Annulus area calculator

Type the outer radius R and the inner radius r. Annulus area is π(R² − r²). R = 2 and r = 1 give 9.424778. R = 5 and r = 3 give 50.265482. R = 3 and r = 0 give 28.274334.

The first field is R, the second is r. The calculator does not swap them. When r > R the result is negative, because that is π(R² − r²).

Input data

Results

Enter data and click Calculate.

How it works

Annulus area is the disk minus the hole. The calculator computes π×(R×R − r×r). With R = 2 and r = 1 you have π×(4 − 1) = 3π. The result is 9.424778.

The fields are outer radius R and inner radius r. R = 5 and r = 3 give 16π, 50.265482. R = 3 and r = 0 leave the whole circle: 9π, 28.274334. That is the same πR² as on the circle area card when the hole is zero.

When r = R you get zero, a ring with no thickness. When r > R the difference of squares is negative and the result goes below zero. The calculator does not swap the fields.

Circle area from one r is on the neighbouring page. A sector takes an angle, not a hole. Here you always stay with two radii and a ring.

The header units switch does not multiply anything. 2 and 1 stay 9.424778 whatever the label says.

R = 2 and r = 1 give 9.424778. R = 5 and r = 3 give 50.265482. R = 3 and r = 0 give 28.274334.

Formula

P = π(R² − r²)

How to use

  1. Type R and r, for example 2 and 1.
  2. Click Calculate. Annulus area comes out 9.424778.
  3. 5 and 3 give 50.265482. 3 and 0 give 28.274334.
  4. The first field is the outer one. When r > R the result is negative.
  5. The whole circle from one radius lives on the circle area card.

R = 2 and r = 1 give 9.424778

Annulus area is π(R² − r²). R = 2 and r = 1 give 9.424778. R = 5 and r = 3 give 50.265482. R = 3 and r = 0 give 28.274334.

Annulus
The disk minus the hole. 2 and 1 give 9.424778. 5 and 3 give 50.265482.
outer
The first field, R. At R = 3 and r = 0 you get 28.274334.
inner
The second field, r. When r > R the result drops below zero.

Examples

Example 1

  • R = 2
  • r = 1

9.424778

What is the annulus area at R = 2 and r = 1? 9.424778. 3π.

Example 2

  • R = 5
  • r = 3

50.265482

What is the annulus area at R = 5 and r = 3? 50.265482. 16π.

Example 3

  • R = 3
  • r = 0

28.274334

What is the annulus area at R = 3 and r = 0? 28.274334. πR² remains.

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Common questions

What is the annulus area at R = 2 and r = 1?

9.424778. π×(4 − 1) = 3π.

What does annulus area mean?

The disk minus the hole. π(R² − r²). R outside, r inside.

What about R = 5 and r = 3?

50.265482. 16π.

What about R = 3 and r = 0?

28.274334. The hole vanishes, circle area remains.

Which field is the outer radius?

The first, R. The second is inner r.

What if r > R?

The result is negative. The calculator does not swap the fields.

What if r = R?

Zero. Two equal radii, no band.

How is this different from circle area?

Two radii here. One there. With r = 0 the result matches.

Do the units have to be centimetres?

No. As long as R and r share one scale. 2 and 1 stay 9.424778.

Does a comma in 2.5 work?

Yes. 2.5 and 2,5 are the same radius.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.