265 hours
Reasonable load range: 166 hours to 442 hours
Calculation
7,800Wh × 85% usable efficiency ÷ (500W × 5% duty cycle) = 265.20 hours.
What can change the result
Actual device wattage, battery age, ambient temperature, inverter standby draw, conversion losses, power-factor behavior and cycling frequency can all reduce or extend runtime.
Check output before connecting
The battery or UPS needs at least 800W continuous capability and about 1200W surge capability. Watt-hours alone do not prove compatibility.