How to determine the total number of charges a portable charger can supply for a phone?

Question

According to can a 3000mAh portable charger charge a 1500mAh battery?, it was mentioned that a 3000mAh Portable charger can only charge a 1500mAh phone's battery 1.33334 times.

So, how do we determine the total number of charges that a Portable charger can supply to a battery given the following parameters:

1. X mAh Portable charger with output of Y volt and Z Amp.

2. P mAh phone battery with input of 5 volt (almost all phone is using 5 volts due to USB Charging) and Q Amp.

The reason for asking is that according to the article, it mention that there is a 20% inefficiency (which I do not know if it is true for most portable charger), so a 3000 mAh Portable Battery charger can only charge a 2400 mAh battery.

If that is the case, the 3000 mAH Portable Battery charger can charge the 1500 mAh battery 1.6 times instead of 1.33334 times. I was thinking why it was stated 1.33334 times and not 1.6 times and I believe that there must be a way to calculate the number of times a Portable charger can charge a phone battery until it have no more electrical charges.

Added Information

Also, according to a user, it mention the following:

As posted above, with voltage conversion there is just 80% capacity of portable charger's battery pack available for your phone.

While charging, your phone needs power for stand-by, so in my experience, you'll have just 65% capacity.

And by industrial standards for batteries is +/- 20% tolerance admitted with capacity.

So, your portable charger might have just 45% of its 3000mAh available for to charge your phone.

So, can one use the magical value 45% as a gauge for portable battery charger? (Meaning that a 5000 mAh battery charger can only charge a 2250 mAh phone battery one time.)

Answer 1

I believe the answer can only be empirical, not definitive.

To examine some of the figures mentioned:

there is a 20% inefficiency (which I do not know if it is true for most portable charger)

A portable charger that is itself charged from USB (5 Volts) would need a boost converter to be able to supply 5 volts at its output. Boost converters commonly mention efficiency of 65 to 85%. TI's TPS61030, TPS61031 and TPS61032 state 96%, and Maxim's MAX8815A states 97% efficiency.

These figures do not account for possible efficiency loss due to external components (ESR of capacitors for instance) or temperature variation. Thus, treat that "20%" number as indicative at best.

your phone needs power for stand-by, so in my experience, you'll have just 65% capacity.

That would depend on whether the phone is kept powered on while charging, what power intensive tasks (e.g. WiFi, social media polling software) are running on the phone, and even the current draw of the phone in the nominal "powered off" state - Some smartphones do not actually power off completely unless the battery is pulled out.

Thus, that 65% number is also indicative at best, though varying it somewhat is within the user's control.

by industrial standards for batteries is +/- 20% tolerance admitted with capacity.

That number would be defined in the datasheet of the specific battery in question. It would also vary widely by age / charge cycle history of the battery, temperature, contact oxidation and possibly several other factors.

So, while the number is a reasonable guesstimate, it is not definitive.

Note that this last figure is applicable to both, the cellphone battery and the portable charger battery.

So, can one use the magical value 45% as a gauge for portable battery charger?

Clearly not. The only numbers that can be used, even as a rule of thumb, are those empirically measured for your particular situation and use pattern. Even so, the percentage will change widely over charge cycles, season and time of day (temperature factors).