# How is a battery's capacity (mAh) compared to a fuel cell capacity?

Batteries (Li-ion, Li-po, Ni-mh etc.) are all rated in mAh, which gives their capacity (C). But what about hydrogen fuel cells? How can we rate their capacity? I have done some research, but fuel cells do not have mAh ratings. I read some tutorials for fuel cells but they don't give a good explanation (rather no explanation) on this matter.

In a few words to make it more clear: if I want to find a fuel cell that is equivalent of a li-po battery rated for 3.7v @ 1000mAh capacity how do I search for it?

• A fuel cell's capacity is as large as the tank of fuel you provide to it. – brhans Mar 26 '16 at 13:19
• @brhans do you wnt to turn that into an answer? – Neil_UK Mar 26 '16 at 13:37
• BMW i3 Power: The i3's 647 cc (39.4 ci) engine reaches its peak power of 34 bhp (25 kW) @ 1 rpm so if you want to run a similar vehicle for say 10 hrs you'd need a capacity of 250kWh – JIm Dearden Mar 26 '16 at 14:00

Let's properly define what this capacity is that you're talking about.

It is the amount of (usable) energy you can extract from the battery of fuel cell.

Battery capacity is specified in Amp-hour where 1 Ah is 1 Ampere of current for 1 hour. For the energy you will also need the cell's voltage because only voltage times current gives you power. So a 3.7 V 1 Ah battery can supply 3.7 V * 1 A = 3.7 W for 1 hour or 3.7 WattHour (3.7 Whr). 3.7 W equals 3.7 Joule/second, 1 hour is 3600 seconds, so 3.7 * 3600 = 13320 Joules. That is the amount of energy you can extract from that battery !

You can do something similar with a fuel cell. I am unfamiliar with fuel cell specifications but I'm guessing it will have a specification for efficiency (how much of the energy in it's fuel it can extract) or amounts of power (in Watts) it can supply given a certain fuel consumption rate.

It all depends on what you know about the fuel cell and then you can do the calculation. It should be possible to end up at the amount of Joules you can extract from the cell, assuming you have the required data.

Fuel cells are generally rated in watts of output, not mA hours. (As brhans pointed out the capacity depends on how big your fuel tank is.) With a limited amount of hydrogen you could generate the rated wattage for a certain amount of time, (with the number of hours equal to the amount of fuel available/fuel consumption per hour).

For a comparason the 3.7v 1000mAh Li-po battery has an equivalent wattage output of 3.7w for 1 hour. So if you had a 3.7w fuel cell assembly and had enough hydrogen to last for 1 hour it would be an equivalent system.