I get a rough estimate by taking the FIO2 times 600.
eg. If you are on 100% O2, your PaO2 should be around 600.
If you are on 50% O2, your PaO2 should be around 300.
If you are on room air, your PaO2 should be around 125.
The gradient is the calculated number minus the PaO2 on the ABG.
It's not exact, but puts you in the right ballpark very quickly.