What is the formula for the perimeter of an annulus?

The perimeter equals 2π × (R + r), where R is the outer radius and r is the inner radius. This accounts for both the outer circumference (2πR) and the inner circumference (2πr).

Why must the inner radius be smaller than the outer radius?

An annulus is defined as the region between two concentric circles. If the inner radius were equal to or larger than the outer radius, there would be no ring-shaped area — just a point or an overlap, not a valid annulus.

Does the perimeter include the area between the circles?

No. The perimeter is the total length of the boundary edges — both the outer and inner circle outlines. The area of the annulus is a separate calculation: π × (R² − r²).

Can I use this for a semicircular annulus?

This tool calculates the full annulus perimeter. For a semicircular annulus, divide the result by 2 and add the two straight edges (each of length R − r) to get the correct boundary length.

What units does this calculator support?

You can enter values in millimeters, centimeters, meters, inches, or feet. The output uses the same unit you select.

Perimeter of an Annulus Calculator

Calculate the total perimeter of an annulus (ring shape) by entering its outer and inner radii.

Enter Radii

Outer Radius (R)

Inner Radius (r)

Unit

Formula

P = 2π × (R + r)

Where R = outer radius, r = inner radius

Results

Enter values to see results

Diagram

An annulus is the planar region between two concentric circles sharing the same center.

Its perimeter consists of two boundary circles: the outer circle of radius R and the inner circle of radius r.

Together they form the complete boundary: P = 2πR + 2πr = 2π(R + r).

Summary

An annulus is the region between two concentric circles. Its perimeter is the sum of the two circular boundaries: the outer circumference and the inner circumference. This calculator computes the total perimeter using the formula 2π(R + r), where R is the outer radius and r is the inner radius.

How it works

Enter the outer radius (R) of the annulus.
Enter the inner radius (r), which must be smaller than the outer radius.
The calculator applies the formula: Perimeter = 2π × (R + r).
Results update instantly, showing the perimeter along with both individual circumferences.
Switch between unit systems (mm, cm, m, in, ft) as needed.

Use cases

Calculating the total edge length of a washer or ring gasket.
Determining material needed to border a circular garden path.
Computing the perimeter of a donut-shaped cross-section in engineering.
Academic geometry problems involving annuli.
Estimating fence or trim length around a circular pond with a ring-shaped layout.
Architectural planning for circular corridors or ring-shaped structures.

Frequently Asked Questions

Last updated: 2026-05-25 · Reviewed by Nham Vu