Arc Length Calculator
Length of a circular arc.
Enter your values
Enter the radius you are working with.
Enter the central angle you are working with.
Choose one of: Degrees, Radians.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Arc length
- 10.0531
- Angle in radians
- 1.25664
- Sector area
- 40.2124
- Chord length
- 9.4046
- Full circumference
- 50.2655
Quick answer
Arc length equals the radius times the central angle in radians.
s = r × θ (θ in radians)
At a glance
| What it does | Length of a circular arc. |
|---|---|
| Category | Math |
| Inputs needed | Radius, Central angle, Angle unit |
| Main output | Arc length |
| Formula | s = r × θ (θ in radians) |
| Cost | Free — no sign-up, no download |
How to use the Arc Length Calculator
- 1Enter the circle's radius.
- 2Enter the central angle.
- 3Pick degrees or radians.
Inputs explained
- Radius
- Enter the radius you are working with.
- Central angle
- Enter the central angle you are working with.
- Angle unit
- Choose one of: Degrees, Radians.
Worked example
Using the values the calculator loads with:
Inputs
- Radius8
- Central angle72
- Angle unitDegrees
Results
- Arc length10.0531
- Angle in radians1.25664
- Sector area40.2124
- Chord length9.4046
- Full circumference50.2655
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180.
What if the angle is a full circle?
The arc length becomes the circumference, 2πr.
What do I need to enter into the Arc Length Calculator?
Just 3 values: radius, central angle, angle unit. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Arc Length Calculator work out the answer?
Arc length equals the radius times the central angle in radians. It applies the formula s = r × θ (θ in radians) and shows the working so you can check each step by hand.
Is the Arc Length Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.