Arc Length Calculator
Arc Length Calculator works out Arc length and Chord length from Radius, Central angle and Central angle in degrees. The default figures on this page give arc length 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
3 steps
- Central angle theta = 3.141592653589793 rad = 180 degrees.
- s = r * theta = 1 * 3.141592653589793 = 3.141592653589793.
- Chord = 2 r sin(theta/2); sector area = r^2 theta / 2.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Arc Length Calculator calculates
Computes the length of a circular arc from its radius and central angle, or the length of a curve given explicitly, parametrically or in polar form.
How to use this Arc Length Calculator
Enter Radius, Central angle, Central angle in degrees and Curve. Arc length 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 Arc length, Chord length and Sector area.
The method follows Geometry and proportional relationships (circular arc s = r theta) and OpenStax Calculus Volume 1, 6.4 Arc Length of a Curve and Surface Area.
Research R1754-GT-1: radius 1, half turn example
With What are you measuring?: circular, Radius: 1, Central angle: 3.14159265, the calculator returns Arc length: 3.14159265. 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 Arc length, Chord length and Sector area. The inputs you can vary are Radius, Central angle, Central angle in degrees, Curve, x(t) and y(t).
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
What is the formula for calculating the length of an arc?
Computes the length of a circular arc from its radius and central angle, or the length of a curve given explicitly, parametrically or in polar form. On this page it is computed from Radius, Central angle and Central angle in degrees and shown as Arc length, Chord length and Sector area.
How to calculate arc in calculator?
Computes the length of a circular arc from its radius and central angle, or the length of a curve given explicitly, parametrically or in polar form. Open “How this is worked out” beside the result to see each step for your own figures.
Is there an arc calculator app?
Computes the length of a circular arc from its radius and central angle, or the length of a curve given explicitly, parametrically or in polar form. On the figures this page opens with — radius 1 and central angle 3.1416 rad — the arc length is 3.141593. Put your own figures in their place and the working updates beside the result.
How to find arc length in math?
It needs Radius, Central angle, Central angle in degrees, Curve, x(t) and y(t). Nothing else is required, and the figures stay in your browser.
How to calculate arc length calculator?
The result gives Arc length, Chord length, Sector area, Central angle, Arc-length integrand and Method, each labelled with its unit so the figure can be read on its own.
What information do I need for the Arc Length Calculator?
You need Radius, Central angle, Central angle in degrees, Curve, x(t), y(t), Variable and From. The page opens with default figures that give arc length of 3.141593, so you can see the scale before entering your own.