What is the difference between arc length and perimeter?

Arc length is just the curved part of the semicircle (πr). Perimeter includes both the arc length and the diameter edge, so P = πr + 2r = r(π + 2).

Why is the semicircle area half of the circle area?

A semicircle is exactly half of a full circle. Since the full circle area is A = πr², the semicircle area is A = (1/2)πr².

Do I need to include the diameter in the perimeter?

It depends on the context. If you need the full boundary length (including the straight edge), use P = πr + 2r. If you only need the curved arc length, use L = πr.

Semicircle Area Calculator

Calculate the area and perimeter of a semicircle using radius or diameter. This calculator provides formulas for both area and perimeter, including the distinction between arc length and full perimeter.

Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)

Semicircle Area Calculator

Input Type

Radius (r)

How It Works

Semicircle area formula: A = (1/2)πr², which is exactly half of the full circle area.

Arc length of semicircle: L = πr (half of the full circle circumference).

Perimeter of semicircle (including the diameter): P = πr + 2r = r(π + 2).

The perimeter includes both the curved arc and the straight diameter edge.

The area is proportional to the square of the radius, just like a full circle.

Step-by-step Examples

Example 1: Using Radius

Calculate the area and perimeter of a semicircle with radius 5 units.

Given: r = 5
Area: A = (1/2)πr² = (1/2)π × 5² = (1/2)π × 25 = 12.5π ≈ 39.27 square units
Arc length: L = πr = π × 5 = 5π ≈ 15.71 units
Perimeter (including diameter): P = πr + 2r = 5π + 10 ≈ 25.71 units

Example 2: Using Diameter

Find the area and perimeter when diameter is 12 units.

Given: d = 12
Radius: r = d/2 = 12/2 = 6
Area: A = (1/2)πr² = (1/2)π × 6² = 18π ≈ 56.55 square units
Perimeter: P = πr + 2r = 6π + 12 ≈ 30.85 units

Common Mistakes

Forgetting to include the diameter when calculating the full perimeter.
Confusing arc length with perimeter - arc length is just the curved part, perimeter includes the diameter.
Using the full circle area formula instead of half: A = πr² instead of A = (1/2)πr².
Not maintaining unit consistency between radius/diameter and area/perimeter.

Use Cases

Architecture: Calculating areas and perimeters of semicircular windows and arches.
Engineering: Determining material requirements for semicircular components.
Mathematics: Solving geometry problems involving semicircles.
Design: Planning semicircular features in layouts and blueprints.
Construction: Estimating materials for semicircular structures.

Frequently Asked Questions

Common questions about semicircle area calculations.

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