Perimeter Calculator — square, rectangle, triangle, circle

How it works

The perimeter is the length of the boundary of a two-dimensional shape — the distance you'd walk going all the way around it. For straight-sided shapes it's just the sum of the side lengths; for a circle it has a special name, the circumference:

• Square: 4 × side = 4a
• Rectangle: 2 × (length + width) = 2(a + b)
• Triangle: side + side + side = a + b + c
• Circle: 2 × π × radius = 2πr (the circumference)

Unlike area, perimeter is a length, so it scales linearly with size: double a shape's dimensions and its perimeter simply doubles.

Worked example

A rectangle 5 by 3 has perimeter 2 × (5 + 3) = 16 units. A triangle with sides 3, 4 and 5 has perimeter 3 + 4 + 5 = 12. A circle of radius 4 has circumference 2 × π × 4 = 8π ≈ 25.13. And a square of side 5 is 4 × 5 = 20.

Frequently asked questions

How do I find the perimeter of a rectangle?

Add the length and width and double it: 2 × (a + b). A 5-by-3 rectangle has perimeter 2 × 8 = 16. A square is the case where all four sides are equal, so its perimeter is 4 × side.

How do I find the perimeter of a triangle?

Add its three side lengths: a + b + c. A triangle with sides 6, 8 and 10 has perimeter 24. The three lengths must be able to form a triangle — each side shorter than the sum of the other two — or there is no triangle to measure.

What is a circle's perimeter?

It's called the **circumference**, and it equals 2 × π × radius (or π × diameter). A circle of radius 4 has circumference 8π ≈ 25.13. The constant π is precisely the ratio of any circle's circumference to its diameter.

What's the difference between perimeter and area?

Perimeter is the **distance around** the shape (a length); area is the **space inside** it (a square measure). They answer different questions — fencing a field is a perimeter problem, turfing it is an area problem — and they scale differently: perimeter linearly with size, area with the square of size.

What units does perimeter use?

The same units as the sides you measured — metres in gives metres out, centimetres give centimetres. This calculator treats the dimensions as plain numbers, so keep every side in the same unit and read the perimeter in that unit.

How do I find a side from a known perimeter?

Reverse the formula. A square's side is perimeter ÷ 4. A rectangle's missing side is perimeter ÷ 2 − the known side. A circle's radius is circumference ÷ (2π). Each just undoes the arithmetic of the perimeter formula.