You are basing your question from the wrong angle. It is not a case of 90 minutes awake time, how long naps will that give me? You start from how long naps are, and use that to inform awake time. Not the other way around.
You are also assuming it is age related, it isn't. You can get a 4 month old having 2h+ naps. You can have a 4 month old having naps never longer than 30 minutes. Both are normal. Both will have very different awake times.
If naps are under an hour (usually) then I would say 90 minutes is the maximum awake time. But 20 minutes awake time would also be perfectly fine, if baby is exhausted.
If naps are usually less than 30 minutes, then I would imagine baby to be tired within 45 minutes of being awake. There is no specific scientific formula (if only!), it is baby-specific. These are just approximations.
It would be much better to understand your baby's series of tired signs and use those to inform the awake time that suits your child best. Mine would be:
- baby happy to roll around on floor without much input from me = happy, awake, not tired
- baby happy to roll around on the floor but starting to need your attention to stay happy = now tired. Not massively so, but tired and ready for a sleep.
- baby needing to be held. Happy while entertained, grumpy when not = very tired and/or hungry
- baby needing to be constantly entertained. Will cry as soon as not distracted by ever changing distractions = now over tired and/or very hungry
- baby unhappy no matter what you do = chronically over tired and exhausted.
So to work out your own, baby-led suggested nap length and awake time, follow baby's cues. Try getting baby to sleep as soon as baby starts needing attention. Give that attention towards getting to sleep, rather than keeping baby awake. See if you notice how long that awake time usually is.
You may well start noticing patterns with your child and be able to predict, based on what previous naps have been like that day, when baby is going to need a sleep.