Arc Length

Definition: The distance along the curved line making up the arc

Try this Drag one of the orange dots that define the endpoints of the blue arc. The arc length will be continuously calculated.

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The arc length is the measure of the distance along the curved line making up the arc. It is longer than the straight line distance between its endpoints (which would be a chord)

Central angle in degrees

The formula the arc measure is:

where:
C is the central angle of the arc in degrees
R is the radius of the arc
π is Pi, approximately 3.142

Recall that 2πR is the circumference of the whole circle, so the formula simply reduces this by the ratio of the arc angle to a full angle (360). By transposing the above formula, you solve for the radius, central angle, or arc length if you know any two of them.

Central angle in radians*

If the central angle is is radians, the formula is simpler:

where:
C is the central angle of the arc in radians.
R is the radius of the arc

This is the same as the degrees version, but in the degrees case, the 2π/360 converts the degrees to radians.

* Radians are another way of measuring angles instead of degrees. One radian is approximately 57.3°
For more on this see Radians definition.

Arc Length

Central angle in degrees

Central angle in radians*

Other circle topics

General

Angles in a circle

Arcs