mAh Is an Industry Mistake

mAh doesn't measure "current", because current is the flow of electrons. It measures charge.

2000 mAh hour is redundant - the 'h' in mAh is hours. :)

But your basic point is 100% correct: All batteries should show their capacity in Wh.

When you make a statement like “A 2000mAh hour battery at 2 volts has half the power of a 2000mAh battery at 4 volts,” it’s a bit nonsensical — a battery does have a certain amount of power available, but that amount is not charge * voltage, nor is it even necessarily proportional to the energy stored.

With USB PD and powerbanks etc that operate at many voltages using mAh is unclear. It's only used historically as a number comparable to previously used numbers. As someone mentioned the implied voltage is that of the cell 3.7V

So the conversion formula is Wh = mAh/1000 * 3.7V (or substitute the standard voltage for the context)

This means that actual Wh will depend on how many amperes the battery has to deliver. When the load is very low, this hardly matters, but when you need to power a high wattage engine/appliance with a small battery, this can be quite significant.

Amp-hours (Ah) has been the 'standard' way to list battery capacity for decades, see for example the boating/marine world. I'm not against changing it to something else, but there's a long-tail of legacy here.

Also, while we're at it, can we change away from listing the brightness of light bulbs in watts: this may made sense with incandescent bulbs initially, but we're not beyond those.

Which voltage is the 10,000mAh capacity in reference to?

Most likely it's actually the internal 3.7v cell voltage, which is even less relevant than any of the potential output voltages.

Your argument makes sense for purchasing raw battery cells (li-ion or plain old AAs) but as soon as those cells are integrated into a sealed consumer electronics device (battery pack, smartphone, laptop) it is no longer an interchangeable unit with a known voltage.

Consumers use batteries that are a specific form factor. They don't buy 1.5V batteries, they buy AA's. They don't know or care what voltage their computer battery is, they buy a Lenovo T14 battery. Et cetera. I can't think of a common single battery where you can buy the correct form factor but get the wrong voltage.

The only two pieces of information that matter are form factor and wattage. You can derive voltage from the form factor, but you can't derive form factor from voltage. You can derive amperage from wattage and voltage.

Edit: I finally thought of an exception. 6V tractor batteries are form factor compatible with 12V tractor batteries. But those are hardly common in 2023.

(W/h is something completely different, and mostly relevant for how a quickly power source (like a power plant) can meet variation in power loads.)

As for the rest of your explanation, it's actually NOT a good reason to label batteries by Ah or mAh over Wh.

Wh is better for almost any purpose as long as it can be accurately determined. You still have to provide the voltage it is designed for, but it is just as easy to find the Ah's in a battery from the Wh as the other way around, when you know the voltage.

The problem, though, is that the true voltage of a battery isn't constant, but tends to vary depending on what load you connect to it. This is because of every battery having an INTERNAL resistance (R_internal). This internal resistance will (for a basic cell) lead to a reduction of the delivered voltage (as seen by the load) by

  U_load = U_nominal - I*R_internal. 

This means that the Ah unit provides a more precise measure for the capacity of a battery than Wh.

This is kind of sort of true for gadgets that take AA or AAA or maybe small lead acid batteries. They need a battery at a specific voltage (except they don’t — NiMH, carbon-zinc, alkaline, and Li (metal) batteries all tend to be interchangeable despite rather different voltages), and they consume roughly constant current.

But many modern devices use fancy power supplies that consume roughly constant power. And, more relevantly to newer devices, how many consumers say “hey, that cool USB charger operates at 16V internally, so I want X mAh?”

(Also, batteries have discharge curves, not constant voltages. But in mAh’s slight defense, the charge delivered from a battery is less likely to vary widely with different rates of discharge than the energy delivered.)

Devices say "it needs AA battery" or "It needs 18V battery"

>W/H is insufficient for describing batteries unless you specify the voltage you are working with.

Yes. Then do exactly that. Describe Wh and voltage.

Nowadays with sealed, non-serviceable batteries, it is not always abundantly clear what voltage the device takes for power (which can be different from its charging voltage) unless it’s in your hand and you can read the specifications that are printed on the back (if it is at all). Breaking out these two datapoints into voltage and amp hour no longer makes sense given that most batteries where consumer-advertised capacity are product specific.

Our relationship with battery powered devices has changed since the days of 1.5V cells that we tossed in at varying amounts (2x = 3V, 4x = 6V, 6x = 9v, etc). Pre-“USB-PD”, it still kind of made sense to use mAh because we knew it was always 5v but that too has changed.

The mistake is not changing to mWh once we stopped describing 5v devices.

It works exactly the same way if you replace mAh with wh.

If I see that two batteries have the same stated voltage and battery A has higher mAh than B I know that A should last longer in my device.

But that's exactly the same if I see A and B have the same voltage but A has higher mWh. It should last longer.

Even if the energy was specified in some completely ridiculous way such as how much mass that amount of energy could lift a 2 liter bottle of diet Pepsi on the moon I'd just have to look at the two numbers and pick the bigger one.

And your second paragraph is bogus anyhow: the voltage would be labelled on the batteries despite whether the other metrics is charge (which is what mAh is unit of) or energy (which is what Wh is unit of).

P.S. It is still beyond me why people in general don't comprehend that both "amper" and "watt" are already units of "speed", no need to divide them by time any further. Maybe we should've given km/h its own name, to ease people into such concept? /rant

My laptop has a 6000mAh battery and will charge from 5V. But my 10,000mAh powerbank will not fully charge it. The question is how to explain this to my mother.

To calculate this properly - you have to do some actual digging to find the nominal battery voltage of the laptop, since it's not any of the USB-PD voltages, and is thus entirely divorced from the laptop's input voltage.

And then you have to know that most powerbank vendors tell you the rating of the cells, not the rating of the product. So they will tell you that it's a 10,000mAh battery, and that it outputs 5V - but these two facts are only honest in isolation. It is not a 50Wh battery, it's a 37Wh battery. Or a 7,400mAh product that is powered by 10,000mAh cells.

Almost anywhere we use USB-PD, stating Wh is a lot more honest to the consumer. If we tell my mother that her laptop is 70Wh and the powerbank is 37Wh, she can infer it'll give her about half a full charge. If we tell her the laptop is 6000mAh and the powerbank is 10,000mAh, she can be forgiven for inferring it'll give her almost two charges.

--

For an example of what I'm calling "white lies": https://www.anker.com/products/a1271

(And to be clear, I'm not blaming Anker for this, I believe it's near-universal. I'm only using Anker as an example because they're a more-trusted brand.)

All the way down the bottom of the page, just above the FAQ, they give the capacity as "20100mAh/72.36Wh". 20100mAh is given 19 times - 72.36Wh is given precisely once. From 72.36Wh / 20.1Ah we get a nominal voltage of 3.6V, not 5V. 3.6V is never otherwise stated. I've never seen any vendor tell you that you're seeing the cell rating, not the product rating - but the better vendors will give you enough information to figure it out yourself.

Of course for linear power supplies or plain resistive loads you'll get different results, so you're right that it's impossible to use a single number to summarize the capacity of a battery.

This is basic middle school physics..

That's a great way of putting it. I tend to agree, but W/h can also do the same.

Nitpick, but Watt-Hours is energy, not power.

Why yes, I am very clever. Thank you for noticing.

https://mm.digikey.com/Volume0/opasdata/d220001/medias/docus...

The second cell has double the energy storage as the first cell.

Really mAh is only useful when comparing cells of the same voltage. It became a common metric since so many battery cells in electronics are 3.7v, so you could assume a constant voltage and just compare mAh.

But not all cells are 3.7v, so sometimes that mAh comparison falls down completely and you should really be using watt-hours (milliamp-hours * volts).

Usually though, batteries are designed with a particular application in mind and that application will define a voltage that is acceptable, such as ~3.8V for phones or ~19V for laptops. Significantly above this would damage the device. Likewise, below that voltage and the device doesn't function. This is why mAh is a decent proxy for Wh; for a given application the voltage is fixed and so the conversion - for that application - is fixed. mAh for a given application can be compared easily.

Comparing batteries for different applications is harder, but not just because you have to convert mAh to Wh: different applications require different performance characteristics beyond just voltage. You might care about weight, physical dimensions, operating temperatures, discharge rates, charge rates, self-discharge rates, output impedance.

Neither measure the "quality" of the battery.

What DOES have to do with quality, though, is the amount by which voltage falls as the load increases, or in other words, how efficient the battery is.

This is similar to the efficiency of a power supply in a computer.

The problem starts with voltage because now you need each battery or battery set connected to have very close capacity or else it will be "wasted", and you need cell balancer to keep them equally charged.

Try that for starter engines that draw 50A, 100A or 200A

One may think that at 100A, the starter engine will be able to consume 1200W

However, if you pull 100A, the internal voltage used to overcome the internal resistance is 2V, so you really only generate 1000W, or 5/6 of the raw energy stored in the battery.

At 50A, the voltage loss is only 1V, so the start engine gets 550W, or 11/12 of the energy tapped from the battery.

Finally, at 200A, the voltage loss is 4V, meaning that the starter engine only gets 1600W, or 2/3 of the energy stored in the battery.

And this is under relatively good conditions. If the battery is freezing cold, the internal resistance can become much higher.

In all cases, the internal resistance leads to heat inside the battery.

Hopefully, it should be clear that for low resistance / high wattage loads, the Wh metric is not very accurate.

the laptop's battery is not 3.7v but more likely to be in the 20-ish volt region because the cells are in series. the assumption of 3.7v is plain wrong.