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Math & Statisticsgeometry

Perimeter Calculator

Perimeter and the area it encloses. For a fixed perimeter a circle encloses the most area of any shape, which is why the ratio is shown.

Also called: circumference calculator, distance around.

Perimeter
18

The perimeter is 18 units, enclosing an area of 20. A circle of the same perimeter would enclose more area than this.

Area enclosed
20
Area per unit of perimeter
1.11
On enclosing efficiency
A circle of the same perimeter would enclose more area than this.
How this is calculated
Method and background

How this is calculated

The distance around the figure. The ratio of area to perimeter is worth seeing because it answers the practical question: fencing a field or edging a room costs by the perimeter and delivers the area, and for any given perimeter a circle encloses more than any other shape, with a square the best of the rectangles.

perimeter is the distance around the figure
a, b
The dimensions

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a rectangle

Shape
Rectangle
First dimension
5
Second dimension
4
Third dimension
0

Perimeter18

arithmetic identity

Open this example

a circle of radius five

Shape
Circle
First dimension
5
Second dimension
0
Third dimension
0

Perimeter31.42

2 pi r and pi r squared, computed independently

Open this example

Method and limits

What it assumes

  • Consistent units.

What it deliberately does not model

  • A trapezoid needs its slant sides, which are not asked for, so its perimeter is not returned.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Which shape encloses the most area for a given perimeter?
A circle, always. Among rectangles it is the square. That is the isoperimetric inequality, and it is why a fence encloses most land in a circle and least in a long thin strip.