Arc Length Calculator
Find the arc length of a circle from a radius and central angle, plus the sector area and chord.
Arc length
7.854
Arc = 2πr × (θ / 360). A radius of 5 swept through 90° gives about 7.85 units.
Sector area
19.635
Chord length
7.0711
Angle (radians)
1.5708
How it works
An arc is a slice of a circle's edge. Its length is just a fraction of the full circumference — the fraction being the central angle divided by 360°. So arc length = 2πr × (θ / 360), which is the same as r × θ once the angle is in radians.
Enter the radius and the central angle in degrees. The tool converts the angle to radians, multiplies by the radius for the arc length, and also gives you the sector area, ½ × r² × θ (in radians) — the pie-slice region bounded by the arc and two radii.
For good measure it reports the chord, the straight line joining the arc's endpoints, found from 2r × sin(θ / 2). A radius of 5 across a 90° angle gives an arc of about 7.85 and a sector area near 19.63.
Frequently asked questions
What's the formula for arc length?
Arc length = 2πr × (θ / 360) when the angle θ is in degrees, or simply r × θ when θ is in radians. Both give the same result — one just skips the degree-to-radian step.
How does the sector area relate to the arc?
The sector is the wedge of the circle bounded by the arc and two radii. Its area is ½ × r² × θ with θ in radians, so it grows with the same angle that stretches the arc.
What's the difference between an arc and a chord?
The arc is the curved path along the circle's edge; the chord is the straight line connecting the arc's two endpoints. The chord is always shorter than the arc it cuts across.