Circle Calculator - Area, Circumference, Arc Length & Sector

Circle formulas

• Diameter: d = 2r
• Circumference: C = 2πr = πd
• Area: A = πr²
• Arc length (central angle θ in radians): s = rθ
• Sector area: A_sector = ½r²θ
• Chord length: c = 2r·sin(θ/2)
• Segment area: A_segment = A_sector − 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. Choose degrees or decimal radians; the displayed angle converts when you switch units, so the geometry stays the same. Enter angles greater than zero and up to 360° or 2π radians, including a full circle.

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. Select radians to enter a decimal value directly; for π/2, enter approximately 1.57079632679. The calculator uses radians internally for the arc, sector, chord, and segment formulas.

Real-world circle examples

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.