Arc Length Calculator
An arc is a section of a circle’s edge. Enter the radius and the central angle, in degrees or radians, to get the length of the arc, the straight-line chord between its ends and the area of the sector it encloses.
- Chord length
- 14.1421 in
- Sector area
- 78.54 in²
- Angle in radians
- 1.5708 rad
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter the radius and its unit.
- Enter the central angle and choose degrees or radians.
- Read the arc length, chord and sector area.
Worked examples
A 90° arc on a 10-inch radius: 15.708 in long (0.399 m), chord 14.142 in
- Arc length
- 15.708 in
- Chord length
- 14.1421 in
- Sector area
- 78.54 in²
- Angle in radians
- 1.5708 rad
A 45° arc on a 2 m radius
- Arc length
- 1.5708 m
- Chord length
- 1.5307 m
- Sector area
- 1.57 m²
- Angle in radians
- 0.7854 rad
Why radians make it simple
A radian is defined as the angle whose arc is exactly one radius long, so in radians the arc length is just radius × angle. A full circle is 2π radians (360°), a half circle is π, and a quarter circle is π ÷ 2, or about 1.5708.
Arc versus chord
The arc follows the curve; the chord cuts straight across. The arc is always the longer of the two. For bending trim, laying a curved path or cutting a curved edge you need the arc; for the opening it spans you need the chord.
Questions people ask
What is the arc length for a 90° angle and a radius of 10?
A quarter of the circumference: (90 ÷ 360) × 2 × π × 10 = 15.71.
How do I convert degrees to radians?
Multiply by π ÷ 180. 45° is 0.7854 radians and 180° is 3.1416 radians.
How do I find the angle from the arc length?
Divide the arc length by the radius to get the angle in radians, then multiply by 180 ÷ π for degrees.