What is the formula for the perimeter of a semicircle?

The perimeter of a semicircle is P = πr + 2r = r(π + 2), where r is the radius. It combines the curved arc length (πr) and the straight diameter (2r).

Why does the perimeter include the diameter?

The perimeter is the total boundary of a shape. For a semicircle, the boundary consists of the curved arc AND the straight edge across the flat side (the diameter), so both must be added together.

How do I find the perimeter from the diameter?

Divide the diameter by 2 to get the radius, then apply P = r(π + 2). Equivalently, P = (d/2)(π + 2) = d(π + 2)/2.

What is the difference between arc length and perimeter?

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

What units does this calculator support?

You can enter measurements in millimeters (mm), centimeters (cm), meters (m), inches (in), or feet (ft). All three outputs (arc, diameter, perimeter) use the same linear unit.

Can I use this for a half-circle with a known diameter?

Yes. Switch the input mode to "Diameter," enter your value, and the calculator converts it to radius internally before computing the perimeter.

Perimeter of a Semicircle Calculator

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

Enter a radius or diameter to instantly get the full perimeter of a semicircle — curved arc plus straight diameter — with step-by-step working.

Calculator Inputs

Input mode

Radius (r)

Unit

Total Perimeter (arc + diameter)

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Arc Length (curved)

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Diameter (straight)

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Semicircle diagram

r = radius | Perimeter = arc + diameter

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Summary

Enter a radius or diameter to instantly get the full perimeter of a semicircle — curved arc plus straight diameter — with step-by-step working.

How it works

Choose whether you are entering the radius or the diameter.
Type your measurement into the input field.
Select the unit of measurement (mm, cm, m, in, or ft).
Click "Calculate" to apply the perimeter formula.
The arc length, diameter, and total perimeter are shown instantly with step-by-step working.

Use cases

Geometry homework involving semicircle boundary length.
Architecture — calculating the trim length for a half-circle arch or window.
Landscaping — estimating edging needed for a half-circle garden bed.
Engineering problems with semicircular sections or channels.
Woodworking — measuring the cut perimeter of a semicircular piece.
Fencing or framing a half-circle feature in construction projects.
Verifying manual semicircle perimeter calculations quickly.

Frequently Asked Questions

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