Degrees to turns
One degree is 0.002777777778 turns, and this shows the working rather than just the answer. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
The factor
One degree is 0.002777777778 turns. That is the whole of the conversion: multiply by it, and nothing else happens.
What this page will not claim
It will not call this conversion exact. The factor is right to every figure shown, but at least one of these two units is not defined exactly in terms of the other, so there is a limit to how far the decimals mean anything.
The degree is π/180 radians. Exact as a fraction of π and never as a decimal, which is why this row is the one that cannot be exact.
The number in your head
Most people use 0.0028 for this, which is the factor to two significant figures. It is high by 0.8% — 8 turns too many in every thousand, and 80 in every ten thousand.
Going the other way
The reverse is not this sum backwards in your head. It is a different factor, 360, and dividing by one is not the same as multiplying by a rounded version of the other.
That one is short enough to write down exactly, which is why the conversion feels easier in this direction than the other.
How many of those decimals mean anything
The box above will give you ten decimal places because it can. Whether they mean anything is decided by your measurement, not by the arithmetic.
If you measured to the nearest degree, your figure is already uncertain by half of one — so the answer is uncertain by about 0.001389 turns, and every digit past that is decoration. Quoting 0.00342933 when you measured with a tape is claiming a precision the tape never had.
Where these two sit
Degrees and turns both measure angle, which is why they can be converted at all. A conversion between families — a length into a weight — is not a conversion, it is a question with a missing quantity in it.
The unit converter pairs degrees with radians rather than with turns, because that is the conversion people ask for most. This page exists because a good many ask for this one instead.
Other conversions from degrees
radians · arcseconds · arcminutes · gradians