Semicircle Calculator: Area, Perimeter, Arc Length and Radius

How it works

Area A = πr² ÷ 2 · Arc length s = πr · Perimeter P = πr + 2r = r(π + 2) · Diameter d = 2r · Centroid ȳ = 4r ÷ (3π) · From area: r = √(2A ÷ π) · From perimeter: r = P ÷ (π + 2) · Largest inscribed square side = 2r ÷ √5 · Largest inscribed rectangle = r√2 × r/√2

A semicircle is half of a circle cut along a diameter, so its area is half the circle’s, πr² ÷ 2. Its outline has two parts: the curved arc, which is half the circumference (πr), and the straight diameter (2r). Adding them gives the perimeter r(π + 2), about 5.14 times the radius. A common mistake is to report only the arc as the perimeter; this calculator shows both so you can pick the one your problem needs (edging for a half-round rug needs the arc, a fence around a half-round patio needs the full perimeter). You can start from any one measurement. The radius is recovered as d ÷ 2, √(2A ÷ π), P ÷ (π + 2) or s ÷ π, and everything else follows. The page also gives the centroid, 4r ÷ (3π) ≈ 0.4244 r above the diameter, which is useful for balancing and statics problems, and the largest circle, square and rectangle that fit inside. The general circle and sector calculators treat a semicircle only as a 180° sector and leave out the straight edge and the centroid; here they are built in.

Worked example

A semicircle with radius 5 cm: area = π × 5² ÷ 2 = 39.2699 cm²; arc length = π × 5 = 15.708 cm; perimeter = 15.708 + 10 = 25.708 cm; diameter = 10 cm. The centroid sits 4 × 5 ÷ (3π) = 2.1221 cm above the diameter, the largest square that fits has side 2 × 5 ÷ √5 = 4.4721 cm, and the largest rectangle is 7.0711 × 3.5355 cm (area 25 cm²).

Sources: Omni Calculator: Semicircle area (2 ft and 10 in worked examples) · Rechneronline: Semicircle calculator · Wikipedia: Semicircle · Wikipedia: List of centroids (semicircle 4r/3π)

Frequently asked questions