Arc Length Calculator ($L$)
Calculate the length of the arc ($L$) along the circumference of a circle, determined by its radius ($r$) and the central angle ($\theta$). Enter your values below and select whether the angle is in degrees or radians.
Enter Dimensions
Key Results
Arc Length ($L$)
Circumference ($C$)
Sector Area ($\mathcal{A}$)
Step-by-Step Solution
Formulas for Arc Length
The arc length is defined as a fraction of the circle's total circumference. The formula used depends on whether the central angle ($\theta$) is measured in radians or degrees.
1. Arc Length using Radians ($\theta$)
The simplest and most fundamental relationship: the arc length ($L$) is the product of the radius and the angle (in radians).
This is the preferred formula for scientific and engineering calculations because of its simplicity.
2. Arc Length using Degrees ($\theta^\circ$)
The formula for degrees explicitly shows the ratio of the partial angle to the full circle:
Radians Conversion
If you start with degrees, you must first convert the angle to radians to use the simpler formula:
Arc Length vs. Chord Length
It is important to distinguish the arc length from the chord length (which is the straight-line distance between the two endpoints of the arc). The arc length is always greater than the chord length, except when the angle is $0^\circ$ or $360^\circ$, where they are equal.