Circle and Sector Calculator
Circle area and circumference plus sector, arc, chord and segment.
Quick answer
With the default inputs: Diameter 2 · Central angle 90°Circle area 3.1416 m²
Edit the inputs below to recalculate.Inputs
Result
Circle area
3.1416m²
| Radius | 1.000m |
| Circumference | 6.2832m |
| Sector area | 0.7854m² |
| Arc length | 1.5708m |
| Chord length | 1.4142m |
| Segment area | 0.2854m² |
| Triangle inside sector | 0.5000m² |
| Inscribed square side | 1.414m |
| Cylinder volume at 1 m height | 3.1416m³ |
π is taken as 3.14159265. Segment area is sector minus triangle; beyond 180° the triangle flips and the tool handles it by absolute value. The circumference is what you need for circular footings and tank formwork or waterstop lengths.
Reverse: known result, work out one input
Enter a target result; the other inputs stay fixed and this one is worked out.
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.
How to work it out
- Convert diameter to radius: r = d ÷ 2. It looks trivial, but substituting diameter for radius is the most frequent error and gives a result four times too large.
- Circle area A = π r², circumference C = π d. This pair covers circular columns, round footings and circular tanks.
- Sector area = π r² × (θ ÷ 360); arc length = 2π r × (θ ÷ 360). θ is the central angle, not an inscribed angle.
- Chord length c = 2r × sin(θ ÷ 2), used for curved beams and arch spans.
- Segment area = sector − triangle = π r² × (θ÷360) − 0.5 r² sin θ. This is the section area for curved concrete, arched slabs and arch lintels.
- Break complex shapes into rectangles, sectors and segments, compute each and add. Faster and less error-prone than integrating or interpolating tables.
Where it goes wrong
- Substituting diameter into A = π r². At d = 2 m the correct area is 3.14 m²; using r = 2 gives 12.57 m², four times too much.
- Computing the sector but not subtracting the triangle. At a half circle the triangle vanishes, but at a small central angle such as 30° the triangle is 82% of the sector, so omitting it nearly doubles the answer.
- Feeding degrees into a function expecting radians. Spreadsheet and calculator trigonometry default to radians, so 30° must be entered as 0.524; typing 30 gives nonsense.
- Mixing degrees and radians in the sector formula. Here θ is in degrees; dividing a radian value by 360 is out by a factor of 57.
Material and cost
Formwork and reinforcement for circular elements are measured on circumference and arc length, and curved formwork costs 30-50% more than straight because of fabrication and propping. A circle also has 12% more perimeter than a rectangle of equal area, raising envelope and formwork cost.
On site
- After computing the concrete volume of a circular footing, remember the blinding layer, typically 100 mm wider all round.
- Measure curved wall formwork by arc length. Arc can exceed chord by up to 57% at a half circle, so cutting to chord always comes up short.
- For setting out arcs on site, a centre peg, a radius and a line is the most practical method — faster than total-station setting out and accurate enough for ordinary building work.
- Segment areas come up constantly for arch lintels and curved stair slabs, so memorise the factors for 30°, 45°, 60°, 90° and 120°.
Basis
- GB 50854-2013 Standard method of measurement for building and decorative works
- GB 50010-2010 (2015 edition) Code for design of concrete structures
- GB/T 50353-2013 Standard measurement for construction area of building
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.
Cite this page
Use this format in reports, method statements or coursework. The link is permanent.
Building Calculator. Circle and Sector Calculator. 2026-10-25. https://jianzhujisuan.com/en/circle-calc
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.