Case 1
- Radius
- 10
- Angle
- 90°
15.707963
Open with these valuesArc Length Calculator
15.707963units
Result: 15.707963 unitsThe arc is the fraction of the full circle that your angle covers: 2πr times θ ÷ 360. A quarter of a circle of radius 10 measures 15.71 — the same as half a circle of radius 5, because both are a quarter of the same total length.
The numbers at a glance
Held fixed: Radius 10.000.
| Angle (°) | Result |
|---|---|
| 0.00 | 0.000000 |
| 25.00 | 4.363323 |
| 50.00 | 8.726646 |
| 75.00 | 13.089969 |
| 90.00Your value | 15.707963 |
| 100.00 | 17.453293 |
| 125.00 | 21.816616 |
| 150.00 | 26.179939 |
| 175.00 | 30.543262 |
Worked examples
Case 2
- Radius
- 3
- Angle
- 60°
3.141593
Open with these valuesCase 3
- Radius
- 10
- Angle
- 360°
62.831853
Open with these valuesHow it's calculated
s = 2 × π × r × θ ÷ 360
- StepEnter the radius in any length unit.
- StepEnter the angle the arc spans, in degrees.
- ResultRead the arc length in the same unit as the radius.
Reference table
| Radius, angle | Exact | Arc length |
|---|---|---|
| 10, 0 | 0 | 0.000000 |
| 1, 90 | π ÷ 2 | 1.570796 |
| 3, 60 | π | 3.141593 |
| 7, 45 | 7π ÷ 4 | 5.497787 |
| 10, 90 | 5π | 15.707963 |
| 10, 360 | 20π | 62.831853 |
Questions
How do you calculate arc length?
Take the full circumference 2πr and keep the fraction your angle covers, θ ÷ 360. Radius 10 over 90° gives 5π, about 15.71.
What if my angle is in radians?
Then it is simpler still: the arc is r times the angle. Convert by multiplying radians by 180 ÷ π before entering it here.
Why do a quarter of a big circle and half of a small one match?
Because 10 × 90 and 5 × 180 are the same product. The arc depends on the radius and the angle only through their product, so those two describe the same length.
At 360 degrees, is that the circumference?
Yes. A full turn gives 2πr — for radius 10 that is 20π, about 62.83.
Sources and last check
Information, not professional advice.