Math Calculators
Circle Calculator - Area, Circumference, Arc Length & Sector
Calculate circle area, circumference, diameter, arc length, sector area, chord length, and segment area. Enter any one property - radius, diameter, circumference, or area - and get all others instantly.
Show calculation steps
- Radius r = 5
- Diameter d = 2r = 10
- Circumference C = 2πr = 31.415927
- Area A = πr² = 78.539816
| Property | Value |
|---|---|
| Radius | 5 |
Circle formulas
- Diameter: d = 2r
- Circumference: C = 2πr = πd
- Area: A = πr²
- Arc length (central angle θ in radians): s = rθ
- Sector area: Asector = ½r²θ
- Chord length: c = 2r·sin(θ/2)
- Segment area: Asegment = Asector − ½r²·sin(θ)
How to use
Select which property you know (radius, diameter, circumference, or area), enter its value, and the calculator instantly derives all other properties. Optionally enter a central angle to compute arc length, sector area, chord length, and circular segment area.
What is a radian?
One radian is the angle subtended at the centre of a circle by an arc whose length equals the radius. 360° = 2π radians; 180° = π radians; 90° = π/2 radians. The calculator accepts degrees and converts internally.
Real-world circle examples
| Object | Diameter | Circumference | Area |
|---|---|---|---|
| Bicycle wheel (26") | 26 in | 81.7 in | 530.9 sq in |
| Pizza (12") | 12 in | 37.7 in | 113.1 sq in |
| Circular pool (15 ft) | 15 ft | 47.1 ft | 176.7 sq ft |
| Dinner plate (10") | 10 in | 31.4 in | 78.5 sq in |
| Quarter (US coin) | 24.26 mm | 76.2 mm | 462 sq mm |
Connection to inscribed and circumscribed polygons
A regular n-gon inscribed in a circle of radius r has a perimeter of 2nr·sin(π/n) and an area of nr²·sin(2π/n)/2. As n increases, these values approach 2πr (circumference) and πr² (area), visually demonstrating why π was historically approximated by inscribing polygons - Archimedes used a 96-sided polygon to establish 3.1408 < π < 3.1429 around 250 BCE.