How do I calculate a central angle from arc length and radius?

Divide the arc length by the radius to get the angle in radians, then multiply by 180/π to convert to degrees.

Can I use this calculator for any circle size?

Yes, as long as you enter the arc length and radius in the same units, the result will be accurate regardless of the circle's size.

What if I only know the diameter instead of the radius?

Divide the diameter by 2 to get the radius, then use that value in the calculator.

Why does the result come out in radians first?

The fundamental formula θ = s / r gives radians by definition; most calculators convert to degrees for easier interpretation.

Is the central angle always less than 360°?

If you enter the full circumference as the arc length, the angle will be 360°; otherwise the angle corresponds to the portion of the circle you specify.

Geometry & Shapes2 options compared

Central Angle Calculator

Calculates the central angle of a circle using simple inputs for arc length and radius. The tool provides an accurate, instant measurement of the angle formed by these two parameters within a circular shape. Users enter numerical values into dedicated fields to determine the precise degree measure without needing manual geometric calculations or specialized software. This straightforward process...

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Number Convert

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Calculate your central angle with our free online tool. Get accurate results instantly. No signup required.

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Omni Calculator
omnicalculator.com
Calculate the central angle of a circle with ease using the central angle calculator. Enter arc length and radius to ...
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Central Angle Calculator options compared

Tool	Best for	Strengths	Limitations
Number Convert numberconvert.com	Fast angle calculation	Instant results No signup required	Ads on the page Formula explanation absent
Omni Calculator omnicalculator.com	Learning the formula	Formula derivation details Sharing options	Community votes lower More steps to use

Buyer's guide

How to choose a central angle calculator

When you need a central angle fast and don't want to sign up, choose Number Convert. If you are trying to understand where the formula comes from or want to share the result, Omni Calculator is the better option.

Questions

Central Angle Calculator FAQ

How do I calculate a central angle from arc length and radius?: Divide the arc length by the radius to get the angle in radians, then multiply by 180/π to convert to degrees.
Can I use this calculator for any circle size?: Yes, as long as you enter the arc length and radius in the same units, the result will be accurate regardless of the circle's size.
What if I only know the diameter instead of the radius?: Divide the diameter by 2 to get the radius, then use that value in the calculator.
Why does the result come out in radians first?: The fundamental formula θ = s / r gives radians by definition; most calculators convert to degrees for easier interpretation.
Is the central angle always less than 360°?: If you enter the full circumference as the arc length, the angle will be 360°; otherwise the angle corresponds to the portion of the circle you specify.

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