Geometry Formulas
A copy-able sheet of area, perimeter, volume, and surface-area formulas.
Click any formula to copy it.
Labeled diagram — see what each dimension means
A = ½·b·h
Geometry formulas come in four families: area (square A = s², circle A = πr²), perimeter and circumference (C = 2πr), volume (sphere V = (4/3)πr³, cylinder V = πr²h), and surface area (sphere SA = 4πr²). Click any formula above to copy it into your work.
Four families of shape formulas
Most geometry problems reduce to picking the right formula and plugging in numbers. Flat (2D) shapes have an area — the space they cover — and a perimeter, the distance around the edge (a circle’s perimeter is its circumference). Solid (3D) shapes have a volume — the space they fill — and a surface area, the total area of their outer faces.
Reading the symbols
Throughout, s is a side, l and w are length and width, b is a base, h is the perpendicular height, and r is the radius. A capital B means the area of a base face, P is a perimeter, and a is either an apothem (regular polygon) or a parallel side (trapezoid). For a cone, l is the slant height, not the vertical height.
Area of common 2D shapes
b and h are a base and its perpendicular height; r is the radius.
| Shape | Area |
|---|---|
| Square | A = s² |
| Rectangle | A = l·w |
| Triangle | A = ½·b·h |
| Circle | A = πr² |
| Trapezoid | A = ½(a + b)·h |
| Parallelogram | A = b·h |
| Regular polygon | A = ½·a·P |
Volume of common 3D solids
B is the area of the base face; r is the radius, h the height.
| Solid | Volume |
|---|---|
| Cube | V = s³ |
| Rectangular prism | V = l·w·h |
| Sphere | V = (4/3)πr³ |
| Cylinder | V = πr²h |
| Cone | V = ⅓πr²h |
| Pyramid | V = ⅓·B·h |
| Triangular prism | V = ½·b·h·l |
Surface area versus volume
Volume and surface area answer different questions, and they scale differently. Volume measures the space enclosed and grows with the cube of the size; surface area measures the outer skin and grows with the square of the size. Doubling a sphere’s radius multiplies its surface area by 4 (SA = 4πr²) but its volume by 8 (V = (4/3)πr³) — the reason large animals shed heat slowly and small ones quickly.
Every circular formula uses π ≈ 3.14159, the ratio of a circle’s circumference to its diameter. Keep your units consistent: areas come out in square units and volumes in cubic units, so a radius in centimetres gives an area in cm² and a volume in cm³.