Annulus Perimeter Calculator

The perimeter of an annulus is both edges of the ring — outer circumference plus inner circumference:

P = 2π × (R + r)

Where R is the outer radius and r is the inner radius. The outer edge contributes 2πR; the inner edge contributes 2πr; together they make 2π(R + r).

Worked example — gasket edge length: A circular gasket has an outer radius of 8 cm and an inner radius of 6 cm. The edge needs a thin rubber seal applied around both the outside and the bolt-hole opening. P = 2π × (8 + 6) = 2π × 14 ≈ 87.96 cm of sealant material.

Where annulus perimeter matters in practice:

• Gasket and washer edges. Any sealant or finishing tape applied around both the outside and inside of a ring shape doubles the perimeter you’d expect from the outer dimension alone.
• Race track border markings. Painting both the inner and outer line of a track’s curved section.
• Trim around a circular skylight. A skylight’s trim band includes both the outer frame and the inner aperture.
• CD/DVD edge protection. Both the rim and the central hub edge of an optical disc are exposed.

Counting carefully:

It’s tempting to write the “perimeter” as just 2πR (the outer edge), but a ring shape has two boundaries — outer AND inner — and any physical trim, sealant, or marking is applied to both. Saying “perimeter of an annulus” without qualification means the total enclosed boundary, which is both edges.

For thin rings:

If the ring is thin (r is close to R), the two circumferences are nearly equal, and the total perimeter is about 4π × R_avg, where R_avg is the average of R and r. For a thin washer with R = 1 cm and r = 0.9 cm, that’s 4π × 0.95 ≈ 11.94 cm — the same as the exact formula.

Sanity check:

• r = 0 (full disc, no hole): P = 2π × R, just the outer circumference. ✓
• r = R (degenerate, no ring): P = 4π × R — but this is a thin loop drawn twice. Mathematically valid; physically a zero-width ring has no real perimeter. Ignore the edge case in real measurements.

Comparing to a sector:

A sector has perimeter 2r + arc length, with the radius contributing twice as straight sides. An annulus has perimeter 2π(R + r), with no straight sides — both boundaries curve. Different shapes, different bookkeeping.