Here is a table that outlines how much time a baby can stay awake before they get tired and need to go down for a sleep again.

Age High sleep needs Low sleep needs
0-4 weeks old 30 minutes 50 minutes
4 – 6 weeks old 40 minutes 60 minutes
6 – 8 weeks old 45 minutes 1 hour 15 minutes
2 months old 50 minutes 1 hour 20 minutes
3 months old * 1 hour 1 hour 30 minutes
4 months old * 1 hour 15 minutes 2 hours
5 months old * 1 hour 45 minutes 2 hours 15 minutes
6 months old * 2 hours 3 hours

I have stopped the awake times at the 6 month mark because this is where babies start to vary quite significantly, and where the awake times throughout the day will also start to vary significantly. For example, the first awake time might be as low as only one hour, however the rest of the day the awake times will be two hours or more.