GeomBench

Annulus (Ring) Area Calculator

Outer circle's area minus the inner circle's area.

Outer radius R

Inner radius r

Ring area

122.522

What you entered

Outer radius: 8Inner radius: 5

1
Outer circle area
π × 8²= 201.0619
2
Inner circle area
π × 5²= 78.5398
3
Ring area = outer − inner
201.0619 − 78.5398= 122.5221

Result

Ring area: 122.522

A ring with outer radius 8 and inner radius 5 has an area of 122.522 — the outer circle's area minus the inner circle's area.

Annulus area from outer and inner radius

An annulus is a ring. Its area is the outer circle's area minus the inner circle's - pi times the difference of the squared radii.

Outer radius R	Inner radius r	Ring area
5	3	50.27
6	4	62.83
8	5	122.52
10	6	201.06
12	8	251.33
15	10	392.70

The area depends on the difference of the squares, not the square of the difference, which is why the first two rows both have a 2-unit wall thickness but different areas - 50.27 against 62.83. A ring of constant thickness encloses more material the further out it sits. This is the calculation for a washer, a pipe wall in cross-section, or a circular path around a pond: subtract the inner circle before you multiply by pi rather than after.

Subtracting circles

An annulus is the region between two concentric circles — just take the big circle's area and subtract the small one's: A = π(R² − r²).

Everyday rings

Washers, pipes viewed end-on, running tracks, and CD/DVD discs are all annuli — this same subtraction trick works for any of them.

Frequently asked questions

How do I calculate the area of a ring?

Area = π × (R² − r²), where R is the outer radius and r is the inner radius. A washer with outer radius 5 cm and inner radius 3 cm: Area = π × (25 − 9) = 50.27 cm².

How do I find the area of a running track?

A standard running track has two straight sides and two semicircular ends. The running area (between inner and outer edges) uses the annulus formula for the curved parts plus rectangle area for the straight parts. For just the curved portion: A = π × (R² − r²).

What is the cross-sectional area of a pipe?

A pipe viewed end-on is an annulus. Area = π × (R² − r²), where R is the outer radius and r is the inner radius (the hole). A pipe with 3 cm outer diameter and 2 cm inner diameter: Area = π × (2.25 − 1) = 3.93 cm² of material.