my question is on how to calculate battery capacity
The problem with your expectations is they assume the battery and solar panel put out constant voltage and current, and that all this energy is transferred to the load with 100% efficiency. 

If the inverter was 85% efficient then to run a 250W light bulb it would need to draw 294W from the battery. 294W * 5 hours = 1470 Watt hours.  

A lead-acid battery's voltage drops as it discharges, and its capacity reduces at high current draw. So a battery rated for 100Ah might only deliver 90Ah at the 5 hour rate, with voltage dropping from 12.5V to 10.5V through that time.  

20.42A * 6.9 hours = 140.9Ah. However a solar panel rated for 245W at 12V will only deliver that power in full sunlight (1000W/m2). In most locations that will not be achievable, and certainly not for 6.9 hours in a single day. The solar charge controller will also have some loss which must subtracted from the total, and the battery's charging voltage is higher (up to 14.4V) so more energy is required to charge it than it will deliver on discharge.

Lead acid batteries don't like being fully discharged or charged at a high rate. The obvious solution is to oversize the battery so it has more capacity than is required. Similarly, a larger solar panel will be needed to produce sufficient power on dull days and during winter when the sun is weaker.