Start with what you want to run
List the appliances you want on during an outage and their wattage. LED bulbs use about 10W, a standing fan 60–75W, a TV with decoder about 120W, a fridge 100–200W and a 1HP air conditioner about 900W.
Add up the watts of everything that can run at the same time. That number, plus about 25% headroom, is the minimum inverter size. Fridges, pumps and ACs draw extra power when they start, so allow more if you have them.
Then decide how many hours of backup
Battery size is energy, not power: watts × hours. Ten LED bulbs, two fans, a TV and a fridge running for 8 hours is roughly 2.5–3kWh.
Lithium (LiFePO4) batteries can safely use about 80–90% of their capacity, so divide by 0.8 to get the battery size. In the example above, a 5kWh battery is a comfortable fit.
Typical sizes for Lagos homes
Self-contain or 1-bedroom (lights, fans, TV, router): 1–2kW inverter with 1–2.5kWh storage, or a portable power station.
2–3 bedroom flat (add a fridge and laptops): 3–5kW inverter with 5–10kWh storage.
Duplex or home with AC: 6–10kW inverter with 10–20kWh storage and enough panels to recharge during the day.
Don't forget the panels
Panels recharge the battery for free. In Lagos, plan on about 4–5 good sun hours a day. To refill a 5kWh battery in a day you need roughly 1.5–2kW of panels — three or four 550–620W panels.