Deg to rad (° to rad)

One degree is pi/180 radians. That is exact as a ratio and irrational as a decimal, which is the opposite of every other conversion on CompoundPage: there is no finite number of digits that states it. 0.01745329252 is a truncation, and anything that needs the exact value has to carry the pi.

Worked through: 60 ° x 0.0174532925 = 1.0472 rad.

Going the other way, one radian is 57.29577951 degrees.

For mental arithmetic: Divide by 57.3. Or remember that 1 radian is just under 60 degrees.

The conversion that exists because a radian is the only angle unit that is not arbitrary. A radian is the angle subtending an arc equal to the radius, so it falls out of the circle itself; 360 degrees is a Babylonian convention that survives because 360 has twenty-four divisors. Every trigonometric function in every programming language takes radians, which is the single most common source of silently wrong geometry code: Math.sin(30) is -0.988, not 0.5, because 30 is read as radians. The landmarks worth knowing: 30 degrees is pi/6, 45 is pi/4, 60 is pi/3, 90 is pi/2, 180 is pi.

Precision is worth matching to the input. A measurement given as 1 ° carries one or two significant figures, and reporting its conversion to six implies a precision the original never had.