19 SAT Math Formulas You Must Know - Plus How to Use the Formula Sheet

Home » The Digital SAT: What’s Tested, How It’s Scored, and How to Improve Your Score » The 17 Digital SAT Math Topics: How Often Each Is Tested and What to Study First » 19 SAT Math Formulas You Must Know – Plus How to Use the Formula Sheet

By Glyn Caddell, BSME · Author of Digital SAT Math Secrets · Tutoring since 2008 — Updated August 27, 2026

The Digital SAT provides a math reference to students during the math modules. It can be accessed during the test by pressing the icon on the top right with an $x^2$ and the word “Reference” underneath it. The reference includes formulas for 2-D shapes, such as circles, rectangles, and triangles. It includes volume formulas for 3-D shapes. However, there are 19 math formulas and concepts that students must know for the test but aren’t included on the provided formula sheet.

Table of Contents

What Formulas Do You Have to Memorize for the SAT?
The Provided Formulas Explained
Tips to Use the Math Sheet Effectively
Frequently Asked Questions
All Math Topics

What Formulas Do You Have to Memorize for the SAT?

Formulas and math concepts that you need to know fall under four categories:

Linear & Quadratic
Circles & Polygons
Growth, Data, Probability, & Proportions
Trigonometry.

Linear & Quadratic

Linear & quadratic formulas and concepts to know include slope formula, slope-intercept form of a line, standard form of a quadratic function, vertex form of a quadratic function, factored form of a quadratic function, and the quadratic formula.

Slope Formula

$m=\dfrac{y_2-y_1}{x_2-x_1}$

To find the slope from one, $(x_1, y_1)$ , point to another, $(x_2, y_2)$

You’ll use this more than any other formula on this list. Linear functions are 15% of the math section, which makes them the most common topic on the test.

Learn more about linear functions

Slope-Intercept Form of a Line

$y=mx+b$

where $m$ is the slope and $b$ is the $y$ -intercept

Most linear function questions either give you an equation in this form or expect you to write one. Knowing which number is the slope and which is the starting value is normally the whole question.

Learn more about linear functions

Standard Form of a Quadratic Function

$f(x)=ax^2+bx+c$

where $a$ , $b$ , and $c$ are constants.

This is the form you’ll see most often, and it’s the form the quadratic formula uses. The c value is the y-intercept.

Learn more about quadratic functions

Vertex Form of a Quadratic Function

$f(x)=a(x-h)^2+k$

where (h, k) is the vertex

If a question asks for the vertex, the minimum, or the maximum, this is the form you want. Both coordinates can be read directly without doing any work.

Learn more about quadratic functions

Factored Form of a Quadratic Function

$f(x)=a(x-p)(x-q)$

- where $p$ and $q$ are the zeros (roots)

The fastest form for finding where a parabola crosses the x-axis. If a question asks for the zeros and gives you this form, you can read them off.

Learn more about quadratic functions

Quadratic Formula

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$a$ , $b$ , and $c$ are the coefficients from the standard form, $f(x)=ax^2+bx+c$

Use it when a quadratic doesn’t factor easily. The part under the radical, b² − 4ac, also tells you how many solutions there are, which comes up on its own.

Learn more about quadratic functions

Circles & Polygons

Circles & polygons formulas and concepts to know include standard form of a circle, sum of the angles of a convex polygon, arc length proportion, and sector area proportion.

Standard Form of a Circle

$(x-h)^2+(y-k)^2=r^2$

where (h, k) is the center and the radius is $r$

The reference sheet gives you the area and circumference of a circle but not its equation. Questions that give you an equation and ask for the center or radius are common, and this is the only way to answer them.

Learn more about circles

The Sum of the Angles of a Convex Polygon

$Sum = (n-2)(180)$

where $n$ is the number of sides

The sum of the exterior angles of any convex polygon is always 360°, no matter how many sides it has.

Learn more about angles, polygons, and 3-D shapes

Arc Length Proportion

The ratio between the central angle and a full circle ( $360^o$ or $2\pi$ radians) is equal to the ratio between the arc length and the full circumference.

$\dfrac{X}{360}=\dfrac{L}{C}$

$X$ is the central angle in degrees, $L$ represents the arc length, and $C$ is the circumference

$\dfrac{\theta}{2\pi}=\dfrac{L}{C}$

$\theta$ is the central angle in radians, $L$ represents the arc length, and $C$ is the circumference

Sector Area Proportion

The ratio between the central angle and a full circle ( $360^o$ or $2\pi$ radians) is equal to the ratio between the sector area and the full area.

$\dfrac{X}{360}=\dfrac{S}{A}$

$X$ is the central angle in degrees, $S$ represents the sector area, and $A$ is the area

$\dfrac{\theta}{2\pi}=\dfrac{S}{A}$

$\theta$ is the central angle in radians, $S$ represents the sector area, and $A$ is the area

Growth, Data, Percentages, & Probability

Formulas to know for growth, percentages, and probability include exponential growth/decay formula, average, average speed, percentages, and probability.

Exponential Growth/Decay Formula

$A=A_0(1\pm r)^t$

Where $A$ is the amount, $A_0$ is the starting amount, $r$ is the percent change, and $t$ is the number of time periods

Use the plus for growth and the minus for decay. Any question about population, interest, or something increasing or decreasing by a percentage over time uses this.

Learn more about exponential growth and decay

Average (Arithmetic Mean)

$Average=\dfrac{Sum}{NumberOfTerms}$ and $Sum=(Average)\times(Number Of Terms)$

The second version matters more than students expect. Questions often give you an average and ask what happens when a value is added or removed, and you need the sum to answer them.

Learn more about data and probability

Average Speed

$Average Speed=\dfrac{d}{t}$

where $d$ is the total distance and $t$ is the total time

The word “average” makes students reach for the mean of the individual speeds, which is wrong when the distances or times aren’t equal. If a car goes 30 mph for one hour and 60 mph for two hours, the average speed isn’t 45. It’s 150 miles divided by 3 hours, which is 50.

Always go back to total distance over total time.

Learn more about ratios and proportions

Percentages

Instead of memorizing three different formulas to find the percent, find the part, or find the whole, you can simply use one proportion to solve for a missing value.

$\dfrac{\%}{100}=\dfrac{Part}{Whole}$

If you want to memorize the three versions, here they are:

Find x percent of a number n:

$n \times (x \div 100)$

Find what percent n is of m:

$(n \div m) \times 100$

Find what number n is x percent of:

$(n \div x) \times 100$

The third one is the version students get wrong most often. If a question says a value is 25% of some number and asks for the original, you divide rather than multiply.

Percent questions are approximately 3.1% of the math section, and they also show up inside other topics. A ratio question, a data question, or an exponential growth question can all require a percent calculation partway through.

Learn more about percent

Probability

$Probability=\dfrac{f}{N}$

where $f$ is the number of desired outcomes and $N$ is the total number of possible outcomes

A probability of 1 means something is certain. A probability of 0 means it can’t happen. Every probability on the SAT falls between those two.

The formula is simple. What makes these questions difficult is figuring out what belongs in the denominator.

Most SAT probability questions give you a two-way table and add a condition, like “if a person is chosen at random from those who recalled at least one dream.” That condition changes the total. You’re no longer dividing by everyone in the table, only by the group the question named.

Reading the condition carefully is the whole question. Data and probability is 8.7% of the math section, which makes it the third most common topic on the test.

Learn more about data and probability

Trigonometry

Trigonometry formulas and concepts to know include the three trigonometric ratios and the cofunction property of sine and cosine.

Three Trigonometric Ratios (SOH-CAH-TOA)

There are three trigonometric ratios to remember, SOH-CAH-TOA, that can only be applied in right triangles. In the three formulas below A represents the measure of one of the acute angles in the right triangle.

$sinA=\dfrac{opposite}{hypotenuse}$
$cosA=\dfrac{adjacent}{hypotenuse}$
$tanA=\dfrac{opposite}{adjacent}$

The reference sheet gives you the Pythagorean theorem and the special right triangles, but no trigonometric ratios at all. If a question involves an angle that isn’t 30, 45, or 60 degrees, you need these.

Cofunction Property of Sine and Cosine

There is another relationship that should be remembered for $sin$ and $cos$ .

If A and B are complementary angles, then:

$sinA=cos(B)$

In other words,

$sinA=cos(90-A)$

Learn more about trigonometry

The Provided Formulas Explained

Below is every formula on the Digital SAT reference sheet, with a video explanation for each one.

Even though these are given to you during the test, it’s worth knowing them. Opening the reference sheet, finding the formula, and closing it again takes time on a section where time is tight.

Area and Circumference of a Circle

The formula for area of a circle is provided.

$A=\pi r^2$

The formula for circumference of a circle is also provided.

$C=2\pi r$

where $A$ is the area, $C$ is the circumference, and $r$ is the radius.

Video Explaining the Circle Formulas with an Example

Area of a Rectangle

The formula for area of a rectangle is provided.

$A=lw$

where $A$ is the area, $l$ is the length, and $w$ is the width.

Video Explaining the Area of a Rectangle with an Example

Area of a Triangle

The formula for area of a triangle is provided.

$A=\dfrac{1}{2}bh$

where $A$ is the area, $b$ is the base, and $h$ is the height.

Video Explaining the Area of a Triangle

Pythagorean Theorem

The formula for Pythagorean Theorem is provided.

$c^2=a^2+b^2$

where $c$ is the hypotenuse (the side across from the 90 degree angle), and $a$ and $b$ are the legs (sides other than the hypotenuse).

Video Explaining the Pythagorean Theorem

30-60-90 Triangle

The relationship among the sides of 30-60-90 right triangle is provided.

There is a ratio that exists among the sides.

The hypotenuse is $2x$

The side opposite (across from) the 30 degree angle is $x$

The side opposite the 60 degree angle is $x\sqrt{3}$

If you know the lengths of any of the sides, you can solve for $x$ and then calculate the lengths of the other sides.

Video Explaining the Side Relationships in a 30-60-90 Triangle with an Example

45-45-90 Triangle

The relationship among the sides of 45-45-90 right triangle is provided.

There is a ratio that exists among the sides.

The hypotenuse is $s\sqrt{2}$

Since two angles are both 45 degrees, this is an isosceles triangle, making the two sides opposite the 45 degree angles congruent. They are both $s$

If you know the lengths of any of the sides, you can solve for $s$ and then calculate the lengths of the other sides.

Video Explaining the Side Relationships in a 45-45-90 Triangle with an Example

Volume of a Rectangular Prism

The formula for volume of a rectangular prism is provided.

$V=lwh$

where $V$ is the volume, $l$ is the length, $w$ is the width, and $h$ is the height.

Video Explaining the Volume of a Rectangular Prism with an Example

Volume of a Cylinder

The formula for volume of a cylinder is provided.

$V=\pi r^2h$

where $V$ is the volume, $r$ is the radius of the circle, and $h$ is the height.

Video Explaining the Volume of a Cylinder with an Example

Volume of a Sphere

The formula for volume of a sphere is provided.

$V=\dfrac{4}{3}\pi r^3$

where $V$ is the volume and $r$ is the radius.

Video Explaining the Volume of a Sphere with an Example

Volume of a Cone

The formula for volume of a cone is provided.

$V=\dfrac{1}{3}\pi r^2h$

where $V$ is the volume, $r$ is the radius, and $h$ is the height.

Video Explaining the Volume of a Cone with an Example

Volume of a Pyramid

The formula for volume of a pyramid is provided.

$V=\dfrac{1}{3} lwh$

where $V$ is the volume, $l$ is the length, $w$ is the width, and $h$ is the height.

Video Explaining the Volume of a Pyramid with an Example

Radians & Degrees Relationship

The math reference states the following two facts:

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is $2\pi$

By stating these two facts, it also tells us how degrees and radians are related:

$360^o=2\pi rad$

Review our circles lesson to see how these relationships come in handy.

Video Explaining the Relationship Between Radians and Degrees, Including How to Convert From One to the Other

Sum of the Angles in a Triangle

The sum of the measures of the angles in a triangle is 180.

Video Explaining the Sum of the Angles in a Triangle with an Example

How to Use the Reference Sheet Effectively

Three things make the difference between the reference sheet helping you and slowing you down.

1. Know What's On It Before Test Day

If you don’t know a formula is on the reference sheet, you won’t think to look for it. Students routinely guess on volume questions without realizing the formula was two taps away.

2. Memorize the Provided Formulas Anyway

This sounds like a contradiction, but it isn’t.

Opening the reference, scanning it, finding what you need, and closing it takes 15 to 20 seconds. Do that six times on a module and you’ve spent two minutes reading a sheet instead of answering questions.

The ones worth memorizing are the ones that come up most:

Area and circumference of a circle
Area of a rectangle
Area of a triangle
Pythagorean theorem
30-60-90 and 45-45-90 triangles
Volume of a rectangular prism
Radians and degrees relationship
Sum of the angles in a triangle

The volume formulas for cylinders, spheres, cones, and pyramids are worth leaving on the sheet. They come up less often and they’re the hardest to remember correctly.

3. Practice With It, Not Without It

Practice using the reference sheet the way you’ll use it on test day, in Bluebook if you can. A formula you’ve only read in a list is not the same as a formula you’ve used to answer a question under time pressure.

Frequently Asked Questions

Students preparing for the Digital SAT frequently ask which formulas are given during the test and which ones they have to memorize.

What formulas are given on the SAT?

The Digital SAT reference sheet provides 13 items, all geometry: area and circumference of a circle, area of a rectangle, area of a triangle, the Pythagorean theorem, the side relationships in 30-60-90 and 45-45-90 triangles, the volumes of a rectangular prism, cylinder, sphere, cone, and pyramid, the number of degrees and radians in a circle, and the sum of the angles in a triangle.

What formulas do I need to memorize for the SAT?

The slope formula, slope-intercept form, the three forms of a quadratic function, the quadratic formula, the standard form of a circle, the sum of the angles of a convex polygon, arc length proportion, sector area proportion, exponential growth and decay, the average formula, average speed, percentages, probability, the three trigonometric ratios, and cofunction of sine and cosine. All 19 are explained above.

Is there a formula sheet on the Digital SAT?

Yes. It’s built into the Bluebook application and available during both math modules. You don’t bring anything with you.

Where is the reference sheet during the test?

Tap the icon in the top right of the screen with an x² and the word “Reference” underneath it. It opens over your screen and closes the same way.

Do I need to memorize the formulas that are provided?

You don’t have to, but it saves time. Each trip to the reference sheet costs 15 to 20 seconds, and on a 35-minute module that adds up. The circle, rectangle, and triangle formulas are worth knowing cold.

Does the SAT reference sheet include the quadratic formula?

No. The reference sheet covers geometry only. The quadratic formula, the slope formula, and everything else in algebra and advanced math has to be memorized.

All Math Topics

Every Digital SAT math topic has a lesson with practice problems and video explanations, and we’ve documented how often each one appears across the ten official practice tests.

If you want the full section covered on your own schedule, our on-demand Digital SAT course includes a video explanation for every practice question and comes with a 100-point score increase guarantee.

Take a Free Diagnostic SAT

Glyn Caddell

Glyn Caddell holds a BS in Mechanical Engineering from NJIT and has been tutoring New York City students since 2008. He founded Caddell Prep in 2012 and is the author of Digital SAT Math Secrets: Lessons & Tricks to Quickly Improve to a Perfect 800 on the Math Test, which contains over 900 practice problems and is used in Caddell Prep’s SAT math classes. He is founding president of the Staten Island Technical High School alumni association and teaches every lesson on this site personally.