Arc Length Of A Circle

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Calculate the distance along the edge of a circle given the radius and angle.

Circle Segment Details

Radius (r)

Central Angle (θ)

Unit

Arc Length Details

15.71

Arc Length (s)

The distance along the curved line of the circle.

Angle in Radians1.5708rad

Circle Fraction (%)25.0%

About this calculator

Arc Length and Circles

The arc length of a circle is the distance between two points on the circumference. It is directly proportional to the central angle and the radius of the circle. If you know the circumference of the entire circle (2πr), the arc length is just a fraction of that total based on the angle.

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Pro Tips

If the angle is in degrees, convert to radians first: θ_rad = θ_deg × (π / 180).
For a full circle (360°), the arc length is equal to the circumference.
Arc length is useful for calculating travel distance on a sphere, like Earth.

Fun Facts

"The 'radian' unit is defined specifically so that for a unit circle (r=1), the arc length equals the angle."
"Ships and planes use arc length (Great Circle distance) to find the shortest path between two points on the globe."
"Eratosthenes used arc length and the angle of the sun to estimate the Earth's circumference over 2,000 years ago!"

Formula: s = r × θ (where θ is in radians)