Arc Length from Radians
Math
Arc Length from Radians with stated conventions, validation and a worked example.
Formula
arc length = radius × angle in radians
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Angles cover 0 to one complete turn.
Example Calculation
Example inputs
- Radius: 3 units
- Central angle: 1.5707963267948966 rad
Radius 3 and angle π/2 give arc length 3π/2 and sector area 9π/4.
Frequently asked questions
How do I use this calculator?
Enter radius, central angle. The result updates automatically. Use Reset to restore the example values.
What method does it use?
arc length = radius × angle in radians. Angles cover 0 to one complete turn.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.