Perimeter Calculator

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.

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 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.

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.

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.

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.

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.

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.

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.