Perimeter Calculator
Pick a shape and enter its sides to get the perimeter of a square, rectangle, triangle, circle, circular sector, trapezoid, ellipse or regular polygon, with the formula worked out.
- FormulaP = 2 × (a + b)
- Substitution2 × (12 + 8) = 40
- In metres0.4 m
In other units of length
How it is calculated
The perimeter is the total length of a flat shape’s boundary, measured in units of length (cm, m). For polygons, add the sides: square 4a, rectangle and parallelogram 2(a + b), triangle a + b + c, trapezoid the four sides, regular polygon n × a. A circle’s perimeter is its circumference: 2πr, or π × diameter. A sector’s perimeter is two radii plus the arc: 2r + 2πr × α ÷ 360. An ellipse’s perimeter has no closed formula in elementary functions; its exact value is a complete elliptic integral: L = 4a × E(k), k² = 1 − b² ÷ a² (NIST DLMF 19.9.9). The calculator uses Ramanujan’s approximation, π(a + b)(1 + 3h ÷ (10 + √(4 − 3h))), h = (a − b)² ÷ (a + b)² (DLMF 19.9.10 without its leading error term 3λ¹⁰ ÷ 2¹⁷; λ² = h); it always comes out slightly short, by less than one part in two thousand even for the flattest ellipse (about 0.04% at most).
4 × a · 2 × (a + b) · a + b + c · 2 × π × ra, b, c: sides · r: radius · π ≈ 3.14159. In order: square, rectangle (and parallelogram), triangle and circle.- Pick the shape; the calculator asks only for the measurements it needs.
- Enter the sides in one unit and choose that unit.
- The perimeter is the sum of all sides; a circle’s is its circumference, 2πr.
- It also checks that the sides can form the shape (the triangle inequality).
Example
A 12 cm × 8 cm rectangle: 2 × (12 + 8) = 40 cm. A circle of radius 5 cm: 2 × π × 5 ≈ 31.42 cm. Fencing a 25 m × 18 m garden takes 2 × (25 + 18) = 86 m of wire, before leaving out a gate.
Frequently asked questions
What is the difference between a circle and its circumference?
The circle’s boundary is the curve of points at one distance from the centre; its length is the circumference (2πr). The area is the size of the region inside it (πr²).
How do I find the circumference from the diameter?
Multiply the diameter by π: C = π × d. A wheel 60 cm across has a circumference of π × 60 ≈ 188.5 cm, the distance it rolls in one turn.
Why are my triangle’s sides rejected?
By the triangle inequality each side must be shorter than the other two together. Sticks of 2, 3 and 6 cm cannot make a triangle, because 2 + 3 < 6.
Which measurements does a trapezoid’s perimeter need?
All four sides: the two bases and the two legs. The height does not enter the perimeter; it is needed only for the area.
How much fencing or skirting board do I need?
Work out the perimeter, subtract doors or gates; leaving some extra for offcuts is advisable (how much depends on the material; there is no rule). A 4 m × 3.5 m room has a 15 m perimeter; less a 90 cm door, 14.1 m.