# SAT Math Formulas You Must Know Updated:
August 28, 2023 Reviewed by:

Former Admissions Committee Member, Columbia University

Reviewed: 5/4/22

The SAT Math portion requires strong prior knowledge going into the exam. Here, we cover all the essential formulas to prepare you for the SAT math section.

When high school students start studying for the SAT, they often ask, “What math formulas should I know for the SAT? To help, students receive a list of common SAT math formulas to review. However, there may be some formulas you need to know that aren’t included in this list. So, which other ones should you know?

The right track for understanding the SAT math formulas is to know which formulas aren’t provided in the SAT. You may recognize these formulas if you’ve taken all of your high school math classes.

Below, we’ll cover a concrete list of the SAT math formulas you’ll need to know for the SAT. We’ll break down which formulas are provided and which ones aren’t to help you study smarter, not harder!

## Formulas Given on the SAT

As mentioned, the SAT provides a list of formulas that students can refer to during the test. Below is the list of SAT math formulas you’ll have access to.

Equation Formula
Area of a Circle A = r2
Circumference of a Circle C = 2r
Area of a Square of Rectangle A = lw
Area of a Triangle A = 12bh
Pythagoras Theorem c2=a2+b2
Volume of a Cube V = lwh
Volume of a Cylinder V= r2h
Volume of a Sphere V=43r3
Volume of a Cone V=13r3h
Volume of a Pyramid V= 13lwh

Source: Collegeboard SAT Study Guide

All SAT math formulas come from high school Geometry, so you should know them before taking the SAT. Expect to use them on the exam. While you won't need to memorize them all, you'll want to practice their applications as you prepare for the SAT.

With these formulas in mind, we’ll break down how to use them to refresh your memory!

### Circle Formulas

The area of a circle equals r2, or the irrational constant of pi, multiplied by the squares of the radius of the circle. The radius, or r, is the distance from the edge of the circle to the center.

The circumference of a circle, 2r, equals pi times twice the radius. The equation can also be written as d, since the diameter, or d, is twice the radius. Remember this if a question only gives you the diameter and asks for the circumference.

### Area of Other Shapes

The standard equation for finding the area of squares and rectangles is lw, or length times width.

Triangles have a different area equation, that of  12bh. A triangle is always half the area of a larger square. The measurements of b and h are the base line’s length and the height, or the distance from the base to the opposite corner. Once multiplied with each other and `½, you have found the area.

### Pythagoras Theorem

The Pythagoras theorem is a common formula for finding the unknown length of the side of a triangle when you know the length of the other two sides, as demonstrated by the SAT math formula c2=a2+b2. The lines a and b have to meet at a right angle for you to be able to find the length of c or the hypotenuse.

### Volume of Solid Shapes

The formula of solid shapes, or the three-dimensional variants of other shapes, builds on the previous formulas by adding the extra line to fill in the third direction of space.

• When looking for the volume of a cube, you use the formula of V = lwh, a form that builds upon the original formula for a square with the added dimension of height. Every corner of a cube or rectangular prison is formed from the intersection of three lines.
• The volume of a cylinder is represented by a bunch of circles stacked on top of each other. The simple circle formula of A=r2 evolves with the new dimension of height into V= r2h.
• The sphere enters the third dimension by cubing the radius, morphing the familiar area of a circle formula into 43r3. The added coefficient of 43 accounts for the size change for each cross-section of the sphere.
• The volume of a cone marries the formula for a sphere with the formula of a triangle to create 13r3h. A cone’s height is equivalent to a triangle’s, which the formula accounts for, along with the flat circular base.

A pyramid, based on the volume formula 13lwh, shows how the space covered by a triangular prism is a third of a larger square, covering the same length, width, and added height.

## Other SAT Math Formulas You Should Know

Below, you'll find a list of the common SAT math formulas you’ll want to memorize before you take the exam. These formulas won’t be included in the SAT formula sheet, so it’s essential that you get familiar with these equations and their applications.

Equation Formula
Linear Equation y=mx+b
Slope (y2-y1)(x2-x1)
Distance d=(x2-x2)2+(y2-y1)2
Vertex form of a Quadratic Function f(x) = a(x – h)2+ k
Binomial Products (a+b)2=a2+2ab+b2
Exponents Rule (am)n = amn
Length of a Circle Arc l=rθ or rθ(180)
Area of a Sector of a Circle A=(θ/360º)r2
Standard Equation of a Circle r2=(x−h)2+(y−k)2
Trigonometric Ratios sin θ = PerpendicularHypotenuse
cos θ = BaseHypotenuse
tan θ = PerpendicularBase
Simple Interest I =prt.
Compound Interest I=P(1+rn)nt
Probability Outcome=desired outcomestotal possible outcomes

The SAT expects students to know all of these formulas without having to provide them. These formulas cover topics from graphing to Geometry and Trigonometry. Your exam practice should cover these from your high school math classes if you aren’t familiar with them.

### Graphing Equations

The SAT includes three main graphing equations that appear on most related SAT problems: linear, distance, and slope.

• The linear equation  y=mx+bis the standard equation of a line, taking the input of the x or horizontal axis to find the value of the opposite y or vertical axis. M is the slope of the line, and b is where the line intercepts the y-axis, where x is zero. It is considered the slope-intercept form of the equation.
• If you have the x and y coordinates of two points on a graph, use the distance formula (x2-x2)2+(y2-y1)2 to solve for the space between the points.
• Similar to distance, if you’re looking for the slope and have coordinates for two points, you can use the slope formula of  (y2-y1)(x2-x1) to find the equivalent of m from the linear equation.

### Algebraic Equations

Expect to see a sizable amount of Algebra on the SAT math test. The following formulas will help you the most with the Heart of Algebra questions.

• If you’ve taken Algebra, you’ve probably come across the Quadratic Equation, orx=(-b)b2-4ac2a, one of the most useful in both the subject and among the unprovided math formulas for the SAT. Use the formula to find an unknown variable of x when you know a and b are the coefficients of the variable x. C is an intercept.
• When graphing quadratic equations, use the formula f(x)=a(x – h)2+k  or the vertex form of the equation to draw the line when you know the peak of the parabola. The coordinates of the peak are the constants of h and k, where h is the distance along the x-axis and k along the y-axis.
• Make sure to know how exponents work with solving Algebraic equations. The exponent's rule (am)n = amn calls for you to multiply exponents together across parentheses.
• As part of Algebra and later calculus, you’ll need to know how to multiply out Binomial Products using the FOIL method. Using the example formula, (a+b)2=a2+2ab+b2you expand exponential statements by multiplying by itself as many times as the exponent is, making a proper equation.

### Circle Equations

The SAT will require you to memorize these other circle equations outside of simple area and circumference.

• When looking for the arc of a circle, you may need to use one of two equations depending on the information. If the question includes a measurement of radians, use the formula l = rθ, where θ is the number of radians. Without a radian measurement, use rθ(180)where θ equals the angle of the arc in degrees.
• The area of a sector of a circle formula uses the similar area of a circle formula but adds to it to make (θ/360º)r2. By dividing the number of degrees of the sector by 360, you find the percentage of the circle the sector takes up. You then use the circle area formula to find the area of the sector.
• When graphing a circle, you can use the standard equation of a circle or r2=(x−h)2+(y−k)2, to find the radius. So long as you have the x and y coordinates of the circle, the height (h), and the width (k), you can then use the formula to find the perfect square of the radius.

### Trigonometric Ratios

The SAT will require that you know a bit of Trigonometry. You will only need to know how the basic three trigonometric ratios work. The three sides of a right triangle used in these ratios are the hypotenuse or the longest side, the opposite, the perpendicular or tall side, and the base or the bottom side.

• The sine of a right triangle equals the opposite divided by the hypotenuse.
• The cosine of a right triangle equals the base divided by the hypotenuse.
• The tangent of a right triangle equals the opposite divided by the base.

A great pneumonic device that makes it easy to remember these functions is SOHCAHTOA, which spells out what you need to do as an acronym.

### Interest Equations

There are two formulas covering interest used on the SAT. You can expect to see both.

• Simple interest breaks down into the formula prt where p is the principal or starting rate of money, r is the interest rate, and t is the amount of time covered.
• Compound interest has a higher rate of increase than simple with the formula of I=P(1+rn)nt. Instead of a fixed interest rate only affected by time, compound charges interest rate several times, represented by n. Compounded interest then increases exponentially. Treat the fraction as a percentage.

### Probability

You'll remember the Probability SAT math formula from the end of high school Geometry. The equation used in probability problems is Outcome=desired outcomestotal possible outcomes. When reading these problems, you can identify the desired outcome likely as the given number or percentage and the total by adding every outcome together if not stated.

## FAQs: Math Formulas for the SAT

Below are some common questions about the math formulas you need for the SAT.

### 1. What Math Formulas Are on the SAT?

The provided SAT math formulas cover Geometry and some Trigonometry. You’ll find them on the instruction sheet to reference during the exam. See the above for the list of the included formulas. However, you should know other formulas, from graphing to algebra and statistics. You can find a complete list of the unprovided formulas above.

### 2. Is There a Formula Sheet for the SAT?

Yes, the SAT math test provides a list of formulas as part of the opening instructions for each portion. They cover most of the common geometric shape formulas. However, you will want to know more formulas beyond these.

### 3. Is SAT Math Mostly Algebra?

No, the SAT is not mostly Algebra. The SAT math exam is broken down into the following topics: Algebra, Problem Solving and Data Analysis, Advanced Math, and additional miscellaneous Math topics. Algebra is a large and focused topic, but Data Analysis and Advanced Math take up equal portions of the exam.

### 4. How Do I Memorize Formulas for the SAT?

The best way to memorize anything is through consistent practice! While studying for the SAT, be sure to work on problems that use the necessary math formulas. If you’re struggling to remember all of them, try using flash cards or any route memorization methods to ensure you know all the SAT math formulas you need.

### 5. Can You Do SAT Math Without a Calculator?

Yes, you can do SAT math without a calculator. The SAT math exam splits questions between two sections, one with and one without a calculator. There are questions on the SAT calculator portions that you may find easier without. However, be aware of the SAT calculator policy to know if your calculator meets the exam guidelines.

### 6. What Are Some Good Tips for the SAT Math Test?

The best tip for studying for the SAT math test is to break down the material in your studying by subject. You then can determine what formulas you need to memorize, which will help you if you plan to study independently.

### 7. How Do I Use the SAT Grid-In?

You use the SAT grid-in by writing in the answer and bubbling for each space. The grid-ins have four total spaces for each digit, fraction line, and decimal point. When using formulas involving circles on grid-in questions, use 3.14 for pi. Read the College Board SAT grid-in instructions and policy for more information.

### 8. Does the PSAT Use Different Formulas From the SAT?

The PSAT provides the same formula sheet at the start as the SAT. However, the PSAT is considered easier, so you may not need to know all the extra formulas like you do on the SAT. You’ll want to take the PSAT as a practice test to find what you need to study for the SAT and its math exam.

### 9. Does the SAT Math Exam Have Any Calculus?

No, the SAT does not have any true calculus on the exam. You may need skills that you would use in Calculus, like multiplying binomial products. However, you may have learned everything you need if you’ve taken Pre-calculus, which is as much as the SAT math exam expects students to take.

## Final Thoughts

When studying for the math exam, SAT math formulas will prove invaluable the more you learn and apply them. While the exam does provide several geometric formulas, you will need to know many more to do well on the exam.

The exam covers math topics from Algebra to Trigonometry, so prepare for them with these formulas.

Good luck with the SAT! 