Battery capacity:
turning amp-hours and mAh into watt-hours

Why amp-hours alone cannot compare two batteries

An amp-hour rating says how much charge a battery can deliver, not how much energy. Charge only becomes energy once it is multiplied by voltage, and batteries come at different voltages. A 100 Ah battery at 12 V and a 100 Ah battery at 24 V hold very different amounts of energy, even though the label number matches.

That is why a capacity figure needs a voltage beside it. Watt-hours (Wh) combine both and are the number to use when comparing a laptop battery with a power bank, or a home backup battery with another one built from different cells.

What 'nominal' voltage means

Battery voltage is not fixed. A fully charged lead-acid battery sits near 12.8 V and falls toward 11.8 V as it empties. Makers therefore quote a single nominal value as an average for calculation. For single lithium-ion cells it is commonly 3.6 or 3.7 V, for lithium iron phosphate 3.2 V per cell, and for lead-acid 2 V per cell.

Use the nominal value printed on the label. A '12 V' lithium iron phosphate battery of 100 Ah actually stores 12.8 × 100 = 1,280 Wh, about 7% more than a lead-acid battery with the same printed numbers.

Converting phone and power bank ratings

Phone batteries and power banks are rated in mAh, a unit that is easy to misread. Divide by 1,000, multiply by voltage. A phone with a 5,000 mAh battery at 3.85 V holds 5 × 3.85 = 19.25 Wh. A 20,000 mAh power bank, whose cells run at 3.7 V, stores 20 × 3.7 = 74 Wh.

Dividing 74 Wh by 19.25 Wh gives 3.84, which is the number of full phone charges you would get if nothing were lost. In practice, converting the cell voltage up to the 5 V USB output and charging losses typically consume a sizeable part of the energy. At an assumed 70% overall efficiency, the figure falls to 74 × 0.7 ÷ 19.25 = 2.7 charges. Efficiency varies by product, so treat 70% as a placeholder.

Series and parallel connections

Adding batteries together changes voltage or amp-hours, but the energy always adds. Connect two 12 V 100 Ah batteries in series and you get 24 V at 100 Ah, which is 2,400 Wh. Connect them in parallel and you get 12 V at 200 Ah, also 2,400 Wh.

• Series: voltages add, Ah stays the same. Use it when the equipment needs a higher voltage.
• Parallel: Ah adds, voltage stays the same. Use it for more run time at the same voltage.
• Mixed banks: count the series strings and the parallel strings, then multiply.
• Keep the batteries identical in age, size and chemistry; mixing causes unequal charging and early failure.

The same arithmetic applies to cells inside a pack. A '4S2P' pack has four cells in series and two strings in parallel; with 3.6 V, 3 Ah cells it is 14.4 V and 6 Ah, which is 86.4 Wh.

Rated capacity versus what you can take out

A rating is measured under stated conditions. Lead-acid batteries are commonly rated at the 20-hour rate: a 100 Ah battery is tested by drawing 5 A for 20 hours. Draw 25 A instead and you will not get a full 100 Ah, because high discharge rates reduce the capacity available. Lithium chemistries hold up better under heavy loads, but they too lose capacity in cold weather and with age.

Depth of discharge is the second filter. If a lead-acid battery should be kept above about 50%, only 600 Wh of the 1,200 Wh nominal figure is practical for daily use. A lithium battery rated for 80% usable gives 960 Wh from the same nominal energy. Check the datasheet for the figure the manufacturer supports, as warranty terms often depend on it.

Capacity limits when you travel

Airlines regulate lithium batteries by watt-hours, which is exactly why Wh is the figure printed on newer power banks. Spare lithium batteries and power banks are generally limited to 100 Wh each in carry-on baggage, with a limited number of larger units, usually up to 160 Wh, allowed with airline approval. The 74 Wh power bank above sits comfortably under the line.

A 27,000 mAh bank at 3.7 V is 99.9 Wh, just inside, whereas a 30,000 mAh unit at 3.7 V is 111 Wh and would need permission. Rules change and differ between airlines and countries, so confirm with your carrier before you travel, and keep spare batteries in the cabin, never in checked luggage.

Putting a capacity number to work

A practical way to compare packs is cost and weight per watt-hour, which is only possible once everything is in Wh. A 20,000 mAh bank at 3.7 V (74 Wh) and a 10,000 mAh bank at 3.7 V (37 Wh) differ by a factor of two, but a bank labelled 10,000 mAh at 7.4 V is also 74 Wh, a fact that the mAh figure hides. Always ask for the voltage, or look for a Wh figure on the label.

Once you have watt-hours, the runtime estimate is simple division: Wh ÷ watts gives hours, before losses. A 1,200 Wh battery feeding a 100 W load lasts 12 hours in theory, and about half that after you apply a 50% usable depth and an inverter efficiency of 90%, 5.4 hours. A battery capacity calculator does that conversion in one step, but the logic is short enough to do by hand when you are comparing products in a shop.