Here’s some good news for test day: the digital SAT gives you a math formula sheet, and you can pull it up at any time during both math modules. But there’s a catch most students miss. The sheet covers geometry only. Every algebra and advanced math formula you need, you have to bring in your own head.
So the real question is not “what formulas does the SAT give me?” It’s “what do I get for free, and what do I have to memorize?” This guide answers both.
We’ll walk through the exact formulas printed on the official digital SAT reference sheet, then cover the formulas that are not on the sheet but show up on the test all the time. By the end, you’ll know precisely what to memorize and what you can safely look up.
Table of Contents
Formulas on the digital SAT reference sheet
On the digital SAT, you can open a reference sheet during both math modules by tapping the reference icon in the Bluebook testing app. It appears at the start of every math section, and it stays available the whole time. Here is what you’ll find on it.
Notice the theme: it’s all geometry. Areas, volumes, the Pythagorean theorem, and special right triangles. There is not a single algebra formula on it. Below is the full list, with a tutor’s note on which ones to actually learn and which ones you can lean on the sheet for.
Area and circumference of a circle
Area = πr²
Circumference = 2πr
Recall these two as naturally as you recall your home address. They show up constantly, and flipping to the sheet for something this common wastes time. Just don’t mix them up. Area uses the radius squared, circumference does not.
Area of a rectangle
Area = length × width
This one is intuitive, so you won’t need the sheet for it. Note that perimeter is not on the reference sheet (and the test won’t give it to you). Perimeter of a rectangle is 2 × (length + width).
Area of a triangle
Area = ½ × base × height
Know this one cold too. Don’t waste time flipping back and forth for a formula you’ll use on multiple questions.
Volume of a rectangular box
Volume = length × width × height
Easy enough that you don’t need to memorize it, but good to know it’s there. One thing the sheet does not give you is the surface area of a box. For a cube, both are simple: volume is s³ and surface area is 6s², where s is the length of a side.
Volume of a cylinder
Volume = πr²h
This is harder to recall under pressure, so it’s genuinely nice to have on the sheet. Look it up if you need it.
Volume of a sphere
Volume = (4/3)πr³
Definitely a “look it up” formula. The (4/3) is easy to forget, so lean on the sheet here rather than risk a memory slip.
Volume of a cone
Volume = (1/3)πr²h
Another good one to leave on the sheet. It’s a cylinder’s volume times one-third, if that helps it stick.
Volume of a pyramid
Volume = (1/3) × length × width × height
Same pattern as the cone: it’s a box’s volume times one-third. Reference it if it comes up.
Pythagorean Theorem
a² + b² = c²
Know this cold. Be fluent at finding any missing side of a right triangle. This is one of the most-tested ideas in SAT geometry, so don’t rely on the sheet for it.
30-60-90 triangle
The sides are in the ratio x : x√3 : 2x (shortest side to longer leg to hypotenuse).
You don’t have to memorize this if you’re comfortable reading the diagram on the sheet, but knowing it will make you faster. Just make sure you understand which side is which when you refer to it.
45-45-90 triangle
The sides are in the ratio s : s : s√2 (the two equal legs to the hypotenuse).
As a tutor, I always want my students to know this one. The key relationship is that the hypotenuse is always √2 times the length of a leg. If you forget, the sheet has you covered, but learning it saves real time on the test.
Three facts at the bottom of the sheet
The reference sheet also reminds you of three things:
- The number of degrees of arc in a circle is 360.
- The number of radians of arc in a circle is 2π.
- The sum of the angles in a triangle is 180 degrees.
These are worth memorizing simply because they’re short and you’ll use them often.
Pro tip: Before you start working, take ten seconds to glance at the reference sheet so you know what’s on it. The students who struggle most are usually the ones who didn’t realize a formula was available and burned time deriving it from scratch.
SAT math formulas you need to memorize
This is the section most “formula sheet” pages skip, and it’s the one that actually moves your score. The reference sheet is geometry only, but most SAT math questions are algebra and advanced math. That means the formulas you need most are exactly the ones the test does not give you.
Here are the formulas to memorize, grouped by the math the SAT tests.
Algebra
These come up on roughly a third of the math questions, so make them automatic.
- Slope: m = (y₂ − y₁) / (x₂ − x₁)
- Slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept
- Distance between two points: d = √((x₂ − x₁)² + (y₂ − y₁)²)
- Midpoint of a segment: ((x₁ + x₂)/2, (y₁ + y₂)/2)
Advanced math
This is where harder questions live, and where having the right formula ready makes the biggest difference.
- Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a, for any equation ax² + bx + c = 0
- Vertex form of a parabola: y = a(x − h)² + k, where the vertex is the point (h, k)
- Equation of a circle: (x − h)² + (y − k)² = r², where the center is (h, k) and the radius is r
- Exponent rules:
- xᵃ · xᵇ = xᵃ⁺ᵇ
- xᵃ / xᵇ = xᵃ⁻ᵇ
- (xᵃ)ᵇ = xᵃᵇ
- x⁻ᵃ = 1 / xᵃ
- x^(1/n) = ⁿ√x
- Exponential growth and decay: y = a(1 + r)ᵗ for growth, y = a(1 − r)ᵗ for decay, where r is the rate and t is time
Problem-solving and data analysis
These show up in word problems, charts, and percentage questions.
- Average (mean): sum of the values ÷ number of values
- Percent change: (new − original) / original × 100
- Probability: favorable outcomes ÷ total outcomes
Geometry and trigonometry (not on the sheet)
The sheet handles areas and volumes, but a few key relationships are still yours to memorize.
- Basic trigonometry (SOHCAHTOA):
- sine = opposite / hypotenuse
- cosine = adjacent / hypotenuse
- tangent = opposite / adjacent
Pro tip: The equation of a circle and the quadratic vertex form trip up more students than any other “memorize” formulas. If you only drill two things from this list, drill those.
Which formulas should you actually memorize first?
If the list above feels long, here’s how to prioritize.
Start with the algebra and advanced math formulas. They’re the ones the test won’t give you, and they cover the largest share of questions. The geometry formulas on the sheet are your safety net, so spend your memorization energy where there is no net.
Memorize the geometry formulas you’ll use most anyway. Circle area, triangle area, and the Pythagorean theorem come up so often that looking them up every time will slow you down. Learn those, and leave the volume formulas (sphere, cone, pyramid) on the sheet.
Don’t try to memorize the whole reference sheet. That’s what it’s there for. The goal is to know what’s on it so you never waste time deriving something the SAT already handed you.
A good way to find your gaps is to take a full-length practice test under real conditions. You can take a free SAT practice test from Magoosh to see which formulas you reach for confidently and which ones you fumble. The ones you fumble are your study list.
Quick reference: the full SAT math formula sheet
Here’s everything in one place. The first table is what the SAT provides. The second is what you need to bring yourself.
Provided on the digital SAT reference sheet (geometry only):
| Concept | Formula |
|---|---|
| Area of a circle | πr² |
| Circumference of a circle | 2πr |
| Area of a rectangle | length × width |
| Area of a triangle | ½ × base × height |
| Pythagorean theorem | a² + b² = c² |
| 30-60-90 triangle sides | x : x√3 : 2x |
| 45-45-90 triangle sides | s : s : s√2 |
| Volume of a box | length × width × height |
| Volume of a cylinder | πr²h |
| Volume of a sphere | (4/3)πr³ |
| Volume of a cone | (1/3)πr²h |
| Volume of a pyramid | (1/3) × length × width × height |
| Degrees in a circle | 360 |
| Radians in a circle | 2π |
| Degrees in a triangle | 180 |
Not provided: memorize these:
| Concept | Formula |
|---|---|
| Slope | (y₂ − y₁) / (x₂ − x₁) |
| Slope-intercept form | y = mx + b |
| Distance between two points | √((x₂ − x₁)² + (y₂ − y₁)²) |
| Midpoint | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Quadratic formula | (−b ± √(b² − 4ac)) / 2a |
| Vertex form of a parabola | y = a(x − h)² + k |
| Equation of a circle | (x − h)² + (y − k)² = r² |
| Exponent product rule | xᵃ · xᵇ = xᵃ⁺ᵇ |
| Negative exponent | x⁻ᵃ = 1 / xᵃ |
| Exponential growth / decay | a(1 + r)ᵗ / a(1 − r)ᵗ |
| Average (mean) | sum ÷ count |
| Percent change | (new − original) / original × 100 |
| Probability | favorable ÷ total |
| Sine, cosine, tangent | opp/hyp, adj/hyp, opp/adj |
How to use the formula sheet on test day
A few things are worth knowing before you sit down.
You can open the sheet any time. On the digital SAT, the reference sheet is available throughout both math modules in the Bluebook app. You won’t lose access partway through.
You also have the Desmos calculator the whole time. Unlike the old paper SAT, the digital SAT lets you use the built-in Desmos graphing calculator for the entire math section. That changes strategy. Many questions that used to require a formula can now be solved by graphing instead, so practice with Desmos until it feels natural.
Ignore old paper-SAT advice. If you find a prep book or website describing a “no-calculator math section” or long, separate math parts, it’s describing the retired paper test. The current digital SAT has two short, adaptive math modules with the calculator available throughout.
The formula sheet is a helpful safety net, but it won’t do the thinking for you. The students who improve most pair knowing their formulas cold with steady practice on real question types. If you want guided lessons and video explanations that show these formulas in action, Magoosh SAT prep walks through them step by step. And once you start practicing, our SAT score calculator can help you turn your practice results into a projected score, while our guide to SAT scores explains what those numbers mean for college admissions.
Learn the formulas the SAT won’t give you, lean on the sheet for the rest, and you’ll spend test day solving problems instead of hunting for formulas.
