Both in the Baḥrī period and the Burjī period. I've been trying to find an answer for about 30 minutes and I've found nothing, so if you know, a source would be good too.
According to Wikipedia the Mamluk Sultanate ruled part or all of the territory of the following countries:
> Today part of
Egypt Israel Jordan Lebanon Libya State of Palestine Palestine Saudi Arabia Sudan Syria Turkey
Thus the maximum area of the Mamluk sultanate must be smaller than the total area of those countries.
Egypt: 1,010,407.87 square kilos
Syria: 185,180 square kilos
Israel: 20,770 square kilos
Jordon: 89,341 square kilos
Lebanon: 10,452 square kilos
Palestine: 6,220 square kilos
total area: 1,322,370.87.
The Mamluk Sultanate probably ruled most of the area of those countries.
Then there are four large countries that the Mamluk Sultanate probably ruled relatively small parts of:
Libya: 1,759,541 Square kilometers
Turkey: 783,356 Square kilometers
Sudan: 1,861,484 Square kilometers
Saudi Arabia: 2,149,690 Square kilometers
total: 6,554,071 square kilometers. But the Mamluk Sultanate ruled relatively small parts of those countries.
Thus the Mamluk Sultanate probably ruled somewhere between about 1,322,370.87 square Kilometers and about 7,886,441.87 square kilometers.