A one-page geometry reference covering area, perimeter, volume, surface area, triangles, circles, angles, and coordinate formulas. For worked explanations of each, see Geometry Formulas Explained.
Perimeter and area (2D shapes)
| Shape | Perimeter / Circumference | Area |
|---|---|---|
| Square (side s) | 4s | s² |
| Rectangle (l, w) | 2(l + w) | l × w |
| Triangle (base b, height h) | a + b + c | ½ b h |
| Parallelogram (b, h) | 2(a + b) | b h |
| Trapezoid (parallel a, b; h) | sum of sides | ½(a + b) h |
| Circle (radius r) | 2πr | πr² |
Volume and surface area (3D solids)
| Solid | Volume | Surface area |
|---|---|---|
| Cube (s) | s³ | 6s² |
| Rectangular prism (l, w, h) | l w h | 2(lw + lh + wh) |
| Cylinder (r, h) | πr²h | 2πr² + 2πr h |
| Cone (r, h, slant l) | ⅓πr²h | πr² + πr l |
| Sphere (r) | ⅔πr³ (4/3 πr³) | 4πr² |
| Square pyramid (base b, slant l) | ⅓b²h | b² + 2b l |
Triangles
| Topic | Formula |
|---|---|
| Pythagorean theorem | a² + b² = c² |
| Triangle area | ½ × base × height |
| Heron’s area (s = (a+b+c)/2) | √(s(s−a)(s−b)(s−c)) |
| 45-45-90 triangle sides | 1 : 1 : √2 |
| 30-60-90 triangle sides | 1 : √3 : 2 |
| Angle sum of a triangle | 180° |
Circles
| Circle measure | Formula |
|---|---|
| Circumference | 2πr or πd |
| Area | πr² |
| Arc length (angle θ in degrees) | (θ / 360) × 2πr |
| Sector area | (θ / 360) × πr² |
Angles and polygons
| Angles and polygons | Rule |
|---|---|
| Interior angle sum of an n-gon | (n − 2) × 180° |
| Each interior angle (regular n-gon) | (n − 2) × 180° / n |
| Complementary angles | sum = 90° |
| Supplementary angles | sum = 180° |
Coordinate geometry
| Coordinate geometry | Formula |
|---|---|
| Distance between two points | √((x₂−x₁)² + (y₂−y₁)²) |
| Midpoint | ((x₁+x₂)/2, (y₁+y₂)/2) |
| Slope | (y₂ − y₁) / (x₂ − x₁) |
Related: Area Formula Chart, Volume Formula Chart, Circle Formula Chart, and Triangle Formula Chart.