What is the formula for the area of a semicircle?

The area of a semicircle is A = (π × r²) / 2, where r is the radius. This is simply half the area of a full circle with the same radius.

What is the perimeter of a semicircle?

The perimeter (total boundary length) of a semicircle is P = π × r + 2r = r(π + 2), where r is the radius. It includes the curved arc (πr) plus the straight diameter (2r).

How do I calculate the area from the diameter?

If you know the diameter (d), the radius is r = d / 2. Substitute into the formula: A = (π × (d/2)²) / 2 = π × d² / 8.

What units does this calculator support?

You can enter measurements in millimeters, centimeters, meters, inches, or feet. Area is returned in the corresponding square unit (e.g., cm²) and perimeter in the linear unit (e.g., cm).

What is the difference between the arc length and the perimeter?

The arc length of a semicircle is just the curved part: πr. The perimeter (total boundary) also includes the straight diameter: πr + 2r. This calculator shows both values.

Is a semicircle half of a circle?

Yes. A semicircle is exactly one half of a circle, created by cutting the circle along a diameter. Its area is exactly half the area of the full circle.

Area of a Semicircle Calculator

Name: Area of a Semicircle Calculator
Availability: InStock
Author: Nham Vu

Enter a radius or diameter to instantly calculate the area and perimeter of a semicircle with step-by-step working.

Calculator Inputs

Input mode

Radius (r)

Unit

Area

—

Perimeter

—

Arc length (curved part only)

—

Semicircle diagram

r = radius | d = diameter

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Summary

Enter a radius or diameter to instantly calculate the area and perimeter of a semicircle with step-by-step working.

How it works

Choose whether you want to enter the radius or the diameter.
Type the measurement value in the input field.
Select your preferred unit (mm, cm, m, in, or ft).
Click "Calculate" to apply the formulas.
Area and perimeter results appear instantly with step-by-step working.

Use cases

Geometry homework and exam problems involving semicircles.
Architecture and design — calculating half-circle window or arch dimensions.
Engineering problems with semicircular cross-sections or channels.
Landscaping — estimating material for a half-circle garden bed.
Flooring and tiling work requiring half-circle area measurements.
Woodworking projects that use semicircular cuts.
Verifying manual semicircle calculations quickly.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu