Radians to degrees (rad to °)

One radian is 180/pi degrees, about 57.29577951. Exact as a ratio, irrational as a decimal, and for the same reason as the other direction: the relationship is defined through pi.

Worked through: 1.5708 rad x 57.2957795 = 90.0002 °.

Going the other way, one degree is 0.0174532925 radians.

For mental arithmetic: Multiply by 57.3.

Going this way is almost always reading a machine's output back into human terms: a trig function, a rotation matrix, a sensor. The number to anchor on is that a radian is 57.3 degrees, which is a slightly awkward amount and is exactly why nobody measures anything in radians by hand. The other useful fact is the small-angle approximation: below about 0.1 radians, the angle in radians, its sine and its tangent agree to within a tenth of a percent, which is why so much optics and surveying arithmetic quietly assumes it.

Precision is worth matching to the input. A measurement given as 0.1 rad carries one or two significant figures, and reporting its conversion to six implies a precision the original never had.