Semicircle Area Calculator
Calculate the area and perimeter of a semicircle from its radius or diameter. A semicircle is exactly half of a circle, and this tool computes all its properties instantly.
A semicircle is half of a circle, formed by cutting a circle along its diameter. It consists of a curved arc (half the circumference) and a straight edge (the diameter).
Semicircle Formulas (radius = r):
- Area: A = pi x r^2 / 2
- Perimeter: P = pi x r + 2r = r(pi + 2)
- Curved Arc Length: L = pi x r (half the circumference)
- Diameter: d = 2r
The perimeter of a semicircle includes both the curved arc and the straight diameter. This is a common point of confusion: the perimeter is not just the arc. The arc length alone is pi x r, and adding the diameter (2r) gives the total perimeter r(pi + 2).
Semicircles appear in architecture (arched doorways and windows, Roman arches), engineering (tunnel cross-sections, bridge shapes), protractor design, and decorative elements. The semicircle is also the basis for understanding radians, as the arc of a semicircle subtends an angle of pi radians.