Great post (found here) on how to compute battery life of your circuit:
To calculate battery life, you first need to be aware of the typical capacity (mAh) of the battery. This will normally be rated at a specific load current. Also, make sure that your project will still work at the specifed limit voltage – if a higher limit is needed, this will reduce the capacity.
You will then need to estimate the average current drawn by your project, say over a 24-hour period. To do this, you would need to be aware of the various current draw levels for all the different operating modes of the project, and estimate the total time that each operating mode would persist within the 24-hour period. You can then calculate the estimated mAh for each operating mode. Totalise these values to get mAh per day, and divide by 24 to get the average current draw.
Then battery life = (battery mAh) / (mAh per day) days.
If the current draw with any of the operating modes greatly exceeds the rated load current specified for the battery, you may need to take into account a reduction of battery capacity for the higher load currents. This data may not always be readily available. For example, if the highest current mode of the project causes a 50 percent reduction of capacity (whilst in this mode) you will need to double the previously calculated mAh for that mode.
If you calculate battery life of more than typically one year, you may also need to consider self-discharge of the battery. I guess you would use a spreadsheet if you need to look at “what if”, especially for different duty cycles for the higher current modes. However, I have been known to use “the back of an envelope” for this sort of calculation.