Degrees to radians

Type an angle in degrees, with or without the ° sign, and the radians appear as a fraction of π and as a decimal. 45 gives π/4 and 0.785398. Degrees, minutes and seconds work too, like `45° 30′ 36″`.

Press swap to go the other way, or use the radians to degrees converter, which reads π fractions like `3π/4` as well as decimals.

Multiply by π/180. A half turn is 180° and also π radians, so one degree is π/180 of a radian.

To keep the answer exact, leave π in and cancel the fraction. 45 × π/180 is 45π/180, and 45 goes into 180 four times, so it's π/4. 270° is 270π/180, which cancels to 3π/2. For a decimal, put in π ≈ 3.14159265. π/4 is about 0.785398.

Nobody knows for certain why a circle has 360 degrees. One idea links it to the year, since the Sun moves about one degree a day against the stars and some ancient calendars ran to 360 days. Another credits Babylonian astronomers, who counted in sixties. What's clear is that 360 is convenient. It has 24 divisors and divides evenly by every number from 1 to 10 except 7, which is why the world splits so neatly into 24 time zones of 15° each.

Radians have a better claim to being natural. One radian is the angle at which the arc is as long as the radius, so the angle in radians is the arc length divided by the radius. That's why calculus uses them: the derivative of sin x is cos x only when x is in radians.