I would like to know how many hours I’ll be able to have an [Arduino Pro Mini (3.3v) running if I program it with the [Rocket Scream low power library in order to only works during approximately 5 hours/day with a [NFC shield (the rest of the day the Arduino will be set in standby mode).
I know that there’re many low consumption modes, but I only want an estimated timing with a 9v battery and with a 3.3v button battery
A rough estimate of battery life in total hours is mAh/I, where mAh=battery capacity in milliampere hours and I = average current draw for the circuit in milliamperes.
You will have to look up the battery capacity for the actual batteries you will be using and it will depend on the average current draw, but for an alkaline 9V battery under light load, the capacity is typically 560 mAh.
The current draw is not 0 when in standby mode for any microprocessor. So you have to add that into the total, and the lower that is the longer you will have. That mode can vary widely depending on what peripherals are running. This is where all the vendors are competing to get that power down mode power as low as possible and still be able to wake up from an alarm or pin wiggling. Many of the NXP parts get down below 1 uA.
3.3V button cells have fairly small capacities, so may not be suitable for your application. If you are using a 9V battery, you should use a switching power supply as with a linear one, you would be throwing 2/3 of that capacity away as heat, but when sleeping you should shut down that switcher and wasting 6V at 1uA would be OK. It will be a bit tricky to wake up as the CPU will have to turn on that supply before fully waking up.
A simple method might be to use a zener diode from the 9V battery to supply the sleep power, and that would be supply something like 2.5 to 3V while sleeping, and have the switcher set to output 3.3V.