Area, perimeter, surface area and volume in one place
Geometry questions in homework, DIY and work tend to ask for one of four quantities. Perimeter is the distance around a flat shape (circumference for a circle), measured in ordinary units. Area is the surface a flat shape covers, in square units. Surface area is the total outside surface of a solid, also in square units. Volume is the space a solid fills, in cubic units. This calculator covers nine common shapes: pick the shape, enter its measurements using the guide below, and the headline shows the area (or surface area for solids), with the perimeter or volume alongside.
Which measurement each shape uses
| Shape | Measurement 1 | Measurement 2 | Measurement 3 | Results |
|---|---|---|---|---|
| Circle | Radius | — | — | Area, circumference |
| Rectangle | Length | Width | — | Area, perimeter |
| Square | Side | — | — | Area, perimeter |
| Triangle | Base | Height | — | Area only (perimeter needs all 3 sides) |
| Cube | Side | — | — | Surface area, volume |
| Box | Length | Width | Height | Surface area, volume |
| Sphere | Radius | — | — | Surface area, volume |
| Cylinder | Radius | Height | — | Surface area, volume |
| Cone | Radius | Height | — | Surface area, volume |
Unused measurements are simply ignored, so a circle only reads Measurement 1. Radius means the distance from the centre to the edge — half the diameter. If you were given a diameter, halve it before entering it, the single most common geometry input error.
The formulas
Every volume here is built from a base area times a height, with two famous adjustments: a sphere packs (4/3)πr3, and a cone is exactly one third of the cylinder on the same base and height. The cone surface area needs its slant height — the distance up its sloping side — which Pythagoras gives as √(h2 + r2) from the vertical height and radius. The step-by-step panel substitutes your measurements into the relevant formula so you can audit the arithmetic.
Worked example
A rectangle 8 units long and 5 units wide has area 8 × 5 = 40 square units and perimeter 2 × (8 + 5) = 26 units. A circle of radius 5 has area pi × 25 = about 78.5398 and circumference about 31.4159.
How to use this calculator
- Choose your shape from the list.
- Look at the guide table or the note under the fields to see which measurements that shape uses.
- Enter the measurements in the matching numbered fields — halve a diameter to get a radius first.
- Read the area or surface area in the green panel, and the perimeter or volume in the breakdown.
- Check the substitution steps below to confirm the formula and numbers.
Units: the quiet source of wrong answers
Geometry formulas only work when every measurement shares one unit. A garden 5 metres by 300 centimetres must be converted first (5 m by 3 m, area 15 m2), and areas then come out in square units while volumes come out in cubic units — 1 m2 is 10,000 cm2, not 100, because the conversion factor is squared along with the unit. For real projects, add a margin: paint, tiles, turf and concrete are all easier to over-order slightly than to match later, and cutting waste is real. For circular areas in landscaping or paving, this calculator plus a 5–10% allowance is a solid estimating habit.