SAT Math: The 15 Formulas You Must Memorize (and 10 You Don't)

Illustration by Lumist AI

Staring at a blank screen during the math section of the Digital SAT is every test-taker's worst nightmare. You know you have studied the concepts, but the exact equation you need has completely vanished from your memory. While the College Board provides a reference sheet, relying on it too heavily will drain your most precious resource: time. To truly excel, mastering the right SAT math formulas is the ultimate cheat code.

The transition to the Digital SAT has brought many changes, including the integration of the Desmos calculator. However, a calculator is only as smart as the person using it. If you do not know the mathematical relationships governing a problem, no amount of graphing software will save you. Based on data from 2,700+ students on Lumist.ai, test-takers who commit core formulas to memory operate with significantly higher confidence and finish sections with minutes to spare for review.

In this comprehensive guide, we are going to break down the exact SAT math formulas you need to know. We will start with the 10 formulas the test gives you (so you can stop stressing about them), and then dive deep into the 15 critical formulas you absolutely must memorize before test day.

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The Reference Sheet: 10 Formulas You Do NOT Need to Memorize

Let's start with the good news. At the beginning of every SAT Math module, you have access to a built-in reference sheet. You do not need to waste brain space memorizing these geometric formulas. However, you do need to know how and when to apply them.

Lumist Pro Tip: Even though these are provided, familiarizing yourself with them beforehand ensures you don't waste 30 seconds searching for the volume of a cylinder when you should be calculating.

Here are the 10 formulas provided to you on test day:

1. Area of a Circle

$A = \pi r^2$ This formula calculates the total space inside a circle. The SAT frequently tests this in conjunction with shaded region problems or sector area questions. Remember that $r$ stands for the radiusThe distance from the center of the circle to any point on its circumference..

2. Circumference of a Circle

$C = 2\pi r$

$C = \pi d$ The circumference is the perimeter of the circle. You will use this when calculating arc length or determining how far a wheel travels in one full rotation.

3. Area of a Rectangle

$A = lw$ Simple and straightforward. The area of a rectangle is its length multiplied by its width. This is often used in word problems involving floor plans or fencing.

4. Area of a Triangle

$A = \frac{1}{2}bh$ Remember that the base ($b$) and the height ($h$) must always be perpendicular to each other. In a right triangle, the legs serve as the base and height.

5. The Pythagorean Theorem

$a^2 + b^2 = c^2$ Used exclusively for right triangles to find a missing side length. The variable $c$ must always represent the hypotenuse (the longest side, directly opposite the right angle).

6. Properties of Special Right Triangles

The reference sheet provides the ratios for both 45-45-90 and 30-60-90 triangles. For a 45-45-90 triangle, the sides are $x$, $x$, and $x\sqrt{2}$. For a 30-60-90 triangle, the sides are $x$, $x\sqrt{3}$, and $2x$. Knowing these ratios saves you from having to use the Pythagorean theorem or trigonometry.

7. Volume of a Rectangular Prism

$V = lwh$ This is the 3D extension of the area of a rectangle. You will use this to find the capacity of boxes, tanks, or rooms.

8. Volume of a Cylinder

$V = \pi r^2 h$ Think of a cylinder as a stack of circles. You find the area of the base circle ($\pi r^2$) and multiply it by the height of the stack ($h$).

9. Volume of a Sphere

$V = \frac{4}{3}\pi r^3$ Questions involving the volume of a sphere are usually straightforward "plug-and-chug" problems, though they may require you to solve for the radius first.

10. Volume of a Cone

$V = \frac{1}{3}\pi r^2 h$ A cone is exactly one-third the volume of a cylinder with the same base and height.

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The 15 SAT Math Formulas You MUST Memorize

Now we reach the core of your SAT prep. The College Board does not provide these formulas, but they appear on almost every single test. Memorizing them is non-negotiable if you are aiming for a score above 700.

We have categorized these into four main areas: Algebra, Advanced Math, Data Analysis, and Geometry/Trigonometry.

Algebra and Coordinate Geometry

1. The Slope Formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$ What it is: This formula calculates the steepness and direction of a line connecting two points, $(x_1, y_1)$ and $(x_2, y_2)$. When to use it: Whenever you are given two points and asked to find the slope, or when interpreting the "rate of change" in a linear word problem.

2. Slope-Intercept Form

$y = mx + b$ What it is: The most common way to write a linear equation. Here, $m$ represents the slope, and $b$ represents the y-intercept. When to use it: This is your go-to formula for graphing lines or creating equations from word problems. In real-world scenarios, $b$ is your starting value (initial fee, base temperature), and $m$ is your constant rate of change (cost per hour, degrees per minute).

3. Point-Slope Form

$y - y_1 = m(x - x_1)$ What it is: An alternative way to write a linear equation when you know the slope ($m$) and a single point $(x_1, y_1)$ on the line. When to use it: This is a massive time-saver. If a question gives you a slope and a random point, do not waste time plugging them into $y = mx + b$ to solve for $b$. Just drop them straight into point-slope form.

4. The Midpoint Formula

$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ What it is: This finds the exact center point between two coordinates. Notice that it is simply the average of the x-values and the average of the y-values. When to use it: Questions asking for the center of a circle given the endpoints of its diameter, or finding the halfway mark on a map grid.

5. The Distance Formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ What it is: A variation of the Pythagorean theorem used to find the exact distance between two points on a coordinate plane. When to use it: Finding the radius of a circle when given the center and a point on the circumference, or determining the length of a line segment.

Advanced Math (Quadratics and Polynomials)

6. The Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ What it is: The universal method for finding the roots (x-intercepts, solutions, or zeros) of any quadratic equation in the form $ax^2 + bx + c = 0$. When to use it: When a quadratic equation cannot be easily factored. This formula is vital. For a deeper dive into how to master this specific equation, check out our comprehensive Quadratic Formula guide.

7. The Discriminant

$\Delta = b^2 - 4ac$ What it is: The portion of the quadratic formula underneath the square root. When to use it: When a question asks how many solutions a quadratic equation has, rather than what the solutions actually are.

• If $b^2 - 4ac > 0$, there are 2 real solutions.
• If $b^2 - 4ac = 0$, there is 1 real solution.
• If $b^2 - 4ac < 0$, there are 0 real solutions.

8. Vertex Form of a Parabola

$y = a(x - h)^2 + k$ What it is: A way of writing quadratic equations that instantly reveals the vertexThe maximum or minimum point of a parabola. of the parabola at the coordinate $(h, k)$. When to use it: Whenever a problem asks for the maximum or minimum value of a quadratic function (e.g., the maximum height of a thrown ball, or the lowest cost of production).

9. Sum of Solutions (Roots)

$\text{Sum} = -\frac{b}{a}$ What it is: A shortcut to find the sum of the two solutions of a quadratic equation $ax^2 + bx + c = 0$. When to use it: If the SAT asks "What is the sum of the solutions to the given equation?" do not waste time factoring or using the quadratic formula. Just use $-b/a$ to get the answer in three seconds.

10. Product of Solutions (Roots)

$\text{Product} = \frac{c}{a}$ What it is: Similar to the sum shortcut, this finds the product of the two solutions. When to use it: When asked to multiply the roots together. Again, this bypasses the need to actually solve the equation.

Problem Solving and Data Analysis

11. The Average (Mean) Formula

$\text{Average} = \frac{\text{Sum of terms}}{\text{Number of terms}}$

$\text{Sum} = \text{Average} \times \text{Number of terms}$ What it is: The standard formula for calculating the arithmetic mean. When to use it: The SAT rarely just asks you to find an average. Usually, they give you the average and ask you to find a missing number. In these cases, always use the rearranged version: $\text{Sum} = \text{Average} \times \text{Number of terms}$.

12. Percent Change

$\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$ What it is: Calculates the percentage by which a value has increased or decreased. When to use it: Questions involving population growth, discount prices, or inflation. Always remember to divide by the original (old) value, not the new one!

13. Exponential Growth and Decay

$A = P(1 \pm r)^t$ What it is: Models a quantity that grows or shrinks by a constant percentage over time. $P$ is the principal (initial amount), $r$ is the rate (as a decimal), and $t$ is time. When to use it: Compound interest problems, bacteria population growth, or radioactive decay. Use $(1 + r)$ for growth and $(1 - r)$ for decay.

Geometry and Trigonometry

14. Equation of a Circle

$(x - h)^2 + (y - k)^2 = r^2$ What it is: The standard equation for a circle graphed on an x-y coordinate plane. The center of the circle is at $(h, k)$ and the radius is $r$. When to use it: Almost every SAT has a circle equation question. You may need to use the "completing the square" algebraic technique to convert a messy equation into this clean, standard form.

15. Trigonometric Ratios (SOH CAH TOA)

$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$ What it is: The fundamental ratios of right triangle trigonometry. When to use it: Whenever you are given a right triangle and an angle (other than the 90-degree angle) and need to find side lengths.

Bonus Rule: You should also memorize the complementary angle relationship: $\sin(x) = \cos(90 - x)$. If the sine of angle A is $0.6$, the cosine of angle B (the other acute angle) is also $0.6$.

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How to Choose the Right Formula

Memorizing the formulas is only half the battle; knowing when to deploy them is what separates average scores from elite scores. Just as you need to know the Comma Rules for the Reading and Writing section to structure your thoughts, mathematical precision requires choosing the right "grammar" (formulas) for the problem at hand.

Here is a visual breakdown of how to approach a math problem and select the correct algebraic formula:

graph TD
A["Read the SAT Math Problem"] --> B{"Identify the Equation Type"}
B -->|"Variables have an exponent of 1"| C["Linear Equations"]
B -->|"Variables have an exponent of 2"| D["Quadratic Equations"]
C --> E["Slope-Intercept: y = mx + b"]
C --> F["Point-Slope: y - y1 = m(x - x1)"]
D --> G["Vertex Form: Find Max/Min"]
D --> H["Quadratic Formula: Find Roots/Intercepts"]

When you encounter a problem, your first step should always be categorization. Is this a linear model? Is it an exponential model? Once you categorize the problem, your brain will naturally queue up the relevant formulas from your memorized list.

Summary Comparison: What to Memorize vs. What is Given

To help you organize your study plan, here is a quick reference table separating the formulas you must commit to memory versus those you can simply reference on test day.

The Role of Desmos on the Digital SAT

It is impossible to talk about SAT math formulas without addressing the elephant in the room: the built-in Desmos graphing calculator. Desmos is an incredibly powerful tool that allows you to graph equations, find intersections, and identify vertices without doing manual algebra.

However, Desmos does not replace the need for memorization.

If an SAT question asks, "The equation of a circle is $x^2 + y^2 - 6x + 8y = 11$. What is the radius?" you could theoretically type this into Desmos and manually measure the radius. But if you have the circle formula memorized and know how to complete the square, you can find the exact algebraic answer in less time than it takes to type the equation and zoom in on the graph.

Furthermore, many SAT questions use abstract constants (like $ax + by = c$) specifically to prevent you from just plugging numbers into a calculator. In these "calculator-proof" questions, your knowledge of the underlying formulas is your only path to the correct answer.

Final Thoughts on SAT Math Preparation

Do not try to memorize all 15 of these formulas the night before the exam. Use spaced repetition. Write them out on flashcards, or better yet, practice using them in context. The more practice problems you complete, the more these formulas will become second nature. When test day arrives, you won't be relying on rote memorization; you will be relying on deep, structural understanding.

Start integrating these formulas into your daily practice, and watch your math score climb.