Not asking for an exact answer clearly.
Let us say that a cellphone user typically watch like 2 hours of video per day and it is say on an iPhone of your choice.
How much power would be needed to charge that phone in order to consume those 2 hours of videos?
How would we calculate this? Variable formulas is ok, but please provide examples of their use.
You may estimate as you like and hopefully using values close the real world. A high and low estimate is fine. Just to get ballpark idea.
First let us assume that your charging device and your battery work with 100 % efficiency. Then the energy consumed by the phone is equal to the energy taken from the power grid.
According to Energy consumption for different parts of the mobile phone
the peak power of a typical smartphone is over 2,000 mW at the maximum.
Since every smartphone consumes this power for 2 of 24 hours, and there are $10^9$ smartphones, the average total power consumed is $$P = 2000 \text{ mW} \cdot \frac{2}{24} \cdot 10^9 = \frac{1}{6} \cdot 10^9 \text{ W} = \frac{1}{6} \text{ GW}$$
On the other hand a typical nuclear plant delivers $1$ GW of power.
See for example INFOGRAPHIC: How Much Power Does A Nuclear Reactor Produce?).
Nuclear energy has been powering the U.S. grid for the past 6 decades and produces around 1 gigawatt of power per plant on average.
So you need roughly $\frac{1}{6}$ of a nuclear power plant for powering the smartphones.
But be aware, this estimation accounts only for powering the cell phones, but not for powering the cell towers (which may be even more than for powering the phones).
The calculation is rather simple, but some parameters need to be defined.
"Typical" in mobile phones is nowadays a very difficult point of comparison because there is a very wide range of mobile phones, from rugged-but-simple 4G-capable phones with 2000mAh capacity batteries to the largest available iPhone 14 Max, with a 4300mAh battery as claimed by the manufacturer, to absurdly large batteries like the WP19 fro Oukitel with a whooping 21000 mAh battery.
To this extent, also note that video playing is a very demanding CPU and GPU task, which is why Apple uses it as a benchmark that people can easily understand. Nonetheless, several factors will determine how long the battery lasts, including screen brightness, device temperature, video quality, video provider (and whether it is locally being watched or streamed, which for example would add the power of the memory or the network chip, respectively).
But assuming, for example, an iPhone benchmark of 29 hours, you can assume roughly that the phone consumes 148mA each hour, at a 3.8V that would be 563mW or 0.563W per hour. (Here I am not using mWh or other per-hour units for convenience and to match the units afterwards).
https://www.eia.gov/electricity/monthly/epm_table_grapher.php?t=epmt_6_07_b
The department of Energy in the USA claims that the time adjusted capacity of ALL nuclear plants on 2022 is set to 95076 MW or 95076000000 W.
Edit: I took the power generated by ALL nuclear reactors in the US, which are 92 according to https://www.eia.gov/tools/faqs/faq.php?id=207&t=3. Therefore the generation is closer to 1GW per nuclear reactor.
Here I would also consider the charger and wall efficiency of the charger, as that would add up in the end. http://www.righto.com/2012/10/a-dozen-usb-chargers-in-lab-apple-is.html this website claims a wall efficiency of 83% for iPhone chargers, which is the power that will keep the battery "on stand-by", therefore overriding having to plug-and-unplug the device for each battery cycle. Also consider that there may be fluctuations in the power measured, but if everything is linear you only power the iPhone itself with its charger (also assuming that there are no power line losses, which there are, power down-conversions from substations which also will have additional losses).
All said and done, you have that with the capacity of a single power plant, you can calcuate how many devices could be powered at a sustained pace (1GW to power 6.573W). A single power plant can power, in this very näive configuration, 144866676.8246 phones or roughly 0.14 billion phones assuming, naturally, that you somehow can generate only 120V-AC and the phones are somehow only plugged directly to an outlet from the generator plant.
Therefore, you need 7 american nuclear reactors to power 1 billion iPhone 14 Max that play video constantly, in a "the cow is spherical" scenario. For any more precise calculations, you need to consider:
