# Semicircle Area Calculator

Calculate semicircle area and perimeter from radius or diameter. Free online semicircle calculator with instant results for area, perimeter.

## What this calculates

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.

## Inputs

- **Input Type** — options: Radius, Diameter — Choose whether to enter the radius or diameter.
- **Value** — min 0 — The radius or diameter of the semicircle.

## Outputs

- **Area** — The area of the semicircle.
- **Perimeter** — The total perimeter (curved arc + straight diameter).
- **Radius** — The radius of the semicircle.
- **Diameter** — The diameter (straight edge) of the semicircle.

## Details

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.

## Frequently Asked Questions

**Q: How do I calculate the area of a semicircle?**

A: The area of a semicircle is exactly half the area of the full circle: A = pi x r^2 / 2. If you know the diameter d, first find the radius (r = d/2), then apply the formula. For example, a semicircle with radius 7 has area = pi x 49 / 2 = 76.969 square units.

**Q: How do I find the perimeter of a semicircle?**

A: The perimeter of a semicircle is the curved arc plus the straight diameter: P = pi x r + 2r = r(pi + 2). For a semicircle with radius 5: P = 5(3.14159 + 2) = 5 x 5.14159 = 25.708 units. Do not forget to include the diameter in the perimeter.

**Q: Is the perimeter of a semicircle half the circumference of a circle?**

A: No. The arc length of a semicircle is half the circumference (pi x r), but the perimeter also includes the straight diameter (2r). So the total perimeter is pi x r + 2r, which is more than half the circumference. Half the circumference would only be correct if the semicircle were an open arc without the straight edge.

**Q: What is the relationship between a semicircle and a protractor?**

A: A protractor is shaped like a semicircle and measures angles from 0 to 180 degrees. The straight edge (diameter) represents the baseline (0 and 180 degrees), and the curved edge is marked with degree measurements. The semicircle subtends an angle of 180 degrees, or pi radians.

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Source: https://vastcalc.com/calculators/math/semicircle-area
Category: Math
Last updated: 2026-04-21