Are you trying to improve your SAT Math score? Not sure which equations or formulas you need to know for the SAT? This is a very common concern for students taking the SAT. While you don’t get to bring a formula cheat sheet to your official SAT, you can put one together for yourself to use to study!
Short on time?
If you have 3 weeks or less before your SAT, spend some focused time memorizing these formulas and equations and make sure you know how and when to use them. That’s really important. If you don’t know how to use the equations, you’re doing yourself no good to memorize them at all!
You’ll see some quick score improvement simply by familiarizing yourself with commonly tested concepts and their corresponding equations or formulas. Most likely you’ve seen some of this stuff before, but do yourself a favor and work through this article before test day.

Have a bit more time?
If you have a month or more before your test date, I recommend spending less time memorizing equations and more time studying the underlying math concepts as well as working through official SAT math practice questions.
Go ahead and bookmark this page. I recommend coming back here to do a “self check” and make sure you do actually know all of the equations you might need on test day after you’ve finished studying the underlying math concepts.
Equations You Get on Test Day
First of all, you do get some equations on test day. The SAT provides a Reference Sheet with each of the two math sections on the test.
We don’t recommend you spend too much time committing these formulas to memory; however, you do need to be familiar with these equations. In other words, if you have no clue how to use these equations, it does you no good to get them for “free” on test day. The SAT is giving them to you because the reality is, they want to test your ability to use the equations, not your ability to memorize them.

These equations break down into four categories:
- Geometry of 2D Shapes (Area, Perimeter, and Circumference)
- Special Right Triangles
- Geometry of 3D Shapes (Volume)
- Other Reference Info
Let’s take a deeper look at each of these formulas, and walk through when and how you would use them on test day.
Kickstart Your SAT Prep with Test Geek’s Free SAT Study Guide.
Geometry of 2D Shapes (Area, Perimeter, and Circumference)

Formula: Area of a triangle
When to use:
- When given height (h) and base (b) of any triangle and asked to find Area (A).
- When given height (h) and Area (A) of any triangle and asked to find the base (b).
- When given Area (A) and base (b) of any triangle and asked to find height (h).

Formula: Pythagorean theorem
When to use:
- When given 2 of the 3 sides of a right triangle and asked to find the third side.

Formula: Area of a rectangle
When to use:
- When given length (l) and width (w) of a rectangle and asked to find Area (A).
- When given length (l) and Area (A) of a rectangle and asked to find width (w).
- When given Area (A) and width (w) of a rectangle and asked to find length (l).

Formula: Area of a circle
When to use:
- When given the radius (r) of a circle and asked to find Area (A).
- When given the Area (A) of a circle and asked to find radius (r).
Formula: Circumference of a circle (distance around the circle)
- When given the radius of a circle and asked to find the circumference (c).
- When given the Circumference of a circle and asked to find the radius (r).

Special Right Triangles
Formula: Special Right Triangles
When to use:
- When given a triangle with 30/60/90 angles and asked to find one or more sides.
- When given a triangle with 45/45/90 angles and asked to find one or more sides.
- When given a triangle with sides that are as shown in either configuration above and asked to find one or more angles.
Geometry of 3D Shapes (Volume)

Formula: Volume of a rectangle
When to use:
- When given the length (l), width (w), and height (h) of a rectangle and asked to find Volume (V).
- When given the Volume (V) and any two of the rectangle (l, w, or h) and asked to find the remaining side (l, w, or h).

Formula: Volume of a cylinder
When to use:
- When given the radius (r) and height (h) of a cylinder and asked to find Volume (V).
- When given the Volume (V) and radius (r) of a cylinder and asked to find the height (h).
- When given the Volume (V) and height (h) of a cylinder and asked to find the radius (r).

Formula: Volume of a sphere
When to use:
- When given the radius (r) of a sphere and asked to find the Volume (V).
- When given the Volume (V) of a sphere and asked to find the radius (r).

Formula: Volume of a cone
When to use:
- When given the radius (r) and height (h) of a cone and asked to find the Volume (V).
- When given the Volume (V) and radius (r) of a cone and asked to find the height (h).
- When given the Volume (V) and height (h) of a cone and asked to find the radius (r).

Formula: Volume of a triangular prism
When to use:
- When given the length (l), width (w), and height (h) of a triangular prism and asked to find Volume (V).
- When given the Volume (V) and any two of the rectangular prism (l, w, or h) and asked to find the remaining side (l, w, or h).

Other Reference Info
If you’re keeping track, there’s a small bit of information on the Reference Sheet that we haven’t covered yet:

Let’s focus on the first two sentences first. These are all about circles and essentially tell us how to convert between radians and degrees. This is important. You may be given some information in degrees and need to convert it to radians (or vice versa). You don’t necessarily need to memorize the conversion rule, but you do need to know how to actually perform the conversion.
We are given the ratio of degrees to radians. We can simplify this by dividing both sides by 2.

Convert Radians to Degrees
Using our ratio above, we can convert radians to degrees by multiplying our radians by the ratio (with the radians on the bottom and the degrees on the top).

Convert Degrees to Radians
Using our ratio above, we can convert degrees to radians by multiplying our degrees by the ratio (with the degrees on the bottom and the radians on the top).

The last sentence tells us that there are 180 degrees in a triangle. You likely know this one already. If you add up all of the internal angles in a triangle, you will always get 180.
And with that, we’ve covered everything on the Reference Sheet you are given on test day. Now, we’ll take a look at the other equations, formulas, and mathematical rules you aren’t given on test day.
What would 200 EXTRA POINTS do for you? Boost Your SAT Score with Test Geek SAT prep.
Top 25 Equations You Should Know for the SAT (That You Don’t Get on Test Day)
At the end of the day, the best way to improve your SAT Math score is to get better at the underlying concepts that are tested. There’s no shortcut. The more time you spend mastering the topics, the better your score will be. As you study and review for the test, you’ll come across equations, formulas, and math rules that you (whether you realize it or not) are using.
If said formula is not one of those listed in the section above, you’re going to need to have it memorized for test day. Let’s go over the top 25 equations you should know for the SAT.
Linear Equations
1. Slope-Intercept Form of a Line
Let’s start out with a formula you might remember from Algebra 1. There are several forms of a line, but this is usually the first form you learn, and it’s the one we recommend you memorize for the SAT.

Where m is the slope of the line, b is the y-intercept, and (x, y) is a point on the line.
Tips:
- b is the y-intercept, and it can also be thought of in terms of a point on the line (0, b).
- y needs to have a coefficient of 1 in order for this form to work. Make sure you rearrange the formula into this exact form before determining slope (m) or y-intercept (b).
2. Slope of a line, given two points
Slope can be thought of as the change in y over the change in x. If you have two points (or can find two points) on a line, you can determine the slope of that line.

Data and Statistics
3. Average / Mean
The average of a set of numbers is the same as the mean of that set of numbers. Average = mean.
This formula is simply a fancy way of saying: add up all of the numbers and divide by the count of the numbers.

4. Simple Interest
The simple interest formula is used to calculate (you guessed it) interest. Interest applies on to the original principal amount, with the same rate of interest during the entire period of time. It does take into account any compounding interest.

Where P is the principal, the amount initially borrowed or invested, R is the rate of interest per year, and T is the time in years that the principal is invested or borrowed.
5. Compound Interest
Compound interest is what often applies in real life scenarios of investing money in a savings or retirement account. Think about it like this: if your account starts with $1000 and you make $50 in interest over a period of time, you now have $1050. Now, over the next period of time, you’ll have $1050 to grow due to interest, not just the original $1000 – hence the compounding part.

Where P is the original principal invested, n is the number of compounding periods per unit of time (t), and t is the time in decimal years (ex. 6 months = .5 years).

Exponents and Radicals
6. Multiplying Numbers with Exponents that have the Same Base
The rules is useful to know for the SAT, as you may be given a problem that has one or more variables int the exponents. If you know this rule, you’ll quickly be able to find your answer. When you multiple numbers with the same base, you can add the exponents, keeping the same base.

7. Dividing Numbers with Exponents that have the Same Base
This rule is similar to the previous one, except we are now dividing two numbers with the same base. In this case, we subtract the exponents.

8. Raising a Number with an Exponent to an Exponent
Raising an exponent to an exponent may look intimidating, but it is actually quite simple. You should multiply the exponents in this case. This rule typically comes up on the non-calculator math section, when you can’t easily plug numbers into a calculator, but instead, you need to know this rule. It could also be useful if you are dealing with variables within your exponents.

9. Working with Negative Exponents
Negative exponents are the inverse of their positive counterpart. Remember these rules, and you may be able to drastically simply a given problem.


10. Converting Exponents and Radicals
Fraction exponents and radials work hand in hand. Depending on the problem, it may be helpful to convert an exponent into its radical form or vise versa.

Quadratics
11. Quadratic Equation
Quadratic equations can generally be solved one or more of the following ways:
- Factoring
- Completing the square
- Graphing
- Using the quadratic formula (see #12 for more info on this)
It’s important, first and foremost, to be able to recognize a quadratic equation in its proper form. We won’t dive into all of the rules for solving them here, but I do recommend you are comfortable using all of the methods for solving quadratic equations before test day.

12. Quadratic Formula
You may have this one committed to memory thanks to a song your algebra teacher taught you… I can still hear it my head years later! It’s not commonly tested on the SAT, but it is good to know just in case. If you are given a quadratic equation, you can always use the quadratic formula to solve it (it just might be a lot easier to use another method, depending on the equation).

13. Factoring Patterns
Being able to recognize that you can factor what you see below on the right side into what’s on the left side could prove helpful on the SAT. If you know these patterns, you may be able to greatly simplify a given problem.


14. Difference of Squares
Again, this one is all about being able to recognize a pattern. You may be given something that looks similar to what’s on the right side, and if you know you can factor it into what’s on the left side, you’ll be able to get to your answer quickly.

15. The Discriminant
This handy formula can tell us how many solutions a quadratic equation has without actually solving the quadratic. This is a commonly tested concept on the SAT. Sometimes you will be told an equation has a particular number of solutions, and that information tells you what your n value is (or at least what range it is in).


Advanced Graphing
16. Graphing Parabolas
You may have seen the standard form of a parabola before, but I doubt you committed it to memory. This one is a bit obscure, but it does come up on the SAT. And, when it does, it’s usually a pretty hard problem..
When you do see a parabola question, it usually involves finding the vertex. This wouldn’t be too difficult if you were given the equation for the parabola in standard form, but that’s usually not the case. Typically, you’ll actually need to complete the square in order to get it into standard form.
Completing the square is one of the trickiest math topics that you’ll see on the SAT. It requires multiple steps, and therefore, there are multiple places where things can go wrong. If you want to review how to complete the square, I recommend checking out Khan Academy.

17. Graphing Circles
The standard form of a circle is similar to the standard form of a parabola, and it’s usually tested in a similar way on the SAT. You’ll likely need to complete the square as part of the path to solving questions that involve graphing circles. Commit this to memory and ensure you know how to confidently complete the square.

18. Distance Formula
If you need to calculate the distance between two points, use the distance formula.


Trigonometry
19. SOHCAHTOA
Do you have SOHCAHTOA memorized? If not, you should. This mnemonic is a favorite tool to remember the trigonometric functions sine, cosine, and tangent. Remember, this is all about the relationship between the sides and angles of a right triangle:

20. Convert Between Radians and Degrees
21. Arc Length in Radians
The distance between two points along a section of curve is called arc length. How you calculate this depends if you are given (or can calculate) the central angle of the sector in radians or degrees.

22. Arc Length in Degrees
If you are given the central angle in degrees, use this equation instead.

23. Area of Sector in a Circle in Radians
The area of a piece (sector) of a circle can be calculated using the central angle of the sector. Which formula you use, just like with arc length, depends on if you have the central angle in degrees or radians.

24. Area of Sector in a Circle in Degrees

25. Complex Number Rules
We’ll end with complex numbers. Complex numbers take the form a + bi. If you see complex number questions on the test, they will usually be testing your ability to combine real numbers with i, which often involves multiplying i by itself. You should know these rules.

Final Thoughts
I hope you use this as a resource as you prepare for test day. Bookmark it. Print out the PDF version. The best way to improve your SAT Math score is to get better at the underlying content, and ensuring you’ve committed these equations, formulas, and mathematical rules to memory is an important piece of that.

Comments