SAT Formula Sheet

Every Digital SAT math formula and the key grammar rules — for quick review.

Geometry & Measurement

Circle areaA = πr²

Circle circumferenceC = 2πr

Rectangle areaA = lw

Triangle areaA = ½bh

Rectangular prism volumeV = lwh

Cylinder volumeV = πr²h

Sphere volumeV = 4⁄3 πr³

Cone volumeV = 1⁄3 πr²h

Pythagorean theorema² + b² = c²

Sum of triangle angles180°

Arc/sectorfraction of 360° × (2πr or πr²)

Slopem = (y₂ − y₁) / (x₂ − x₁)

Line equation (slope-intercept)y = mx + b

Point-slope formy − y₁ = m(x − x₁)

Distance between points√[(x₂−x₁)² + (y₂−y₁)²]

Midpoint((x₁+x₂)/2, (y₁+y₂)/2)

DiscriminantD = b² − 4ac

Quadratic formulax = (−b ± √D) / 2a

Parabola vertexx = −b / 2a

Percent change(new − old) / old × 100%

Meansum / count

Probabilityfavorable / total outcomes

Exponential growthy = a(1 + r)ᵗ

Exponential decayy = a(1 − r)ᵗ

Direct proportiony = kx

Sinesin θ = opposite / hypotenuse

Cosinecos θ = adjacent / hypotenuse

Tangenttan θ = opposite / adjacent

Radiansπ rad = 180°

Subject–verb agreementThe verb agrees with the subject in number, even if a phrase is inserted between them.

Pronoun agreementA pronoun matches its antecedent in number and gender; avoid unclear reference.

Comma spliceTwo independent clauses can't be joined with just a comma — use a semicolon or a conjunction.

SemicolonJoins two independent, closely related clauses.

ColonAfter an independent clause — introduces a list, explanation, or quotation.

Dashes (paired)Set off an aside — like paired commas, but stronger.

ModifiersA modifier sits next to the word it describes (a dangling modifier is an error).

ParallelismItems in a list or comparison share the same grammatical form.

Apostrophesits = possessive, it's = it is; possessive plural = s'.

Transitionshowever (contrast), therefore (consequence), moreover (addition), for instance (example).