# Circle and Sector Calculator

Circle area and circumference plus sector, arc, chord and segment.

- Page: https://jianzhujisuan.com/en/circle-calc
- Category: Area and volume (https://jianzhujisuan.com/en/c/area-volume)
- Chinese version: https://jianzhujisuan.com/zh/circle-calc.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Diameter 2 m, Central angle 90 °): **Circle area 3.1416 m²**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Diameter | number | 2 | m |  |
| Central angle | number | 90 | ° |  |

## 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

## Worked example

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.

## Questions

### 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.

## Related tools

- [Room Area Calculator](https://jianzhujisuan.com/en/room-area): Floor, ceiling, walls, skirting and volume, all at once.
- [Wall Area and Paint Calculator](https://jianzhujisuan.com/en/wall-area): Net wall area with openings deducted, plus paint and filler.
- [Roof Area Calculator](https://jianzhujisuan.com/en/roof-area): True sloped roof area, rafter length and ridge rise from pitch.
- [Triangle Area Calculator](https://jianzhujisuan.com/en/triangle-area): Area from three sides, with angles, inradius and circumradius.
- [Battered Pit Volume Calculator](https://jianzhujisuan.com/en/pit-volume): Top dimensions and frustum volume from base size, depth and batter.
- [Cylinder Volume Calculator](https://jianzhujisuan.com/en/cylinder-volume): Volume, capacity, surface areas and weight for any cylinder.

---

Generated by BuildCalc. All calculations run in your browser; no data is uploaded. Formulas follow national standards and common trade practice; local codes govern.