What size power station do you need to run home essentials for three days?

Short answer: 8,174 Wh of rated capacity — that's the 4 kWh+ — expandable system or generator territory. Three days is where expandable batteries and solar input become the sensible answer.

The math, appliance by appliance

ApplianceAvg drawHours usedEnergy
Refrigerator (full-size)60 W72 h4,320 Wh
Wi-Fi router + modem12 W72 h864 Wh
Phone charging × 210 W6 h120 Wh
LED light bulbs × 39 W18 h486 Wh
Energy needed over 72 hours5,790 Wh
÷ 0.85 inverter efficiency6,812 Wh
× 1.2 headroom (ageing, cold, overrun)8,174 Wh
Recommended: 4 kWh+ — expandable system or generator territory. Output check: 209 W continuous, 959 W surge.

Fridges and freezers use their average cycling draw for energy and full compressor draw for the output check — that's why the numbers differ from the label.

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Quick answers

Can a smaller unit than 8,174 Wh work?
The bare energy need is 6,812 Wh after inverter losses; the extra 20% covers battery ageing, cold weather, and outages running long. A smaller unit works on a good day — this size works on a bad one.
What about output watts, not just capacity?
The station must sustain 209 W continuous and survive a 959 W start-up surge. Nearly every unit in the 4 kWh+ clears both comfortably.
Could solar keep this running indefinitely?
Roughly 643 W of panels replaces a day's usage with ~4 hours of decent sun at real-world (75%) efficiency. Half that solar doubles your runtime instead of sustaining it.