SAT Math Formula Sheet: What Is Provided and What to Know

Bluebook provides a reference sheet throughout the SAT Math section. It contains common geometry formulas, special-right-triangle diagrams, volume formulas, and three angle facts. It does not contain every algebraic relationship or statistical definition that might help with a question.

That distinction does not mean you should memorize one enormous list. Use the provided sheet when it helps, and build fluency with unprovided relationships that repeatedly appear in your own practice. This reference separates those two jobs and gives an example of when each relationship is useful.

Table of Contents

• What Bluebook provides
• Reference-sheet formulas and facts
• Algebra relationships worth recognizing
• Advanced Math relationships
• Problem-Solving and Data Analysis relationships
• Geometry and trigonometry beyond the sheet
• How to decide what to learn fluently
• Common formula errors
• Official sources

What Bluebook Provides

College Board states that a reference sheet and calculator are available throughout the Math section. The sheet lists common formulas; it is not a complete map of the four Math domains.

The current sheet provides:

• Circle area and circumference.
• Rectangle and triangle area.
• The Pythagorean theorem.
• Side relationships for 30°-60°-90° and 45°-45°-90° triangles.
• Volumes of a rectangular prism, cylinder, sphere, cone, and rectangular pyramid.
• The facts that a circle contains 360 degrees or 2π radians and that a triangle's interior angles sum to 180 degrees.

The reference sheet is there to be used. Knowing a provided relationship fluently may reduce lookup time, but the article does not treat every provided formula as a mandatory memorization assignment.

Reference-Sheet Formulas and Facts

Circles

Before substituting, confirm whether the given length is a radius or diameter. The formulas use radius. For deeper work with equations, arcs, and sectors, see the SAT Circles skill guide.

Rectangles, Triangles, and Right Triangles

In the Pythagorean theorem, c is the side opposite the right angle. In the triangle-area formula, height must be perpendicular to the chosen base.

Special Right Triangles

The sheet includes diagrams rather than only text:

• 30°-60°-90°: short leg x, long leg x√3, hypotenuse 2x.
• 45°-45°-90°: legs s and s, hypotenuse s√2.

Use these ratios only after the angle information establishes the special triangle. A right triangle is not automatically one of these two types. The Right Triangles and Trigonometry guide covers the identification step.

Volumes

Unit reasoning is a useful check: area uses square units, while volume uses cubic units. The Area and Volume skill guide covers composite figures and scale changes.

Angle Facts

The bottom of the sheet states:

• A circle contains 360°.
• A circle contains 2π radians.
• The interior angles of a triangle total 180°.

These facts support proportional reasoning about arcs, sectors, angle sums, and degree-radian relationships.

Algebra Relationships Worth Recognizing

These relationships are not printed on the geometry reference sheet. Whether you need deliberate recall practice should depend on your error history, but you should be able to derive or recognize them during Math work.

Linear Forms and Slope

Parallel nonvertical lines share a slope. Perpendicular nonvertical lines have slopes whose product is −1. Vertical-line cases need separate reasoning because their slopes are undefined.

The Linear Equations in Two Variables guide connects each form to graphs and context.

Coordinate Relationships

• Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2).
• Distance: √((x₂ − x₁)² + (y₂ − y₁)²).

Both can be derived: midpoint averages corresponding coordinates, while distance applies the Pythagorean theorem to horizontal and vertical changes. Derivation is safer than treating the notation as an unexplained spell.

Exponent Rules

For a common nonzero base where the expressions are defined:

• xᵃ · xᵇ = xᵃ⁺ᵇ
• xᵃ / xᵇ = xᵃ⁻ᵇ
• (xᵃ)ᵇ = xᵃᵇ
• x⁰ = 1
• x⁻ᵃ = 1/xᵃ

The key restriction is the common base. Exponents do not combine this way across addition, and dividing by a variable expression requires attention to values that make the denominator zero.

Systems of Linear Equations

For two lines:

• Different slopes imply one intersection.
• Equal slopes with different intercepts imply no intersection.
• Equivalent equations describe the same line and have infinitely many shared points.

These are relationships to recognize, not a formula to insert blindly. Comparing proportional coefficients can be more direct than converting both equations to slope-intercept form.

Advanced Math Relationships

Quadratics

When the discriminant is positive, there are two distinct real solutions; when it is zero, there is one repeated real solution; when it is negative, there are no real solutions. Keep the entire numerator of the quadratic formula over 2a.

The Nonlinear Equations and Systems guide covers choosing between factoring, graphing, substitution, and the quadratic formula.

Factoring Identities

• Difference of squares: a² − b² = (a + b)(a − b).
• Perfect-square trinomial: a² + 2ab + b² = (a + b)².
• Perfect-square trinomial: a² − 2ab + b² = (a − b)².

Verify the middle term before applying a pattern. For example, a² + b² does not factor as a difference of squares over the real numbers.

Exponential Models

A common form is A(t) = A₀(b)ᵗ, where A₀ is the initial value and b is the factor per time interval.

• Growth rate r: b = 1 + r.
• Decay rate r: b = 1 − r.

The interval matters. A factor of 1.03 means 3% growth per unit represented by one increase in the exponent, not necessarily per calendar year.

Problem-Solving and Data Analysis Relationships

Percents

• Part from a percent: part = decimal rate × whole.
• Percent change: (new − original) / original × 100%.
• Reverse percent: original = final / multiplier.

The denominator in percent change is the original value. For successive changes, multiply their factors rather than simply adding signed percentages. The Percentages skill guide provides targeted examples.

Ratios, Rates, and Proportions

Equivalent ratios satisfy a/b = c/d when denominators are nonzero. Unit labels are often more useful than memorized cross-multiplication: arrange conversion factors so unwanted units cancel.

For a part-to-part ratio a:b, the total contains a + b ratio parts. A 3:5 split does not mean the first group is 3/5 of the total; it is 3/8 of the total. See Ratios, Rates, and Units for dimensional checks.

Mean and Weighted Mean

• Mean: sum of values / number of values.
• Recover a sum: mean × number of values.
• Weighted mean: sum of (value × weight) / sum of weights.

Use the weights as counts or proportions consistently. When combining groups of different sizes, averaging the two group means without weighting generally gives the wrong result.

Probability

For equally likely outcomes, probability = favorable outcomes / total outcomes. In tables and conditional-probability questions, the condition defines the denominator. If the question asks “among students in Group A,” the total for Group A—not the grand total—is the reference group.

Scale and Units

If every length is multiplied by a scale factor k, corresponding areas scale by k² and volumes by k³. This relationship follows from the number of length dimensions being multiplied; it is not listed as a separate formula on the sheet.

Geometry and Trigonometry Beyond the Sheet

Arc Length and Sector Area

For a central angle θ measured in degrees:

• Arc length: (θ/360) · 2πr.
• Sector area: (θ/360) · πr².

These formulas apply the fraction of the full 360-degree circle. When an angle is expressed in radians, reason from the full 2π-radian circle or convert units consistently.

Right-Triangle Trigonometry

Relative to an acute angle θ in a right triangle:

• sin θ = opposite / hypotenuse
• cos θ = adjacent / hypotenuse
• tan θ = opposite / adjacent

The labels opposite and adjacent depend on the chosen angle; the hypotenuse does not. For acute complementary angles, sin θ = cos(90° − θ).

Circle Equations

The standard coordinate form (x − h)² + (y − k)² = r² represents a circle with center (h, k) and radius r. Notice that the signs inside the squared terms are opposite the center coordinates.

When a circle equation is expanded, completing the square can recover center-radius form. Preserve equality by applying the same numerical addition to both sides.

How to Decide What to Learn Fluently

Use practice evidence instead of treating every unprinted relationship as a mandatory recall assignment.

1. Take a mixed Math set or official Bluebook practice test.
2. Mark every item where formula recall, setup, or symbol interpretation slowed you down.
3. Separate provided but slow to locate, unprovided but derivable, and unprovided and not yet fluent relationships.
4. Practice the underlying question type, not the isolated symbols alone.
5. Retest in a mixed set so you must identify which relationship applies.

The official-question workflow guide explains how to choose domain, skill, and difficulty filters without turning practice into a random-question marathon.

Common Formula Errors

• Radius versus diameter: circle and cylinder formulas use radius.
• Area versus circumference: πr² measures square units; 2πr measures linear units.
• Base-height pairing: a triangle's height must be perpendicular to the selected base.
• Missing parentheses: in the quadratic formula, divide the complete numerator by 2a.
• Wrong percent base: percent change divides by the original value.
• Unlabeled units: convert units before comparing or combining quantities.
• Wrong triangle: use a special-triangle ratio only when the angle information supports it.
• Blind substitution: identify what each variable represents before inserting values.

Official Sources

• College Board: Assessment Framework for the Digital SAT Suite
• College Board: The SAT Math Section
• College Board: What to Expect on Test Day

Reference-sheet details last reviewed August 30, 2026. Explanations, organization, and examples are Grind1600 editorial guidance. Grind1600 is not affiliated with College Board.