What size power station do you need to run a CPAP for two nights?

Short answer: 904 Wh of rated capacity — that's the ~1 kWh — mid-size class. Two nights of CPAP without recharging — a weekend power cut or an off-grid weekend.

The math, appliance by appliance

ApplianceAvg drawHours usedEnergy
CPAP (no humidifier)40 W16 h640 Wh
Energy needed over 48 hours640 Wh
÷ 0.85 inverter efficiency753 Wh
× 1.2 headroom (ageing, cold, overrun)904 Wh
Recommended: ~1 kWh — mid-size class. Output check: 40 W continuous, 40 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 904 Wh work?
The bare energy need is 753 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 40 W continuously with no motor surges — any unit big enough on capacity is big enough on output.
Could solar keep this running indefinitely?
Roughly 107 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.