Shape Calculator
Work out area, perimeter, surface area or volume for common shapes, from rectangles and circles through to cylinders, cones and spheres.
Formula
Cube: V = s³ · Sphere: V = ⁴⁄₃πr³ · Cylinder: V = πr²h
- Surface area and volume scale differently: double a length and area goes up 4×, volume 8×
A cylinder of radius 3 and height 10: π × 9 × 10 = 282.74
Choosing the Right Measure
Three different questions, three different units:
- Perimeter is the distance around a shape, in metres — fencing, skirting, edging.
- Area is the surface covered, in square metres — paint, turf, carpet.
- Volume is the space enclosed, in cubic metres — concrete, water, soil.
Getting the wrong one is the commonest error in practical work, and the units give it away: an answer in m² when you needed m³ means you missed a dimension.
Surface Area Versus Volume
For 3D shapes these answer different jobs: surface area tells you how much paint or cladding you need, volume how much the shape holds.
They also scale differently, which has real consequences. Doubling a cube's side multiplies surface area by four and volume by eight, so the ratio of surface to volume falls as things get bigger.
This is why small animals lose heat faster than large ones, why crushed ice melts quicker than a block, and why cooking times do not scale neatly with portion size.
Breaking Down Awkward Shapes
Real rooms and gardens are rarely simple rectangles. The reliable approach is to split an irregular shape into rectangles, triangles and part-circles, calculate each, and add them together — subtracting any voids such as alcoves or a pond.
Keep every measurement in the same unit before you start. Mixing centimetres with metres is the single most frequent source of wrong answers, and the mistake is invisible until the delivery arrives.
Quick Reference
| Solid | Volume | Surface area |
|---|---|---|
| Cube | s³ | 6s² |
| Cuboid | l × w × h | 2(lw + lh + wh) |
| Sphere | ⁴⁄₃πr³ | 4πr² |
| Cylinder | πr²h | 2πr² + 2πrh |
| Cone | ⅓πr²h | πr² + πrl |
Frequently Asked Questions
- What is the difference between area and volume?
- Area measures a surface in square units, volume the space enclosed in cubic units. Paint needs area; concrete needs volume.
- How do I calculate an irregular shape?
- Divide it into rectangles, triangles and part-circles, work out each, then add them and subtract any voids.
- Why does surface area matter separately from volume?
- Surface area determines coverings such as paint or cladding, and it scales more slowly than volume, which is why large objects have relatively less surface per unit of content.
- Why are my answers out by a large factor?
- Almost always mixed units. Convert everything to the same unit before calculating, since errors are squared for area and cubed for volume.