What is the perimeter?
Pick a shape and type its sides, or the radius of a circle. The perimeter calculator adds up the distance around it and shows the formula with your numbers. The answer is in the same unit as your lengths.
- Perimeter
- 104
The perimeter is 104.
- Working
- P = 2L + 2W = 2 × 32 + 2 × 20 = 104
Perimeter: 104. The perimeter is 104.
How to calculate
Finds the perimeter of a square, rectangle, triangle, circle (its circumference), regular polygon, or any polygon from its side lengths, with the formula worked out.
Example with the default inputs (Shape Rectangle or parallelogram, Length 32, Width 20): The perimeter is 104.
Method: Square P = 4a; rectangle or parallelogram P = 2L + 2W; triangle P = a + b + c; circle C = 2πr; regular polygon P = n × s; any polygon P = the sum of its sides.
- Lengths are in any one unit; the perimeter is in the same unit.
- A triangle’s longest side must be shorter than the other two together; a polygon’s longest side shorter than all the others together.
- The circumference uses π to double precision, not 3.14.
Worked examples
Each example is checked against the calculator on every build.
- Shape Rectangle or parallelogram, Length 32, Width 20 gives Perimeter 104, Working P = 2L + 2W = 2 × 32 + 2 × 20 = 104.Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids (P = 2L + 2W, P = a + b + c; Example 9.27: a 32 m by 20 m rectangle has P = 104 m), https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-02)
- Shape Triangle, Side a 4, Side b 9, Side c 11 gives Perimeter 24.Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids (P = 2L + 2W, P = a + b + c; Example 9.27: a 32 m by 20 m rectangle has P = 104 m), https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-02)
- Shape Circle (circumference), Radius 2 gives Perimeter 12.566371, Diameter 4.Source: OpenStax, Prealgebra 2e, §9.5 Solve Geometry Applications: Circles and Irregular Figures (C = 2πr = πd; Example 9.42: a 4 ft diameter gives C ≈ 12.56 ft with π ≈ 3.14), https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures (retrieved 2026-10-02)
- Shape Square, Side a 31 gives Perimeter 124.Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids (P = 2L + 2W, P = a + b + c; Example 9.27: a 32 m by 20 m rectangle has P = 104 m), https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-02)
- Shape Regular polygon, Number of sides 6, Side length 4 gives Perimeter 24, Working P = n × s = 6 × 4 = 24.Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids (P = 2L + 2W, P = a + b + c; Example 9.27: a 32 m by 20 m rectangle has P = 104 m), https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-02)
- Shape Any polygon (all sides), Side lengths 10, 6, 4, 5 gives Perimeter 25, Working P = 10 + 6 + 4 + 5 = 25.Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids (P = 2L + 2W, P = a + b + c; Example 9.27: a 32 m by 20 m rectangle has P = 104 m), https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-02)
How it works
| Shape | Perimeter |
|---|---|
| Square with side a | P = 4a |
| Rectangle (length L, width W), or parallelogram with sides L and W | P = 2L + 2W |
| Triangle with sides a, b, c | P = a + b + c |
| Circle with radius r | C = 2πr (the diameter is 2r) |
| Regular polygon with n sides of length s | P = n × s |
| Any polygon with sides s₁, s₂, …, sₖ | P = s₁ + s₂ + … + sₖ |
All sums are in double-precision floating point, and π is Math.PI (3.141592653589793). OpenStax’s Prealgebra 2e is used because Algebra and Trigonometry 2e has no perimeter section.
Rules
- Every length is more than 0 and at most 10¹² (any one unit). A regular polygon has 3 to 1,000 sides; any polygon has 3 to 100 sides, each more than 0.
- A triangle needs its longest side shorter than the sum of the other two; otherwise there is no answer. Any polygon needs its longest side shorter than the sum of all the others; otherwise there is no answer.
- A polygon perimeter beyond the largest double-precision number has no answer.
Output format. The perimeter and diameter are numbers in the unit typed. The working shows each number to 10 significant digits, for example “P = 2L + 2W = 2 × 32 + 2 × 20 = 104”, “C = 2πr = 2 × π × 2 = 12.56637061”, or “P = 10 + 6 + 4 + 5 = 25”.
Worked examples by hand
Rectangle 32 by 20. P = 2 × 32 + 2 × 20 = 64 + 40 = 104.
Triangle 4, 9, 11. P = 4 + 9 + 11 = 24 (11 < 4 + 9 = 13, so it is a triangle).
Circle with radius 2 (a 4 ft table). C = 2 × π × 2 = 4π ≈ 12.566371; the diameter is 4.
Square with side 31. P = 4 × 31 = 124.
Regular hexagon with side 4. P = 6 × 4 = 24.
Trapezoid with sides 10, 6, 4, 5. P = 10 + 6 + 4 + 5 = 25 (10 < 6 + 4 + 5 = 15).
Other questions people ask
What is a perimeter?
The total length of the edges around a flat shape: how much fence goes around a yard, or trim around a picture. It is a length, so it is measured in inches, feet, or meters, not square units.
How do I find the perimeter of a rectangle?
Add twice the length and twice the width: P = 2L + 2W. A rectangle 32 m long and 20 m wide has P = 64 + 40 = 104 m. A parallelogram works the same way with its two side lengths.
How do I find the perimeter of a triangle?
Add the three sides: P = a + b + c. Sides of 4, 9 and 11 ft give 24 ft. The longest side must be shorter than the other two added together, or the sides do not meet.
What is the perimeter of a circle?
It is called the circumference: C = 2πr, or π times the diameter. A table 4 ft across (radius 2 ft) has C = 4π ≈ 12.57 ft. With π rounded to 3.14 you get 12.56 ft.
How do I find the perimeter of a trapezoid or another polygon?
Add the lengths of all its sides. Pick “Any polygon” and type every side, such as 10, 6, 4, 5 for a trapezoid: the perimeter is 25.
How do I find the perimeter of a regular polygon?
Multiply the number of sides by the side length: P = n × s. A regular hexagon with 4 cm sides has P = 6 × 4 = 24 cm.
What is the difference between perimeter and area?
Perimeter is the length around a shape; area is the space inside it, in square units. A 32 m by 20 m rectangle has a perimeter of 104 m and an area of 640 m².