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What size power station do you need to run a home server or NAS for 12 hours?

Short answer: 1,355 Wh of rated capacity — that's the ~2 kWh — large class. Longer than any UPS: keep the homelab up through a serious outage.

The math, appliance by appliance

ApplianceAvg drawHours usedEnergy
Home server / NAS80 W12 h960 Wh
Energy needed over 12 hours960 Wh
÷ 0.85 inverter efficiency1,129 Wh
× 1.2 headroom (ageing, cold, overrun)1,355 Wh
Recommended: ~2 kWh — large class. Output check: 80 W continuous, 80 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.

Adjust this in the calculator See current prices

Quick answers

Can a smaller unit than 1,355 Wh work?
The bare energy need is 1,129 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?
These loads draw 80 W continuously with no motor surges — any unit big enough on capacity is big enough on output.
Could solar keep this running indefinitely?
Roughly 640 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.