What will it take to run this load?

There are several factors:

1. current (power), in Amps (A)
2. Watt-hours (Wh) ¹⁾ (energy)
3. any charging sources that are active at the time
4. recharging afterward

And a couple formulas we will use to convert units back and forth:

1. Watts = Volts x Amps.
2. Amps = Watts / Volts.

about these summaries

Note: when discussing current we often use Amps, since that informs our wiring/fusing choices.

If we are talking about DC loads the current will be the watts / bank nominal voltage.²⁾. So a 400w DC load running off a 12v bank will pull ~33.3A (400w / 12.0v).

A more usual case is running 120vac loads off an inverter. This will involve both the load itself and inverter losses caused by the conversion. Inverter efficiencies vary by model and actual loads applied on them, but we can ballpark 85% for the purposes of this discussion. So 15% additional losses.

1. So a 400w DC load running off an inverter from will pull 33.3A from the 12v bank
2. plus an additional 15% penalty, giving us ~39A (33.3A / 0.85) or 518W if you like.

The inverter should probably be run with some headroom below its rating. So perhaps a 500w continuous rating for our example 400w load.

Different battery bank chemistries and capacities have a certain amount of current they can comfortably deliver.

• with lead chemistries³⁾ the battery bank will usually exhibit voltage sag when driven too hard.
• LiFePO4 batteries have little sag to let us know when it's straining, so we typically stick to 0.5C limits or whatever the mfg recommends. 0.5C of a 100Ah LFP would be 50A (110Ah x 0.5C).

In practice the loads on the battery bank might be greater (other loads running) or lesser (alternator, solar, or shore power charging active).

Energy use is often done in Watt-hours, although Amp-hours will also work.

This is time (hours) x watts. Our 518W (39.3A at 12v) load run for 20 minutes would be ~173Wh (518 x 20 minutes / 60 minutes in an hour) or 13.1Ah.

Battery chemistries have recommended depths of discharge.

• Lead batts are usually run down to 50%, so we would need at least 28.8Ah of lead to run our 173Wh load for one day (173Wh / 0.5 / 12.0v nominal).
• LiFePO4 batts are usually run down to 20%, so we would need at least 16.9Ah of LFP to run our 173Wh load for one day (173Wh / 0.8 / 12.8v nominal).

Then multiply by the “days of autonomy” (ie, without recharging). If you want two days then multiply the above by 2, for example. If you know you will be able to recharge fully each day then days of autonomy is 1.

Note that running loads while sufficient charging is active is basically a freebie and does not count against the battery capacity.⁴⁾

If you are recharging LiFePO4 the 173Wh used is basically what you'd need to recharge that battery to its former state of charge.

Lead battery charging is much less efficient, varying by chemistry and charging stage. For the purposes of this discussion we can assume they are 80% charge-efficient, so replacing 173Wh would actually require 216Wh of charging (173Wh / 0.8).