What size power station do you need to charge phones and run lights through an evening blackout?

Short answer: 181 Wh of rated capacity — that's the ~300 Wh — compact class. The minimum-viable blackout kit: light and communication.

The math, appliance by appliance

ApplianceAvg drawHours usedEnergy
Phone charging × 210 W1 h20 Wh
LED light bulbs × 39 W4 h108 Wh
Energy needed over 4 hours128 Wh
÷ 0.85 inverter efficiency151 Wh
× 1.2 headroom (ageing, cold, overrun)181 Wh
Recommended: ~300 Wh — compact class. Output check: 47 W continuous, 47 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 181 Wh work?
The bare energy need is 151 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 47 W continuously with no motor surges — any unit big enough on capacity is big enough on output.
Could solar keep this running indefinitely?
Roughly 256 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.