Area is how much surface something covers; perimeter is how far it is around the edge. You need the first for paint, turf and tiles, and the second for fencing, skirting and trim. They are not interchangeable: two shapes with the same perimeter can enclose very different areas, which is why a circle uses the least fence for the most ground.

Using it in three steps

1. 1 Choose the shape. The boxes change to ask for exactly the measurements that shape needs, and nothing else.
2. 2 Enter the measurements in one unit and stick to it. Mixing metres with centimetres gives a number that looks fine and is wrong.
3. 3 Read the area in square units of whatever you entered, and the perimeter in the same units you typed.

Why some perimeters are missing

A base and a height fix the area of a triangle but not its shape: you can slide the top corner sideways as far as you like, keeping the same area while the two slanted sides grow without limit. There is no single perimeter to report, so the tool says so instead of printing a number that would only be true for one of infinitely many triangles.

The ellipse is the odd one out

Its area is simply π times the two radii, but its perimeter cannot be written as a finite formula at all - it needs an infinite series. The figure shown here uses Ramanujan's approximation, which is accurate to better than one part in a billion for ordinary ellipses and returns the exact 2πr when the two radii are equal.