# Perimeter Calculator > Free perimeter calculator to find the perimeter of any shape. Calculate perimeter of rectangle, square, triangle, circle, polygon with step-by-step formulas. **URL:** https://calculators.im/perimeter-calculator **Category:** math **Last updated:** 2026-07-03 Calculate the perimeter of any shape including rectangle, square, triangle, circle, parallelogram, trapezoid, ellipse, rhombus, and regular polygons. See step-by-step formulas and unit conversions. This perimeter calculator helps you find the perimeter (or circumference for circles) of any common geometric shape. Select your shape, enter the dimensions, and get instant results with detailed step-by-step calculations, formulas, and area as a bonus. Supports 10 different shapes with unit conversions between metric and imperial. ## Formula ``` Rectangle: P = 2(l + w) | Square: P = 4s | Triangle: P = a + b + c | Circle: C = 2πr | Polygon: P = n × s ``` **Variables:** - **** — - **** — - **** — - **** — - **** — The perimeter is the total distance around a two-dimensional shape. For circles, this is called the circumference. Each shape has its own formula based on its defining dimensions. ## Worked Example ### Rectangle Perimeter Example A rectangle with length 12m and width 8m has a perimeter of 2 × (12 + 8) = 2 × 20 = 40 meters. The area (as a bonus) is 12 × 8 = 96 m². ## Pro Tips - Perimeter is always measured in linear units (m, cm, ft) — not square units - For circles, perimeter = circumference = 2πr ≈ 6.2832 × radius - Regular polygons: just multiply side length by the number of sides - For irregular shapes, measure and add all sides individually - Doubling all sides doubles the perimeter (linear scaling) ## Frequently Asked Questions ### What is the difference between perimeter and area? Perimeter is the total distance around the outside of a shape, measured in linear units (meters, feet). Area is the amount of space inside the shape, measured in square units (m², ft²). Think of perimeter as the length of fence needed to enclose a yard, while area is the amount of grass inside. ### How do you calculate the perimeter of an irregular shape? For irregular shapes, measure each side individually and add all the lengths together. There is no shortcut formula — the perimeter is simply the sum of all outer edges. Use a ruler or measuring tape for physical objects, or coordinates for mathematical problems. ### Is circumference the same as perimeter? Yes, circumference is the specific term for the perimeter of a circle. While 'perimeter' applies to any shape, 'circumference' is used exclusively for circles and is calculated with C = 2πr or C = πd, where r is the radius and d is the diameter. ### How do you find the perimeter of a triangle with only two sides? You cannot find the exact perimeter with only two sides — you need all three. However, if you know two sides and the included angle, you can use the Law of Cosines to find the third side: c² = a² + b² - 2ab·cos(C), then add all three sides for the perimeter. ### What is the formula for the perimeter of a rectangle? The perimeter of a rectangle is P = 2(l + w), or equivalently 2l + 2w, where l is the length and w is the width. For example, a rectangle 12 m long and 8 m wide has a perimeter of 2(12 + 8) = 40 m. Both measurements must be in the same unit before adding. ### How do you find the perimeter of a square? Multiply the side length by 4: P = 4s. A square is a special rectangle with all four sides equal, so a square with 5 m sides has a perimeter of 4 × 5 = 20 m. If you know the perimeter, the side length is s = P ÷ 4. ### How do you calculate the perimeter of a circle? The perimeter of a circle is called the circumference, found with C = 2πr or C = πd, where r is the radius and d is the diameter. A circle with a 3 m radius has a circumference of 2π(3) ≈ 18.85 m. Use π ≈ 3.14159 for hand calculations. ### How do you find the perimeter of a regular polygon? For a regular polygon where every side is equal, multiply the number of sides by the side length: P = n × s. A regular hexagon with 4 cm sides has a perimeter of 6 × 4 = 24 cm, and a regular octagon with 250 mm sides has 8 × 250 = 2000 mm. ### What units is perimeter measured in? Perimeter is always measured in linear units — metres, centimetres, feet, inches, or yards — never in square units. Square units (m², ft²) measure area, the space inside a shape, not the distance around it. Convert perimeter with simple length factors, e.g. 1 m = 3.28084 ft. ### How much fencing do I need for a yard? Calculate the perimeter of the yard, then add about 10% for gates, corners, and cutting waste. A 30 ft × 20 ft yard has a perimeter of 2(30 + 20) = 100 ft, so order roughly 110 ft of fencing. Divide by the panel length (e.g. 8 ft panels = 14 panels) and add a post every panel. ### Can a perimeter calculator handle multiple shapes at once? Yes. For composite shapes — an L-shaped room or a yard combining a rectangle and a semicircle — calculate the perimeter of each outer segment and add only the exposed outer edges, ignoring any internal shared boundaries. This calculator supports 10 individual shapes; combine results manually for composite outlines. ## Deep Dive Perimeter — the total length of the boundary around a two-dimensional shape — is essential for fencing, framing, trim work, border construction, and any project requiring material along edges. From basic rectangles (P = 2l + 2w) and circles (circumference C = 2πr) to irregular polygons and composite shapes, each geometry has specific formulas. A rectangular yard measuring 60 × 40 feet requires P = 2(60) + 2(40) = 200 feet of fencing. A circular garden with 10-foot radius needs C = 2π(10) = 62.8 feet of edging material. Our perimeter calculator supports rectangles, squares, triangles, circles, regular polygons (pentagon through decagon), ellipses, and parallelograms, with results in both metric and imperial units. It also calculates the perimeter of composite shapes formed by combining basic geometries, handles unit conversions, and estimates material quantities with waste factors for real-world project planning. ### Perimeter formulas for common shapes - **Rectangle:** P = 2(l + w). - **Square:** P = 4s. - **Triangle:** P = a + b + c (sum of all three sides). For right triangles, the hypotenuse c = √(a² + b²) via the Pythagorean theorem. - **Circle (circumference):** C = 2πr = πd. - **Regular polygon** with n sides of length s: P = ns — a regular hexagon with 5-inch sides has P = 30 inches. - **Ellipse (approximate):** P ≈ π[3(a+b) - √((3a+b)(a+3b))] using Ramanujan's formula, where a and b are semi-major and semi-minor axes. - **Parallelogram:** P = 2(a + b) where a and b are adjacent sides. - **Trapezoid:** P = a + b + c + d (sum of all four sides). For irregular shapes, measure each side segment individually and sum. ### Practical perimeter applications **Fencing:** always add 10% to calculated perimeter for gate openings, corners, and cutting waste. A 200-foot perimeter needs approximately 220 feet of fencing material. Standard fence panels are 6 or 8 feet long — 200 feet ÷ 8 = 25 panels plus posts every 8 feet (26 posts). **Crown molding and baseboard:** room perimeter minus door openings. A 12×15 foot room has P = 54 feet minus two 3-foot doorways = 48 linear feet of trim needed. Purchase 10-15% extra for miter cut waste at corners. **Garden edging:** for curved beds, lay a garden hose along the desired border and measure its length, or use the circumference formula for circular and semi-circular sections. Always round up when purchasing materials — returning excess costs nothing, but running short delays the project. ### Perimeter vs area: when each matters **Perimeter and area** measure fundamentally different properties and are not directly related. A 10×10 square and a 20×5 rectangle have the same area (100 sq units) but different perimeters (40 vs 50 units) — the more elongated shape has more perimeter per unit area. This relationship matters in construction: a circular house encloses the maximum area for a given perimeter (most efficient use of wall material), while long narrow buildings require more wall material per square foot of floor space. In landscaping, a square garden maximizes growing area for a given amount of fencing. For **heat loss calculations**, perimeter matters because heat escapes through exterior walls — a compact square building loses less heat than a long rectangular building with the same floor area. ### Rectangle Perimeter Calculator: Length and Width A rectangle's perimeter is the sum of all four sides, which simplifies to **P = 2(l + w)** because opposite sides are equal. To use a rectangle perimeter calculator, enter the length and width in the same unit, add them, and double the result. A room that is 14 ft long and 11 ft wide has a perimeter of 2(14 + 11) = 50 ft — the linear footage of baseboard or crown molding you would need before subtracting doorways. For a rectangular pool measuring 8 m × 4 m, the coping runs 2(8 + 4) = 24 m around the edge. A square is a special rectangle where length equals width, so its perimeter collapses to **P = 4s**: a 5-metre square plot needs 4 × 5 = 20 m of fencing. If you know the perimeter and one side, solve for the other with w = P/2 − l. ### Triangle Perimeter Calculator With Three Sides The perimeter of a triangle is simply **P = a + b + c**, the sum of its three side lengths. A triangle perimeter calculator needs all three sides because, unlike a rectangle, no two sides are guaranteed equal. A triangle with sides 6 cm, 8 cm, and 10 cm has a perimeter of 6 + 8 + 10 = 24 cm — and because 6² + 8² = 10², it is also a right triangle. For an **equilateral triangle**, all sides match, so P = 3s. For an **isosceles triangle** with two equal sides a and a base b, P = 2a + b. If you only know two sides and the included angle, find the third side with the Law of Cosines, c = √(a² + b² − 2ab·cos C), then add all three. For a right triangle where only the two legs are known, the hypotenuse comes from the Pythagorean theorem before you can total the perimeter. ### Circle Perimeter Calculator: Circumference The perimeter of a circle has its own name — **circumference** — and is found with C = 2πr or C = πd, where r is the radius and d is the diameter. A circle perimeter calculator multiplies the radius by 2π ≈ 6.2832. A circular garden bed with a 3 m radius has a circumference of 2π(3) ≈ 18.85 m of edging. A round table 1.2 m across (diameter) needs π × 1.2 ≈ 3.77 m of edge trim. Working backward, the radius from a known circumference is r = C ÷ (2π): a running track lane of 400 m around an idealised circle would have r ≈ 63.7 m. For a **semicircle**, the perimeter is half the circumference plus the diameter: P = πr + 2r. For a **circular sector**, add the arc length (θ/360 × 2πr, with θ in degrees) to the two straight radii. ### Polygon Perimeter Calculator for Regular and Irregular Shapes For a **regular polygon** — every side equal — the perimeter is P = n × s, where n is the number of sides and s is the side length. - a regular pentagon with 7-inch sides has P = 5 × 7 = 35 in - a regular hexagon with 4 cm sides has P = 6 × 4 = 24 cm - a regular octagon (stop-sign shape) with 250 mm sides has P = 8 × 250 = 2000 mm A polygon perimeter calculator handles pentagons, hexagons, heptagons, octagons, and beyond by changing n. **Irregular polygons** have no shortcut: measure each edge individually and add them all. For shapes defined by coordinates, compute the distance between consecutive vertices with the distance formula √((x₂−x₁)² + (y₂−y₁)²) and sum every edge, returning to the start point to close the boundary. ### Perimeter Calculator With Unit Conversion Because perimeter is a **linear measurement**, convert it with simple length factors — never square-unit factors. 1 metre = 3.28084 feet, 1 foot = 0.3048 m, 1 metre = 100 cm, 1 inch = 2.54 cm, 1 yard = 3 feet. A perimeter of 200 ft equals 200 × 0.3048 = 60.96 m; a 24 m fence line equals 24 × 3.28084 ≈ 78.7 ft. Always work in one consistent unit before adding sides — mixing feet and inches is the most common perimeter mistake. When buying materials, convert the final perimeter to the unit the product is sold in (fence panels in feet, edging rolls in metres) and round up. Our calculator outputs results in both metric and imperial so you can order materials without a second conversion step. ### How to Calculate Perimeter Step by Step - **Step 1:** Identify the shape — rectangle, square, triangle, circle, regular polygon, or irregular outline — because each has its own formula. - **Step 2:** Measure every dimension the formula needs in a single consistent unit (all metres or all feet). - **Step 3:** Apply the formula: 2(l + w) for a rectangle, 4s for a square, a + b + c for a triangle, 2πr for a circle, n × s for a regular polygon, or the sum of all sides for an irregular shape. - **Step 4:** Add a waste allowance for real projects — typically 10% for fencing (gates, corners, cutting) and 10–15% for trim (mitre cuts). - **Step 5:** Round up to the nearest whole unit or panel when ordering material. **Worked example:** a 30 ft × 20 ft yard → P = 2(30 + 20) = 100 ft → add 10% → order 110 ft of fencing. ## Related Calculators - [area-calculator](https://calculators.im/area-calculator) - [volume-calculator](https://calculators.im/volume-calculator) - [triangle-calculator](https://calculators.im/triangle-calculator) - [ratio-calculator](https://calculators.im/ratio-calculator) ## Authoritative Sources - [Khan Academy - Perimeter](https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter) — Educational resource for perimeter concepts and formulas - [Math is Fun - Perimeter](https://www.mathsisfun.com/geometry/perimeter.html) — Clear explanations of perimeter for various shapes - [Wolfram MathWorld - Perimeter](https://mathworld.wolfram.com/Perimeter.html) — Perimeter definitions and formulas - [Math Open Reference - Perimeter](https://www.mathopenref.com/) — Interactive perimeter references --- *Source: https://calculators.im/perimeter-calculator — calculators.im, 299+ free online calculators.*