Circle calculator
Radius, diameter, circumference, area, arc, sector and chord.
2πr
πr²
Arc, sector, chord and segment
rθ, θ in radians
½r²θ
2r·sin(θ/2)
½r²(θ − sin θ)
How it works
Every property of a circle follows from one number — the radius — and the constant π, the ratio of any circle's circumference to its diameter.
circumference = 2πr = πd
area = πr²
arc length = rθ (θ in radians)
sector area = ½r²θ
chord = 2r·sin(θ/2)
segment area = ½r²(θ − sin θ) Radians make the formulas simple
Arc length is rθ only when θ is in radians — that is the definition of a radian: the angle that cuts an arc equal in length to the radius. In degrees you would need an extra π/180 in every formula, which is why calculus abandons degrees entirely.
Sector versus segment
A sector is the pizza slice: two radii plus the arc. A segment is what is left when you cut straight across on the chord — the sector minus the triangle. Hence the −sin θ term.
Doubling the radius quadruples the area
Area goes with r², so a 16-inch pizza has 78% more food than a 12-inch, not 33% more. It is the single most useful piece of geometry in everyday life.