Math

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.

Results
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 doesLength of a circular arc.
CategoryMath
Inputs neededRadius, Central angle, Angle unit
Main outputArc length
Formulas = r × θ (θ in radians)
CostFree — no sign-up, no download

How to use the Arc Length Calculator

  1. 1Enter the circle's radius.
  2. 2Enter the central angle.
  3. 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.