Annulus (Ring) Area Calculator

How it works

An annulus is the flat ring left when a smaller circle is cut out of the centre of a larger one: a washer, the end of a pipe, the wall of a round planter, a path around a circular lawn. Its area is simply the big circle's area minus the small circle's area, πR² − πr², which factors to π(R − r)(R + r): the ring width times the mean circumference, π(R + r).

Give the two radii (centre to edge) or the two diameters (edge to edge through the centre); diameters are what calipers and pipe tables give, and the calculator halves them. The ring width is the difference of the radii, which for a pipe is the wall thickness. Both circumferences come from 2πr.

The unit box does not convert anything. It records the unit you measured in so the results are labelled correctly: lengths in that unit, areas in that unit squared.

Formula

R = D ÷ 2,  r = d ÷ 2            (when diameters are given)
area  = π(R² − r²) = π(R − r)(R + r)
width = R − r
outer circumference = 2πR     inner circumference = 2πr

Example

A ring with an outer radius of 5 ft and an inner radius of 3 ft has an area of π(25 − 9) = 16π ≈ 50.27 ft². The ring is 2 ft wide, and the circumferences are 2π × 5 ≈ 31.42 ft outside and 2π × 3 ≈ 18.85 ft inside.

A 2-inch Schedule 40 steel pipe has an outside diameter of 2.375 in and an inside diameter of 2.067 in. Switching to diameters and inches, the wall cross-section is π(1.1875² − 1.0335²) ≈ 1.0745 in² and the wall is 0.154 in thick, matching the 1.075 sq in metal area in published pipe tables.

Assumptions and limitations

• The two circles share the same centre. An off-centre bore has the same area but an uneven wall.
• All lengths are in the unit you chose. The calculator labels the results with it and does not convert between units.
• The result is a flat area. Multiply it by a length to get the volume of a pipe wall or a tube.
• Results are rounded for display only.

Frequently asked questions