What measure of angle is based on arc length?

The radian is a measure of angle that is directly based on the arc length. One radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. This relationship highlights the radian's intrinsic link to the properties of circles and makes it particularly useful in various areas of mathematics and engineering, especially when working with trigonometric functions and calculus.

In contrast, the degree is a more conventional and widely used unit of measuring angles but does not relate directly to arc length in a consistent manner. The gradian, used mainly in some fields such as surveying, divides a right angle into 100 parts, whereas the minute is a subdivision of degrees and not a primary measure of angular magnitude. The radian's unique definition provides a natural way to relate angle measures to linear dimensions, particularly useful when applying formulas involving circular motion or wave phenomena.