Circle and Sector Calculator
Circle area and circumference plus sector, arc, chord and segment.
Inputs
Result
Formula
| Radius | r = d ÷ 2 |
| Area | A = π r² |
| Circumference | C = π d = 2π r |
| Sector area | A = π r² × (θ ÷ 360) |
| Arc length | L = 2π r × (θ ÷ 360) |
| Chord | c = 2r × sin(θ ÷ 2) |
| Segment area | A = sector − 0.5 r² sin θ |
A 2 m diameter at 90°: radius 1.000 m, area 3.1416 m², circumference 6.2832 m, sector 0.7854 m², arc 1.5708 m, chord 1.4142 m and segment 0.2854 m².
FAQ
Pipes are quoted in inches — how does that relate to area?
The inch is 25.4 mm, but nominal diameter DN is neither bore nor outside diameter. Flow area must use the bore: a DN50 galvanised pipe has about 53 mm bore against 50 mm for plastic, a 12% area difference and therefore 12% in flow at the same pressure.
Why is formwork cheaper for a circular footing?
A circle encloses the most area for a given perimeter — equivalently, it has the least perimeter for a given area. A 10 m² square footing has 12.65 m of edge against 11.21 m for a circle, an 11% saving. But curved formwork needs bespoke panels and more bracing, so it rarely pays except on silos, tanks and piers.
When is segment area actually used?
Arched openings, the sides of curved beams, the junction of a circular wall with a straight one, and openings cut for pipes. Another frequent case: estimating repair mortar for a spalled or honeycombed patch on a circular section, where measuring the chord with a rule and the sagitta with a feeler gauge beats trying to measure an angle.
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Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.