Cir Calculator
Cir calculator works out Radius and Diameter from Its value, Central angle and Angle unit. The default figures on this page give area of 3.141593; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
6 steps
- Radius from the known radius: r = 1.
- Circumference C = 2*pi*r = 6.283185307179586; area A = pi*r^2 = 3.141592653589793.
- Central angle = 90 deg = 1.5707963267948966 rad.
- Arc s = r*theta = 1 * 1.5707963267948966 = 1.5707963267948966.
- Chord = 2 r sin(theta/2) = 1.414213562373095; sector area = r^2*theta/2 = 0.7853981633974483.
- Segment area = r^2 (theta - sin theta)/2 = 0.2853981633974483; sagitta = r(1 - cos(theta/2)) = 0.2928932188134524.
Its 9 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the cir 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 cir calculator
Enter Its value, Central angle and Angle unit. Radius updates as you type, and “Use a worked example” loads checked figures you can adjust. 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).
Radius 5 example
With Which measurement do you know?: radius, Its value: 5, Central angle: 90, the calculator returns Diameter: 10, Circumference: 31.4159265, Area: 78.5398163. This example is checked against an independent source in the test suite.
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, Central angle and Angle unit.
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
What is the formula for CIR?
On the figures this page opens with — its value 5 and central angle 90 — the area is 3.141593. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
Is CIR the same as circle?
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 and central angle 90 — the area is 3.141593. Put your own figures in their place and the working updates beside the result.
How big is a 12 inch circle?
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.
What is the radius of an 8-inch circle?
It needs Its value, Central angle and Angle unit. Nothing else is required, and the figures stay in your browser.
What information do I need for the cir calculator?
You need Its value, Central angle and Angle unit. The page opens with default figures that give area of 3.141593, so you can see the scale before entering your own.
What does this cir 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.