Circumference Calculator
Circumference calculator works out Radius and Diameter from Its value. The default figures on this page give circumference of 31.415927; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
7 steps
- Asked for the circumference: C = 2 pi r = pi d = 31.41592653589793.
- Radius from the known diameter: r = 5.
- Circumference C = 2*pi*r = 31.41592653589793; area A = pi*r^2 = 78.53981633974483.
- Central angle = 90 deg = 1.5707963267948966 rad.
- Arc s = r*theta = 5 * 1.5707963267948966 = 7.853981633974483.
- Chord = 2 r sin(theta/2) = 7.071067811865475; sector area = r^2*theta/2 = 19.634954084936208.
- Segment area = r^2 (theta - sin theta)/2 = 7.134954084936207; sagitta = r(1 - cos(theta/2)) = 1.4644660940672622.
Its 9 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the circumference calculator calculates
Computes radius, diameter, circumference and area of a circle from any one of them, plus arc length, chord, sector area, segment area and sagitta for a given central angle.
How to use this circumference calculator
Enter Its value. Radius updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Radius, Diameter and Circumference.
The method follows Weisstein, Eric W. "Circle", "Circular Sector" and "Circular Segment", MathWorld, CRC Standard Mathematical Tables and Formulae, Geometry: the circle and NIST Digital Library of Mathematical Functions, 4.14 (circular functions).
What you can compare
Change one input at a time to see how it affects Radius, Diameter and Circumference. The inputs you can vary are Its value.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to calculate the circumference?
Computes radius, diameter, circumference and area of a circle from any one of them, plus arc length, chord, sector area, segment area and sagitta for a given central angle. Open “How this is worked out” beside the result to see each step for your own figures.
Is the circumference 3.14 times the diameter?
Computes radius, diameter, circumference and area of a circle from any one of them, plus arc length, chord, sector area, segment area and sagitta for a given central angle. On the figures this page opens with — its value 5 — the circumference is 31.415927. Put your own figures in their place and the working updates beside the result.
What is the circumference of a 20 inch circle?
On the figures this page opens with — its value 5 — the circumference is 31.415927. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
How do I convert diameter to circumference?
It needs Its value. Nothing else is required, and the figures stay in your browser.
What information do I need for the circumference calculator?
You need Its value. The page opens with default figures that give circumference of 31.415927, so you can see the scale before entering your own.
What does this circumference calculator show?
It shows Radius, Diameter, Circumference, Area, Central angle, Central angle in degrees, Central angle in radians and Arc length, with the working and any warnings for your entries.