Area & Volume
Pick a shape, enter its dimensions, and get the area of a 2D figure or the volume of a 3D solid — with the formula worked through.
Area is a 2D measure, so the answer is in square units (unit²).
To find the area of a circle, square the radius and multiply by π: A = π × r². For a circle with radius r = 5, that is π × 25 ≈ 78.54 square units. Area (a 2D measure) comes out in square units; volume (a 3D measure) comes out in cubic units.
Area and volume — what each one measures
Area measures the flat space inside a 2D shape, so it is always reported in square units (cm², m², in²). Volume measures the space inside a 3D solid, so it is reported in cubic units (cm³, m³, in³). Each shape has its own formula, but they all reduce to multiplying lengths together — area multiplies two lengths, volume multiplies three.
Area and volume formulas
2D shapes give an area; 3D solids give a volume. r is the radius, π ≈ 3.14159.
| Shape | Dimension | Formula | Gives |
|---|---|---|---|
| Rectangle | length l, width w | A = l × w | Area (unit²) |
| Triangle | base b, height h | A = ½ × b × h | Area (unit²) |
| Circle | radius r | A = π × r² | Area (unit²) |
| Box (rectangular prism) | l × w × h | V = l × w × h | Volume (unit³) |
| Cylinder | radius r, height h | V = π × r² × h | Volume (unit³) |
| Sphere | radius r | V = 4⁄3 × π × r³ | Volume (unit³) |
Worked example — area of a circle, r = 5
Pick Circle, enter r = 5, and the calculator follows these steps:
- 1 Choose the shape. Select a 2D shape (rectangle, triangle, circle) for area or a 3D solid (box, cylinder, sphere) for volume. The tool shows only the dimensions that shape needs.
- 2 Enter the dimensions. For a circle that is just the radius, r = 5. Use the same length unit for every dimension you type in.
- 3 Apply the formula. A circle uses A = π × r², so A = π × 5² = π × 25.
- 4 Read the result with its unit. π × 25 ≈ 78.54, an area, so the answer is 78.54 square units (unit²). A volume would instead be in cubic units (unit³).
Keeping units and π straight
Units follow the dimension count. Area is two lengths multiplied, so it is squared (unit²); volume is three lengths multiplied, so it is cubed (unit³). Keep every dimension in the same unit before you calculate — mixing centimetres with metres gives a meaningless answer; convert first. π is the constant ratio of a circle’s circumference to its diameter, about 3.14159; this tool uses the full-precision value and rounds only the displayed result.