Skip to content
Math Calculators

Arc Length Calculator

Verified formula Updated Jun 2026 Private — runs on your device

Enter details
units
degrees
Verified formula Private

Arc length

9.4248

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Arc Length Calculator

The Arc Length Calculator works out your arc length in an instant. Enter radius and central angle and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the radius.
  2. Enter the central angle.
  3. Read off your arc length — the calculator updates automatically, with no button to press.

Formula

The Arc Length Calculator uses the formula:

Arc length = 2 × 3.141592653589793 × Radius × Central angle ÷ 360

Worked example

For example, with radius of 6 units and central angle of 90 degrees, the arc length is 9.4248.

Inputs used
Radius 6 units
Central angle 90 degrees
Results
Arc length 9.4248

Results are estimates for educational use, not professional advice.

Key terms explained

Radius
The distance from the centre of a circle or sphere to its edge.

Frequently asked questions

Multiply the circumference by the fraction of the circle: arc = 2πr × angle ÷ 360. A 90° arc of radius 6 is about 9.42 units.

An arc is a portion of the circle's circumference between two points on the edge.

At 360° the arc equals the full circumference, 2πr.

Both use the same fraction of the circle. Arc length scales the circumference, while sector area scales the circle's area.

Enter the radius. Enter the central angle. Read off your arc length — the calculator updates automatically, with no button to press.

Arc Length Table: Arc length by Radius

Reference table of arc length for Arc Length across a range of radius values — exact, engine-computed figures you can read off at a glance.

1 min read

Related calculators