# What is the perimeter? 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. - Page: https://www.acalculator.org/math/perimeter-calculator - JSON spec: https://www.acalculator.org/math/perimeter-calculator.json - Version: 059874a6375b ## Default answer Example with the default inputs (Shape Rectangle or parallelogram, Length 32, Width 20): The perimeter is 104. ## Inputs | Key | Label | Description | | --- | --- | --- | | shape | Shape | The shape whose perimeter you want. | | a | Side a | The length of one side. | | l | Length | The length of the rectangle (or one side of the parallelogram). | | w | Width | The width of the rectangle (or the other side of the parallelogram). | | b | Side b | The length of the second side. | | c | Side c | The length of the third side. | | r | Radius | The distance from the centre to the edge: half the diameter. | | n | Number of sides | How many equal sides the regular polygon has, from 3 to 1,000. | | s | Side length | The length of each side of the regular polygon. | | sides | Side lengths | The length of every side, in order, separated by commas: 3 to 100 sides. | ## Outputs | Key | Label | Description | | --- | --- | --- | | perimeter | Perimeter | The total length around the shape, in the unit of the lengths you typed. | | formula | Working | The formula with your numbers. | | diameter | Diameter | For a circle: twice the radius. | ## 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. ## Assumptions - 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 1. shape = rectangle, l = 32, w = 20 gives perimeter = 104, formula = 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). 2. shape = triangle, a = 4, b = 9, 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). 3. shape = circle, r = 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). 4. shape = square, 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). 5. shape = regular, n = 6, s = 4 gives perimeter = 24, formula = 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). 6. shape = polygon, sides = 10 or 6 gives perimeter = 25, formula = 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). ## FAQ ### 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. ## Sources - 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; Example 9.34: sides 4 ft and 9 ft with P = 24 ft leave 11 ft). https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-02) - 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)