Circle Calculator
Radius, diameter, circumference, area, arc, sector and chord.
About this tool
Choose which measurement you know (radius, diameter, circumference or area) and enter it. Then set a central angle to get the arc length, sector area, chord, segment area and segment height, with a diagram.
Circle formulas
From the radius r: diameter = 2r, circumference = 2πr and area = πr². Working backwards, r = C ÷ 2π or √(A ÷ π). A circle of radius 5 cm has a circumference of 31.42 cm and an area of 78.54 cm². For a slice with central angle θ: the arc length is r × θ in radians (2πr × θ/360 in degrees); the sector area is ½r²θ; the chord joining the ends of the arc is 2r sin(θ/2); and the segment, the region between chord and arc, has area ½r²(θ − sin θ). Its height (the sagitta) is r(1 − cos(θ/2)). A 60° slice of the 5 cm circle has an arc of 5.24 cm and an area of 13.09 cm², and its chord exactly equals the radius because the triangle formed is equilateral. These are useful for pizza slices, curved paths, arches, round tables and pie charts. Honest limits: values use π to full precision and are rounded to four decimal places for display. The polygon calculator and the unit circle are related.
Frequently asked questions
How do I find a circle's area from its circumference?
Area = C² ÷ (4π). A circumference of 31.42 gives an area of about 78.54.
What is the formula for arc length?
Arc length = r × θ, with θ in radians, or 2πr × θ ÷ 360 in degrees.
What is a sector of a circle?
The 'pizza slice' between two radii and the arc; its area is ½r²θ.
What is the difference between a chord and an arc?
A chord is the straight line between two points on the circle; the arc is the curved part between them.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.