Arc Length Calculator
Find the length of a circular arc — the distance along the curve between two points on a circle. Enter the radius and central angle (degrees or radians), and this calculator returns the arc length, chord length, and sector area.
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Arc Length Calculator
An arc is a piece of the circumference. Unlike a chord (the straight-line shortcut between two points), the arc follows the curve. Arc length is how far you'd walk if you traced the circle between those two points.
Arc vs. chord
The chord is the straight-line distance between two endpoints on the circle. The arc is the curved distance along the circle between those same points. For small angles they're nearly equal, but as the angle grows, the arc becomes much longer than the chord. At 180°, the chord equals the diameter while the arc equals half the circumference.
Why arc length matters
Arc length determines the actual material needed for curved structures — bent steel, curved glass, or circular track sections. Road engineers use arc length to design highway curves. Clock repairers use it to calculate how far a hand tip travels. It's the real-world distance along any circular path.
Arc Length Formula
Arc length takes a fraction of the full circumference. Click each part of the formula to understand its role.
Click each part to explore
In radians, the formula simplifies to: L = rθ
How to Calculate Arc Length
Four steps from measurements to the curved distance. Enter a radius to follow along.
Measure the Radius
rFind the radius of the circle containing the arc.
Measure the Central Angle
θFind the central angle (θ) subtended by the arc.
Compute the Fraction
θ / 360Divide the angle by 360° to find what fraction of the circumference the arc covers.
Multiply by 2πr
L = (θ/360) × 2πrMultiply the fraction by the full circumference (2πr) to get the arc length.
Formula Variations
Three ways to compute arc length depending on your inputs.
The standard arc length formula using degrees. The ratio θ/360 gives the fraction of the full circumference that the arc represents.
Example
Find the arc length for a 90° angle. Change the radius to solve your own problem.
A circle with radius 10 cm and a central angle of 90 degrees.
Frequently Asked Questions
Common questions about arcs, chords, and curved distances.