The normal thing to do is to take the typical forward voltage drop and subtract that from the supply voltage.
Single red LEDs are never more than about 2 V forward voltage drop. What colour are the ultrabrights that you are quoting?
If you have a red LED with a drop of 2 V and you want to light if at 20 mA from a 5 V supply, there is (5 - 2) = 3 V across the resistor, so you want 150 Ω.
On a 12 V supply, it is usual to put a few LEDs in series. So to light four of the same LEDs from 12 V the total drop is 8 V, so there is 4 V left on the resistor, which should be 200 Ω.
You could go to 5 LEDs but not on a car battery because the voltage regulation is poor, so the brightness would vary too much.