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SAT Geometry & Trigonometry Formula Sheet

Every formula on the SAT reference sheet plus the trig identities and circle equations you need for the Geometry & Trigonometry domain.

Below are the 23 formulas tested in this category, with the situation each one applies to. Drill until you can write the whole sheet from memory in under two minutes — that's the standard top scorers reach by test day.

Each formula links back to the topic page where it's worked into example problems. If a formula doesn't yet feel automatic, click into the topic page and grind that topic's six practice questions.

Formulas

ConceptFormulaWhen to use it
Area of triangle A = ½ b h Base and perpendicular height.
Area of rectangle A = ℓ w Length × width.
Area of trapezoid A = ½ (b₁ + b₂) h Average of bases × height.
Area of circle A = π r² r = radius.
Circumference of circle C = 2 π r r = radius, or πd.
Pythagorean theorem a² + b² = c² Right triangle, c = hypotenuse.
45-45-90 triangle sides 1 : 1 : √2 Both legs equal.
30-60-90 triangle sides 1 : √3 : 2 Short leg : long leg : hyp.
Volume of rectangular prism V = ℓ w h Box.
Volume of cylinder V = π r² h Circle base × height.
Volume of sphere V = ⁴⁄₃ π r³ Solid ball.
Volume of cone V = ⅓ π r² h ⅓ of cylinder volume.
Volume of pyramid V = ⅓ ℓ w h ⅓ of corresponding prism.
Sum of interior angles (n − 2) · 180° For an n-sided polygon.
Each interior angle (regular) (n − 2) · 180° / n Regular polygon.
Equation of a circle (x − h)² + (y − k)² = r² Centre (h,k), radius r.
Sine sin θ = opposite / hypotenuse SOH.
Cosine cos θ = adjacent / hypotenuse CAH.
Tangent tan θ = opposite / adjacent TOA.
Pythagorean identity sin² θ + cos² θ = 1 For any angle θ.
Arc length s = r θ θ in radians.
Sector area A = ½ r² θ θ in radians.
Degree-radian conversion 180° = π rad Multiply by π/180 or 180/π.

How to memorise this sheet in a week

Day 1. Read every row out loud. Connect each formula to a worked example by clicking into the topic page on which it appears. Goal: understand why each formula is true, not just memorise it.

Day 2. Cover the right-hand columns and quiz yourself on each concept. Write the formula and the use case from memory. Mark the ones you missed.

Day 3. Re-quiz only the ones you missed yesterday. Keep cycling until your error count hits zero.

Day 4. Re-do the full quiz. You should know every row.

Day 5. Apply each formula in a problem context — pick a topic page from the list below and solve all six questions.

Day 6–7. Sit a real past paper. Note any formulas you blanked on under time pressure and add them back to your daily quiz.

Topics that use these formulas

Common mistakes when applying these formulas

Three errors account for the majority of dropped points on formula-driven questions:

  • Substituting before simplifying. Always simplify symbolically as far as you can before plugging numbers in. It cuts arithmetic errors in half.
  • Mixing units. If a formula expects metres and you have centimetres, convert first, not at the end. The number you compute is meaningless until the units agree.
  • Forgetting the ½ in area or volume formulas. Triangle, trapezoid, sector, cone, pyramid — all have a ½ or ⅓ that's easy to drop. Write the formula on the page before plugging in.