Radians per Degree

One degree is exactly π/180 radians, or 0.01745329 rad — the reciprocal of 57.29578. Because the constant is literally the measure of a one-degree angle, the conversion table on this page reads as that single angle in every unit the site knows: 60 arcminutes, 3600 arcseconds, 1.1111 gradians, 1/360 of a revolution.

The convenient consequence is the small-angle approximation. For angles under about 10°, sin θ ≈ tan θ ≈ θ in radians, so a 1° slope rises 0.01745 units per unit of run — pipe fitters, machinists and optical designers all use that as a mental shortcut and it is accurate to better than 0.02 % at one degree. It also explains the surveyor's convention of quoting small angles in seconds: one arcsecond is 4.848 microradians, which at 100 m is a displacement of half a millimetre.