daily studying. We created a printable Magoosh ACT Math Formulas PDF with the formulas from this post. <strong><a href=\"https:\/\/act.magoosh.com\/math-formulas\">Download your free copy here<\/a><\/strong>, print it, and keep it wherever you study.<\/p>\n<p>Sometimes it&#8217;s easier to memorize formulas by reviewing a little bit every day. A printed sheet on your desk (or a photo on your phone) makes that habit almost automatic.<\/p>\n<h2 id=\"memorize\" style=\"color: #4D2079; padding: 0;\">How to Memorize ACT Math Formulas<\/h2>\n<p>Reading a formula list won&#8217;t make it stick. Here&#8217;s what works for the students I&#8217;ve seen improve fastest:<\/p>\n<ol>\n<li><strong>Work in tiers.<\/strong> Master the 18 must-know formulas before touching the rest. A shaky grasp of 32 formulas is worth less than a solid grasp of 18.<\/li>\n<li><strong>Use active recall.<\/strong> Cover the formula, say it from memory, then check. Writing a formula from scratch beats re-reading it ten times.<\/li>\n<li><strong>Apply each formula to real questions.<\/strong> A formula becomes permanent when you&#8217;ve used it. Take a <a href=\"https:\/\/act.magoosh.com\/practice_tests\/free\">free ACT practice test<\/a> and notice which formulas you reached for, and which ones you blanked on.<\/li>\n<li><strong>Re-derive the geometry you forget.<\/strong> If you blank on the diagonal of a box on test day, the Pythagorean theorem applied twice gets you there. Knowing <em>where formulas come from<\/em> is your safety net.<\/li>\n<\/ol>\n<blockquote style=\"border-left: 4px solid #4d2079; background: #F9FAFB; padding: 1em 1.2em; margin: 1em 0; border-radius: 6px; box-shadow: 0 1px 2px rgba(0,0,0,0.05);\">\n<p><strong>Pro tip:<\/strong> When you miss a practice question because of a formula, add that formula to a &#8220;personal must-know list.&#8221; Your own miss list beats any generic study guide, because it targets exactly what <em>your<\/em> brain drops under pressure.<\/p>\n<\/blockquote>\n<h2 id=\"faqs\" style=\"color: #4D2079; padding: 0;\">Frequently Asked Questions<\/h2>\n<h3 style=\"color: #C5168C;\">Does the ACT give you a formula sheet?<\/h3>\n<p>No. The ACT does not provide any formula sheet or reference page during the Math section. You&#8217;re expected to know the formulas from memory. The only exception: questions that rely on genuinely advanced formulas usually include the formula in the question itself.<\/p>\n<h3 style=\"color: #C5168C;\">How many formulas do I need to memorize for the ACT?<\/h3>\n<p>About 18 core formulas cover the majority of formula-based ACT Math questions, and roughly 32 give you thorough coverage. Focus on the must-know tier first; the ACT rewards deep familiarity with common formulas far more than shallow familiarity with rare ones.<\/p>\n<h3 style=\"color: #C5168C;\">Did the Enhanced ACT change the math content?<\/h3>\n<p>No. The Enhanced ACT (standard since September 2025) changed the structure: 45 questions in 50 minutes, 4 answer choices instead of 5, and Science became optional, making Math one of three sections in your Composite score. The math topics, skills, and difficulty are unchanged, so the same formulas apply. For the full rundown, see our <a href=\"https:\/\/magoosh.com\/act\/enhanced-act\/\">Enhanced ACT guide<\/a>.<\/p>\n<h3 style=\"color: #C5168C;\">Can I use a calculator instead of memorizing formulas?<\/h3>\n<p>A calculator is allowed on the whole ACT Math section, but it can&#8217;t tell you <em>which<\/em> formula a problem needs. ACT&#8217;s calculator policy does let you keep stored formulas and programs on an approved calculator, as long as they don&#8217;t include computer algebra system (CAS) functionality (CAS calculators like the TI-89 are banned entirely). Still, scrolling through calculator menus is slow. With just over a minute per question, memory is faster than any calculator.<\/p>\n<h3 style=\"color: #C5168C;\">Do I need to memorize the quadratic formula for the ACT?<\/h3>\n<p>It&#8217;s a bonus-tier formula. Many quadratic questions on the ACT can be solved faster by factoring or by backsolving from the answer choices. Know the quadratic formula if you&#8217;re chasing a top score, but master factoring first.<\/p>\n<h2 style=\"color: #4D2079; padding: 0;\">Need More Help?<\/h2>\n<p>Now that you know which ACT math formulas to study, put them to work: download the <a href=\"https:\/\/act.magoosh.com\/math-formulas\">PDF<\/a>, drill the must-know tier, and test yourself under real conditions. And if you want structure for the whole journey, <a href=\"https:\/\/act.magoosh.com\/\">Magoosh ACT prep<\/a> includes lessons, practice questions, and study schedules to carry you through <a href=\"https:\/\/magoosh.com\/act\/act-test-dates\/\">test day<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The ACT doesn&#8217;t give you a formula sheet. Here are the 32 ACT math formulas to memorize, ranked by priority, plus a free printable PDF.<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[],"ppma_author":[24868],"class_list":["post-558","post","type-post","status-publish","format-standard","hentry","category-all"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>32 Math Formulas on the ACT - What to Absolutely Study [PDF]<\/title>\n<meta name=\"description\" content=\"Here are the most common ACT Math formulas you should know with an easy-to-study downloadable PDF. 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She had a PhD from the University of California, Irvine, an MA degree from The Catholic University, and BA degrees in Secondary Education and English Literature from the University of Maryland, College Park. She was the recipient of the 2013 Excellence in Teaching Award and the Chancellor\u2019s Club Fellowship from the University of California, Irvine. She\u2019s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. She now develops accessible and effective edtech products for Magoosh. Her free online content and YouTube videos providing test prep and college admissions advice have received over 6 million views in over 125 countries. Kristin is an advocate for improving access to education: you can check out her TEDx talk on the topic. 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She had a PhD from the <a href=\"https:\/\/drama.arts.uci.edu\/graduate-programs\/phd\/alums\">University of California, Irvine<\/a>, an MA degree from The Catholic University, and BA degrees in Secondary Education and English Literature from the University of Maryland, College Park. She was the recipient of the 2013 Excellence in Teaching Award and the <a href=\"https:\/\/grad.uci.edu\/funding\/fellowships-awards\/internal\/chancellors-club-fellows.php\">Chancellor\u2019s Club Fellowship<\/a> from the University of California, Irvine. She\u2019s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. She now develops accessible and effective edtech products for Magoosh. 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