This is the one-page cheat sheet I wish I’d had in school. Every formula you’ll actually use in geometry — area, perimeter, volume, surface area, angle sums, distance, midpoint, slope — organized by category and ranked by frequency. Bookmark this page for quick reference.
1. Triangle Formulas
- Perimeter: P = a + b + c (any triangle)
- Area: A = ½ × base × height (most common)
- Heron’s formula: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2 — use when only sides are known
- Pythagorean theorem: a² + b² = c² (right triangles only, c = hypotenuse)
- Law of Cosines: c² = a² + b² − 2ab·cos(C) (any triangle)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- 45-45-90 triangle: sides in ratio 1 : 1 : √2
- 30-60-90 triangle: sides in ratio 1 : √3 : 2
→ Try the Triangle Solver
2. Quadrilateral Formulas
- Square: A = s², P = 4s
- Rectangle: A = l × w, P = 2(l + w)
- Parallelogram: A = b × h (perpendicular height, NOT slanted side), P = 2(a + b)
- Rhombus: A = ½ × d₁ × d₂ (diagonals)
- Trapezoid: A = ½ × (b₁ + b₂) × h, midsegment m = (b₁ + b₂)/2
- Kite: A = ½ × d₁ × d₂
→ Try the Quadrilateral Calculator
3. Circle Formulas
- Area: A = π × r²
- Circumference: C = 2π × r = π × d
- Sector area: A = ½ × r² × θ (θ in radians)
- Arc length: L = r × θ (θ in radians)
- Standard equation: (x − h)² + (y − k)² = r² (center (h, k), radius r)
→ Try the Circle Calculator
4. Polygon Formulas
- Sum of interior angles: S = (n − 2) × 180°
- Each interior angle (regular): a = (n − 2) × 180° / n
- Sum of exterior angles: 360° (always, for any convex polygon)
- Each exterior angle (regular): e = 360° / n
- Shoelace formula (any polygon area): A = ½ × |Σᵢ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|
→ Try the Polygon Angle Calculator
5. 3D Solid Formulas
- Cube: V = s³, SA = 6s²
- Rectangular prism: V = l × w × h, SA = 2(lw + lh + wh), space diagonal = √(l² + w² + h²)
- Cylinder: V = πr²h, SA = 2πr² + 2πrh, lateral SA = 2πrh
- Sphere: V = (4/3)πr³, SA = 4πr²
- Cone: V = (1/3)πr²h, SA = πr² + πrl, slant height l = √(r² + h²)
- Square pyramid: V = (1/3) × b² × h
→ Try the Sphere/Cylinder/Cone Calculator
6. Coordinate Geometry Formulas
- Distance: d = √((x₂−x₁)² + (y₂−y₁)²)
- Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)
- Slope: m = (y₂ − y₁) / (x₂ − x₁)
- Section formula (m:n internal): P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
- Slope-intercept: y = mx + b
- Point-slope: y − y₁ = m(x − x₁)
- Parallel lines: m₁ = m₂ | Perpendicular lines: m₁ × m₂ = −1
→ Try the Distance & Midpoint Calculator
How to Use This Cheat Sheet Effectively
- Print it. Paper next to your homework beats scrolling on a phone.
- Test yourself first. Look at a problem, recall the formula from memory, then verify here.
- Re-derive when stuck. Many of these formulas come from one or two basics — perimeter is “add the sides”, area of triangle = ½ × base × height, Pythagorean for right-triangle sides. If you can recover the rest from these, you’ll never feel lost.
- Use the calculators to check your work after solving by hand.
For an interactive version with copy-pasteable formulas and clickable calculator links, see our complete geometry formulas reference page.