Wh and mAh

[Firestrider]

Most laptop batteries list their capacity in Wh (watt-hours), which is easy to understand because 1 Wh is equivalent to 3600 joules, and if you had a device that used 1 watt using a battery with a capacity of 1 Wh, the device would be powered for 1 hour.

For cell phones it is a little different as most of the batteries are measured in mAh. I'm guessing that would mean that if a device used 1 milliamp using a battery with a capacity of 1 mAh, the device would be powered for 1 hour. But what is the equivalence in Wh and therefore, joules?

 

[hitokiri_808]

You can convert between watt hours and amp hours by multiplying or dividing the battery voltage.

ex. my lumix battery is 3.7v and 1000mah, that equals 3700mwh or 3.7wh. You would divide 3.7wh by the voltage to get the ah.

It pretty much comes down to how the battery manufacturer wants to show the capacity. You understand wh so I'll leave it at that.

 

[Chixofnix]

I feel the need to interject/clarify the units we're talking about... This may help to address your original confusion? Here's where I think you fell "off the path:"

...1 Wh is equivalent to 3600 joules, and if you had a device that used 1 watt using a battery with a capacity of 1 Wh, the device would be powered for 1 hour.

A Watt broken down is joules-per-second.
1W = 1J/s
A Watt-hour is a measure of power (W) consumed over one hour.
1Wh = 1W load applied over 1 hour = 1(J/s)/h = 3600 joules

Electrical utility bills for example charge monthly consumption based on kWh measured at the company's meter.

As hitokiri pointed out, converting between mAh and Wh needs to involve the voltage being talked about. Batteries typically show capacity in mAh because the voltage is a constant based on the type of battery. AA and AAA batteries are for example always 1.5V. The voltage is likely listed alongside/nearby any mAh figure you see on a battery label.

To understand the "how" in your question, recognize that your units (mAh and Wh) are measures of current and power - apples and oranges.

Start with:
1W=1V×1A
1Wh=1Vx1Ah
1Wh=1Vx1mAhx1000

If you'd like to review your units understanding further:
P=VI (energy/time=energy/charge x charge/time)