Everyday Tools

Annulus Area Calculator

Calculate the area of an annulus from outer radius and inner radius.

Updated April 16, 2026
Free online tool
Planning and research use

Why this page exists

Ring-shaped geometry problems get easier when the inner and outer radius are turned into one area result instead of being worked out by hand. This calculator helps visitors calculate annulus area from outer radius and inner radius using standard annulus-area math.

Interactive tool

Run the estimate

Enter your numbers and read the result first, then use the sections below to understand what affects the outcome.

Calculator

Annulus area calculator

Calculate the area of an annulus from the outer radius and inner radius entered.

Result

190.8518

Estimated annulus area based on pi multiplied by the difference between the outer-radius square and inner-radius square.

Annulus area190.8518

Outer radius used9.00

Inner radius used4.50

Ring thickness4.50

Using an outer radius of 9.00 and an inner radius of 4.50, the annulus area comes out to about 190.8518.
The ring thickness between the two radii is 4.50 in the same unit system.
This result uses the same radius unit throughout, so the area is expressed in square units of whatever measurement system you use.

This is standard annulus-area math. Make sure the inner radius does not exceed the outer radius or the result will not represent a valid ring.

Planning note

Last updated April 16, 2026. Use this tool to compare scenarios and plan ahead, then confirm important details with the lender, employer, insurer, contractor, or other qualified provider involved in the final decision.

How it works

What the calculator is doing

Enter the outer radius and inner radius.

The calculator squares both radii and subtracts the inner-radius square from the outer-radius square.

It multiplies that difference by pi to estimate the annulus area.

Understanding your result

This is standard annulus-area math. The inner radius must not be larger than the outer radius for the result to describe a valid ring.

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Examples

Ways people use this tool

Example scenarios help turn a quick estimate into a more useful comparison or planning step.

Work out ring-shaped area quickly

The annulus formula can save time when the shape is defined by two radii instead of one.

Check homework or worksheet answers

A quick calculation can make geometry practice easier to verify.

Use it with circle and perimeter tools

Annulus area often fits naturally beside circle-area, circumference, and other geometry checks.

FAQ

Common questions

How is annulus area calculated here?

The calculator uses pi multiplied by the outer radius squared minus the inner radius squared.

Why must the inner radius be smaller?

Because an annulus is a ring. If the inner radius is larger than the outer radius, the dimensions no longer describe a valid ring-shaped area.

What unit is the area shown in?

The result is shown in square units of whatever measurement unit you used for the radii.

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Everyday ToolsUpdated April 14, 2026