Atmospheres to bars
One atmosphere is 1.01325 bars, 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 atmosphere is 1.01325 bars. 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 atmosphere is defined as exactly 101,325 pascals. Not quite a bar.
The bar is exactly 100,000 pascals, and near enough atmospheric pressure at sea level.
The number in your head
Most people use 1 for this, which is the factor to two significant figures. It is low by 1.3077% — 13.077 bars too few in every thousand, and 130.77 in every ten thousand.
Going the other way
The reverse is not this sum backwards in your head. It is a different factor, 0.986923266716, and dividing by one is not the same as multiplying by a rounded version of the other.
Rounded, the way back is 0.987, which is high by 0.0078%. 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 atmosphere, your figure is already uncertain by half of one — so the answer is uncertain by about 0.506625 bars, and every digit past that is decoration. Quoting 1.25091792 when you measured with a tape is claiming a precision the tape never had.
Where these two sit
Atmospheres and bars both measure pressure, 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 atmospheres
pascals · kilopascals · mmHg · psi · torr · millibars · inHg · hectopascals