Arc Length Calculator
An arc is a fraction of the circumference, so multiply the full circumference by angle over 360. In radians it simplifies to radius times angle.
Your numbers
Arc length
31.416cm
Radians
1.5708rad
Circumference
125.66cm
Formula
Arc length = 2π × Radius × Angle (°) ÷ 360
Useful for curved cuts or measuring part of a circular border.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 20 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 90 | 0 ~ 360 |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Arc length (cm) | Radians (rad) | Circumference (cm) |
|---|---|---|---|
| 10 | 15.708 | 1.5708 | 62.83 |
| 15 | 23.562 | 1.5708 | 94.25 |
| 20 | 31.416 | 1.5708 | 125.66 |
| 30 | 47.124 | 1.5708 | 188.5 |
| 40 | 62.832 | 1.5708 | 251.33 |
What each result means
| Result | At default values |
|---|---|
| Arc length (cm)The length of the curved piece cut from a circle’s edge. | 31.416 |
| Radians (rad)An angle in radians; a full turn is 2π. | 1.5708 |
| Circumference (cm)The distance once around a circle. | 125.66 |
Common mistakes
Useful for curved cuts or measuring part of a circular border.
Glossary
- Radius
- Centre to edge — half the diameter.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Arc length
- The length of the curved piece cut from a circle’s edge.
- Radians
- An angle in radians; a full turn is 2π.
- Circumference
- The distance once around a circle.
Frequently asked questions
Q. How is Arc Length Calculator calculated?
Arc length = 2π × Radius × Angle (°) ÷ 360 — An arc is a fraction of the circumference, so multiply the full circumference by angle over 360. In radians it simplifies to radius times angle.
Q. Can you walk through an example?
With Radius 20cm, Angle (°) 90°, the answer is Arc length 31.416cm.
Q. What do I need to enter?
Enter Radius, Angle (°). The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Radius (cm) moves the answer to Radius (cm) 10 → Arc length (cm) 15.708 and Radius (cm) 40 → Arc length (cm) 62.832. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Useful for curved cuts or measuring part of a circular border.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.