1.4.1—Radians

One radian is the angle subtended by an arc equal to the radius. A full turn is 2π radians, and θ radians correspond to arc length s=rθ.

Convert degrees before using calculus, arc length or sector formulas. Keep θ dimensionless in the formula and attach units to s or area.

A radius 5 cm and angle 1.2 rad give arc length 6.0 cm; the same numerical angle in degrees would give a wrong result.

A radian is not a physical length, and writing s=rθ with θ in degrees silently introduces a factor of π/180.