Circle Calculator
Enter a radius, diameter, circumference or area and get the other three — with the circle drawn, the unit label you pick, and arc, chord and sector areas.
A slice of it
The sector is the pie slice between the two radii; the segment is what the straight chord cuts off on its own.
Radius: 1 Diameter: 2 Circumference: 6.283185 Area: 3.141593 Arc length: 1.570796 Chord: 1.414214 Sector area: 0.785398 Sector perimeter: 3.570796 Segment area: 0.285398
Circumference: 2π Area: π Arc length: 0.5π Sector area: 0.25πResult: 4 lines, 61 characters
Any one measurement gives you the rest
Say which measurement you have — radius, diameter, circumference or area — type it in, and the other three appear immediately. Everything is derived from the radius: the diameter is twice it, the circumference is 2πr, and the area is πr², using the full precision of π rather than 3.14 — unless a textbook says otherwise, when “Value of π” switches to 3.14, 3.1416 or 22/7 and the working prints the π it used. The circle is drawn beside the numbers with the radius and diameter marked on it, so it is clear which measurement is the radius and which the diameter.
Units label the answers
Pick a unit — mm, cm, m, km, in, ft, yd or mi — and every length is labelled with it and every area with its square. The tool labels the answers but does not convert between units. Leave the unit unset and the results stay plain numbers.
A slice of the circle
Give a central angle — or set "I know the slice’s…" to its arc, chord or sector area and the angle is worked out from that — and the page adds the measurements of that piece: the arc along the edge, the chord straight across it, the area of the sector — the pie slice between the two radii — its perimeter, two radii and the arc, and the area of the segment, which is what the chord alone cuts off. A chord fits two slices, and the page says it gives the smaller. The wedge is shaded on the diagram so it is clear which piece the numbers describe. The number of decimal places is yours to set, from none to ten. Set “Round to” to “Significant figures” and the same box counts figures instead, which keeps a tiny circle from rounding to 0. To convert an answer into another unit, use the unit converter.
Frequently asked questions
What formulas does it use?
Diameter = 2r, circumference = 2πr, and area = πr². Working backwards, r = diameter ÷ 2, r = circumference ÷ 2π, and r = √(area ÷ π).
What is the difference between the sector and the segment?
The sector is the pie slice: the two radii and the arc between them. The segment is what the straight chord cuts off on its own — the sector with the triangle removed. Past a half turn the triangle falls on the other side of the chord, so the major segment is the larger of the two, which is correct rather than a bug.
Can it convert between units?
No. Choosing a unit labels the answers so an area reads as cm² rather than an unnamed number; whatever unit goes in comes out. Use a unit converter first if your measurement is in something else.
Why does the answer have so many decimals?
Because π does. Set the decimals box to however many places you actually need — anywhere from none to ten — and everything, including the slice, is rounded to that.
Can I enter the angle in radians, or see the answer in terms of π?
Yes. The sector angle can be typed in degrees or radians. The results are also given in terms of π, and “Show the working” writes out each formula with your numbers in it.
Can I find the angle from an arc, a chord or a sector area?
Yes. Set "I know the slice’s…" to arc, chord or sector area and type it; the central angle is worked out from it, shown in degrees and radians, and everything else follows. A chord fits two slices, so the page gives the smaller one and says so.
Can I use 3.14 or 22/7 for π, or round to significant figures?
Yes. “Value of π” offers π at full precision, which is the default, 3.14, 3.1416 or 22/7, and every answer — the slice included — is worked with the one you pick, with the working printing it. “Round to” switches the decimals box from Decimal places to Significant figures, which keeps a very small circle from rounding to zero.