Arc length calculator

Type an angle in degrees and a radius. Arc length is a fraction of the circle: (α/360)×2πr. 180° and r = 1 give 3.141593. 90° and r = 2 give 3.141593. 360° and r = 1 give 6.283185.

The angle is in degrees, not radians. 180° and r = 1 give a half circle, 3.141593. A full 360° at r = 1 is 6.283185.

Input data

Results

Enter data and click Calculate.

How it works

Arc length is a piece of the circle. The calculator computes (α/360)×2×π×r. With 180° and r = 1 you have half of 2π, which is π. The result is 3.141593, six decimals from machine float, not a bare 3.14.

The fields are angle α in degrees and radius r. 90° and r = 2 give π again, a quarter of 2π×2. 360° and r = 1 close the whole circle: 6.283185. That is the same 2πr as circumference, only here the angle may be other than 360.

0° leaves zero. 720° at r = 1 gives two circles, 12.566371. A minus angle gives a minus length. The calculator does not stop the drawing, it only multiplies.

Sector area takes the same angle and the same r, but computes area, not length. Circle area from r alone is on the neighbouring page. Here you always stay with the arc.

The header units switch does not multiply anything. 180 and 1 stay 3.141593 whatever the label says.

180° and r = 1 give 3.141593. 90° and r = 2 give 3.141593. 360° and r = 1 give 6.283185.

Formula

L = (α/360) × 2πr

How to use

  1. Type the angle in degrees, for example 180, and the radius, for example 1.
  2. Click Calculate. Arc length comes out 3.141593.
  3. 90° and r = 2 give 3.141593. 360° and r = 1 give 6.283185.
  4. The angle is in degrees. 180 means a half circle, not 180 radians.
  5. Sector area from the same angle lives on the neighbouring card.

180° and r = 1 give 3.141593

Arc length is (α/360)×2πr. 180° and r = 1 give 3.141593. 90° and r = 2 give 3.141593. 360° and r = 1 give 6.283185.

arc
A piece of the circle. 180° and r = 1 give 3.141593. 360° closes 6.283185.
angle
The first field, in degrees. 90° with r = 2 again gives 3.141593.
radius
The second field. At r = 1 the full circle is 6.283185. At r = 2 a quarter is 3.141593.

Examples

Example 1

  • α = 180°
  • r = 1

3.141593

What is the arc at 180° and r = 1? 3.141593. Half a circle, π.

Example 2

  • α = 90°
  • r = 2

3.141593

What is the arc at 90° and r = 2? 3.141593. A quarter of 2π×2.

Example 3

  • α = 360°
  • r = 1

6.283185

What is the arc at 360° and r = 1? 6.283185. The whole circle, 2π.

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Common questions

What is the arc at 180° and r = 1?

3.141593. That is π, half of the 2π circle.

What does arc length mean?

A piece of the circle. The angle fraction times 2πr. 90° is a quarter.

What about 90° and r = 2?

3.141593. A quarter of 4π, π again.

What about 360° and r = 1?

6.283185. The whole circle, 2π.

Is the angle in radians?

No. The field takes degrees. 180 means 180°, not 180 radians.

Does 0° give zero?

Yes. Zero degrees, zero arc.

Does an angle larger than 360° pass?

Yes. 720° and r = 1 give 12.566371, two circles.

How is this different from sector area?

Here the edge length. There the sector area from πr².

Where is the area of the whole circle?

On the circle area card. No angle there, only r.

Does a comma in 90.5 work?

Yes. 90.5 and 90,5 are the same angle.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.