Stone to kilograms
One stone is 6.35029318 kilograms, 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 stone is 6.35029318 kilograms. That is the whole of the conversion: multiply by it, and nothing else happens.
And it is exact
Not rounded, not measured, not a convention that might be revised. The factor above is the definition, so an answer from it is as exact as the number you typed.
The stone is 14 pounds, so exactly 6.35029318 kg.
The number in your head
Most people use 6.4 for this, which is the factor to two significant figures. It is high by 0.7827% — 7.827 kilograms too many in every thousand, and 78.27 in every ten thousand.
Going the other way
The reverse is not this sum backwards in your head. It is a different factor, 0.157473044418, and dividing by one is not the same as multiplying by a rounded version of the other.
Rounded, the way back is 0.157, which is low by 0.3004%. So the two roundings do not cancel: go out and back with both and you do not land where you started.
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 stone, your figure is already uncertain by half of one — so the answer is uncertain by about 3.175147 kilograms, and every digit past that is decoration. Quoting 7.83981795 when you measured with a tape is claiming a precision the tape never had.
Where these two sit
Stone and kilograms both measure mass, 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.
Other conversions from stone
pounds · ounces · grams · milligrams · tonnes