What size power station do you need to run a fridge and chest freezer for 24 hours?

Short answer: 3,558 Wh of rated capacity — that's the ~3–4 kWh — extra-large class. Fridge plus a chest freezer full of food — the highest-value loads in most homes.

The math, appliance by appliance

ApplianceAvg drawHours usedEnergy
Refrigerator (full-size)60 W24 h1,440 Wh
Chest freezer45 W24 h1,080 Wh
Energy needed per day2,520 Wh
÷ 0.85 inverter efficiency2,965 Wh
× 1.2 headroom (ageing, cold, overrun)3,558 Wh
Recommended: ~3–4 kWh — extra-large class. Output check: 270 W continuous, 1,020 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 3,558 Wh work?
The bare energy need is 2,965 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 270 W continuous and survive a 1,020 W start-up surge. Nearly every unit in the ~3–4 kWh clears both comfortably.
Could solar keep this running indefinitely?
Roughly 840 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.