Arc Length Calculator
Calculate the length of an arc of a circle from its radius and angle.
A slice of the circumference
An arc is a portion of a circle's circumference, and its length depends on the radius and the angle it spans. This calculates the arc length from those, useful in geometry, engineering and anything involving curves and circular motion.
Enter the radius and angle to find the arc length.
A fraction of the way around
The idea is intuitive once you see it: an arc is just a fraction of the full circumference, and that fraction is the arc's angle as a share of a full turn. So an arc spanning a quarter of a circle is a quarter of the circumference, and the formula simply scales the circumference by the angle's share of a complete rotation. This is where radians show their elegance — measured in radians, the arc length is simply the radius times the angle, with no conversion factor, which is one of the reasons radians are the natural unit for circular measurement. Arc length matters in real applications from designing curved roads and gears to calculating distances along the curve of a circular path.
Common questions
How is arc length related to the circumference?
An arc is a fraction of the full circumference, equal to its angle as a share of a full turn — a quarter-circle arc is a quarter of the circumference.
Why are radians convenient for arc length?
In radians the arc length is simply the radius times the angle, with no conversion factor, which is why radians are the natural unit for circles.
Is anything uploaded?
No. The calculation happens in your browser.