100 amp service 100 amp main. Enough space to add adequate breaker. But need to know if load calculations are within code. Home has 1200 sq ft of living space. 1 30amp electric dryer circuit NOT USED. Gas Dryer, Gas Water Heater. Electric Range on 50 amp breaker. Central air on 40 amp breaker. 6 15 amp breakers 4 20 amp breakers. 1 30 amp breaker.
Can a 50 amp 240v Hot Tub circuit be added to this configuration. Or will I have to convert the range to gas.

In my opinion, you would be pushing the limits of your service. Changing out the range would help but a 100 amp service for a primary residence is a thing of the past. Spend your hot tub money on a new 200 amp service... at least for now.