Formula
Watt-hours are amp-hours times volts. Amp-hours are watt-hours divided by volts. Milliamp-hours are amp-hours times 1,000. A kilowatt-hour is 1,000 watt-hours. A watt is one joule per second, so a watt-hour is 3,600 joules. Watts are volts times amps, and energy is watts times hours.
Wh = Ah × V
V_bank = V × series
Ah_bank = Ah × parallel
usable = Wh × DoD × inverter efficiency
Series stacks voltage. Parallel stacks amp-hours. The watt-hours are the product either way, which is why four 12 V 100 Ah batteries are 4,800 Wh in series or in a 2-by-2 split. Nominal voltage is the voltage a manufacturer multiplies to print a watt-hour rating. A resting voltage off the charger is not that number.
Usable energy is the rated watt-hours times a depth of discharge you type. Inverter efficiency is applied only when the load is AC. A DC load skips it. The 80 percent LiFePO4 and 50 percent lead-acid figures are the same starting points as the battery runtime page. They are not a standard, and this page is not citing a datasheet for them. Ninety percent inverter efficiency is an assumption. Hours here are usable watt-hours divided by watts. Peukert’s exponent, which shortens a lead-acid battery at a high current, is on the runtime page.
FAA PackSafe limits a lithium-ion battery to a rating of 100 watt hours for the usual allowance. With airline approval, a passenger may carry up to two spare larger lithium-ion batteries in the 101 to 160 Wh range. Batteries over 160 Wh are forbidden. Spare batteries, including power banks, are carry-on only, and the terminals have to be protected from a short. The same page says many airlines set stricter limits. Check the airline. Nothing here is a packing approval.
Worked examples
100 Ah at 12.8 V. 1,280 Wh, 1.28 kWh. 1,000 Wh at 12 V is 83.33 Ah. 5,000 mAh at 3.7 V is 18.5 Wh, 66,600 J. 20,000 mAh at 3.7 V is 74 Wh, under the 100 Wh tier.
60 W for 5 hours. 300 Wh. Four 12 V 100 Ah batteries in series are 48 V, 100 Ah, 4,800 Wh. The same four as two series pairs in parallel are 24 V, 200 Ah, still 4,800 Wh.
Usable. 1,280 Wh at 80 percent depth of discharge and 90 percent inverter efficiency is 921.6 Wh. At a 100 W AC load that is 9.22 hours, before Peukert. A 12 V 100 Ah lead-acid bank at 50 percent, on a DC load, is 600 Wh usable. The inverter is not applied.
Reference
Voltage buttons are nominal labels you can overwrite. Depth of discharge is yours.
| Starting point | DoD |
|---|---|
| Flooded lead-acid | 50% |
| AGM | 50% |
| LiFePO4 | 80% |
Questions
How do I convert amp-hours to watt-hours?
Multiply amp-hours by volts. 100 Ah at 12.8 V is 1,280 Wh, or 1.28 kWh. Watt-hours let you compare a 12 V battery with a 48 V one. Amp-hours do not.
How many watt-hours is a 100 Ah battery?
It depends on the voltage. At 12 V, 100 Ah is 1,200 Wh. At 12.8 V it is 1,280 Wh. The label’s nominal voltage is the one manufacturers use for that rating.
How do I convert mAh to Wh?
Divide milliamp-hours by 1,000, then multiply by the cell voltage. 5,000 mAh at 3.7 V is 18.5 Wh. A power-bank label that prints mAh without a voltage is leaving out half of the product.
How many watt-hours can I take on a plane?
FAA PackSafe limits a lithium-ion battery to 100 Wh for the general allowance. A spare from 101 to 160 Wh needs airline approval, and two is the limit they state. Over 160 Wh is forbidden in passenger baggage. Spare batteries and power banks are carry-on only. Airlines can be stricter. Check yours. This page only does the arithmetic.
What is the difference between Ah and Wh?
Amp-hours are electric charge. Watt-hours are energy. Energy is charge times voltage. A joule is a watt-second, so one watt-hour is 3,600 joules.
How many watt-hours do I need for my solar setup?
Add the loads. The off-grid solar calculator turns a daily watt-hour list into panels and a battery. This page only converts a rating you already have.
Does wiring in series increase capacity?
Series multiplies voltage and leaves amp-hours alone. Parallel multiplies amp-hours and leaves voltage alone. Watt-hours come out the same if you use the same cells. Use matched batteries. This page does not size a fuse or a cable.
Sources
- The watt is the SI unit of power, one joule per second. A watt-hour is therefore 3,600 joules. Amp-hours times volts are watt-hours by that same definition.
- FAA PackSafe, lithium batteries, and the airline-passenger battery chart. Lithium-ion batteries are limited to 100 Wh. Spares of 101–160 Wh need airline approval, two per person. Over 160 Wh is forbidden. Spare batteries and power banks are carry-on only. Airlines may be stricter.
- Depth of discharge starts from the figures already on this site’s battery runtime page: flooded and AGM 50 percent, LiFePO4 80 percent. Those are typical practice there, not a datasheet read for this page. Inverter efficiency at 90 percent is an assumption.