Perimeter & Circumference Calculator

Perimeter is the total length of the boundary of a two-dimensional shape, measured in linear units (cm, m, in, etc.). For circular shapes, this boundary length is called the circumference. Our perimeter calculatorcomputes the boundary length for 10 common 2D shapes — from simple squares and circles to right-angled triangles (with automatic hypotenuse calculation), circle sectors (with arc length), and ellipses (using Ramanujan's approximation). The formula is displayed for every shape so you always understand the calculation. All results are instant and run entirely in your browser.

1. 1. Select a Shape and Unit: Choose from 10 two-dimensional shapes using the shape selector. Select your unit of measurement (mm, cm, m, km, in, ft, or yd) — the perimeter result will be labelled in the same linear unit.
2. 2. Enter the Dimensions: Fill in the required dimensions for your chosen shape. The formula is displayed above the inputs so you always know what each field represents. All inputs accept integers and decimals.
3. 3. Get Instant Results: Click Calculate Perimeter and instantly see the perimeter or circumference, plus any extras (hypotenuse for right triangles, arc length for sectors). All processing happens locally in your browser — your dimensions are never sent to any server.

• Square & Rectangle: Square perimeter = 4a where a is the side length. Rectangle perimeter = 2(w + h). These are the most common shapes for room boundaries, garden fencing, and frame borders.
• Circle & Circle Sector: Circle circumference = 2πr. A circle sector perimeter = arc length + 2r, where arc length = (θ/360) × 2πr. The sector mode also shows the arc length separately as an extra result.
• Triangle — Two Methods: Triangle (three sides): perimeter = a + b + c, with triangle inequality validation. Right-angled triangle: enter base and height — the calculator computes the hypotenuse c = √(a² + b²) using the Pythagorean theorem, then returns perimeter = a + b + c with the hypotenuse shown separately.
• Trapezoid & Parallelogram: Trapezoid perimeter = a + b + c + d (all four sides). Parallelogram perimeter = 2(a + b) where a is the base and b is the slant side. Both shapes require all side lengths as inputs.
• Ellipse — Ramanujan's Approximation: Ellipses have no exact closed-form perimeter formula — they require elliptic integrals. Our perimeter calculator uses Ramanujan's first approximation: P ≈ π[3(a+b) − √((3a+b)(a+3b))], which is accurate to within 0.1% for most practical ellipses.
• Regular Polygon: A regular polygon with n equal sides of length s: perimeter = n × s. Works for any polygon with 3 or more sides — triangle, pentagon (5), hexagon (6), octagon (8), and beyond.

Our perimeter calculator uses JavaScript's 64-bit floating-point arithmetic (IEEE 754 double precision), providing approximately 15–17 significant digits of precision. The ellipse circumference uses Ramanujan's first approximation (P ≈ π[3(a+b) − √((3a+b)(a+3b))]), which is accurate to within 0.1% for most practical ellipses. For the triangle (three sides) mode, the calculator validates the triangle inequality and throws a clear error if the sides cannot form a valid triangle. Results are formatted to up to 6 decimal places, with scientific notation used for very large or very small values.