About the Annulus Calculator
An annulus is a flat ring: a big circle with a smaller circle cut out of its middle. Washers, pipes seen end-on, running tracks and flower rings are all annuli. The area is the area of the big circle minus the area of the hole, and this calculator does the sum from the two radii. Type the outer and the inner radius and the area of a ring appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Annulus Calculator
- 1Enter the outer and the inner radius.
- 2Pick the units or options from the menus if the area of a ring tool offers them.
- 3Read the area of a ring in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the area of a ring
Engineers use the area of a washer to work out how much metal there is, or how much of a pipe's cross-section is wall rather than hole. Gardeners use it to find how much soil or paint a circular border needs, and crafters use it for rings of fabric or card.
Setting the inner radius to zero gives a full circle, which is a handy check. The width of the ring is shown because it is often easier to measure than the inner radius.
How the area of a ring is worked out
Area = π × (outer radius² − inner radius²). The width of the ring is outer radius − inner radius. A ring with an outer radius of 10 and an inner radius of 6 has an area of π × (100 − 36) = 201.06 square units. The ring is 4 wide, and its two edges measure 62.83 and 37.70 round.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Outer and inner radius
- Ring width
- Both circumferences
Mistakes to avoid with area of a ring
Be careful not to subtract the radii before squaring: the area is the difference of squares, not the square of the difference. Also, use the radius, not the diameter. If you have diameters, halve them first.
On phone and computer
On a phone, type into the boxes one after another and read the area of a ring underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the area of a ring move. The annulus calculator works the same on both. A ring is built from simple circles, so Circle Calculator checks the outer and inner circles on their own. Sector Calculator handles part of a ring's curve, Torus Calculator covers the three-dimensional doughnut, and Area Calculator is useful for the flat shapes around it.
Features
- Square each radius first
- Radius, not diameter
- Inner 0 gives a full circle
- Clear messages when the area of a ring inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate area of a ring?
Area = π × (outer radius² − inner radius²). The width of the ring is outer radius − inner radius. A ring with an outer radius of 10 and an inner radius of 6 has an area of π × (100 − 36) = 201.06 square units. The ring is 4 wide, and its two edges measure 62.83 and 37.70 round.
What is the formula for area of a ring?
Area = π × (outer radius² − inner radius²). The width of the ring is outer radius − inner radius. The annulus calculator applies it exactly and rounds only the displayed answer to six significant figures.
What if I know diameters?
Halve each diameter to get the radius, then enter them.
How do I find the area of a pipe wall?
Use the outer radius of the pipe and the inner radius of the bore. The result is the cross-section of the metal.
Is an annulus the same as a torus?
No. An annulus is flat. A torus is the three-dimensional doughnut shape, which has its own calculator.
Is this annulus calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.