Area, perimeter, volume and surface area
Geometry formulas are needed far beyond the classroom: working out how much paint covers a wall, how many tiles a floor needs, how much water a tank holds or how much fabric covers a cushion. This calculator covers the most common flat (2D) and solid (3D) shapes, shows the formula it uses and gives the answer in the right square or cubic units.
How to use the calculator
- Choose the shape and the unit of your measurements.
- Enter the measurements shown. All of them must be in the same unit.
- Read the results and the formula used.
Key formulas
| Shape | Area or volume | Perimeter or surface |
|---|---|---|
| Circle | A = πr² | C = 2πr |
| Rectangle | A = l × w | P = 2(l + w) |
| Triangle | A = ½ × b × h | P = a + b + c |
| Trapezoid | A = ½(a + b) × h | — |
| Cuboid | V = l × w × h | SA = 2(lw + wh + lh) |
| Sphere | V = ⁴⁄₃πr³ | SA = 4πr² |
| Cylinder | V = πr²h | TSA = 2πr(r + h) |
| Cone | V = ⅓πr²h | TSA = πr(r + l) |
Worked examples
- Water tank: a cylindrical tank with radius 0.5 m and height 1.2 m holds π × 0.5² × 1.2 ≈ 0.942 m³. Since 1 m³ = 1,000 litres, that is about 942 litres.
- Pizza: a 12-inch pizza (radius 6) has an area of about 113 in², almost double a 9-inch pizza (63.6 in²).
- Triangle with three sides: sides 5, 6 and 7 give s = 9 and area = √(9 × 4 × 3 × 2) ≈ 14.7, using Heron's formula.
Units matter
Area is measured in square units (cm², m², ft²) and volume in cubic units (cm³, m³). Converting between them is not the same as converting lengths: 1 m = 100 cm, but 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³. Convert your measurements to one unit before entering them, or use the Unit Converter.
Frequently asked questions
What value of π is used?
JavaScript's built-in value, 3.141592653589793. School problems that use 22/7 or 3.14 will give slightly different answers.
How do I find the area of an irregular room?
Split it into rectangles and triangles, calculate each one, and add them up.
What is the slant height of a cone?
The distance from the tip down the side to the edge of the base: l = √(r² + h²).