Question

When calculating the length of an arc, does it matter which unit of measurement (radians or degrees) you use when measuring the central angle?

Answer 1

No, it does not matter.

If you measure the central angle in degress, you use the proportion

circumference / 360° = length of arc / central angle in degrees,

and if you measure the angle in radians, you use the proportion

circumference / (2π) = length of arc / central angle in radians.