Ada Fruit sells a 3.7v to 5v powerboot for such projects. You can use the 1000C model.
Project Overview: https://learn.adafruit.com/7-portable-r ... t/overview
Wiring Diagram: https://learn.adafruit.com/7-portable-r ... it-diagram
The files to take to a 3d printer for the case can also be found there. Note that you can upgrade to a higher aH battery as long as it is within the 3.7v range with this board. Mine was $28 US dollars off amazon.
Also some useful Info:
when dealing with batterys and runtime, aH(amp Hour) is used.
the rating means if the battery is rated at 2aH, than a device pulling 1 amp will run for 2 hours.
the scale of ma and maH is this. 1000ma = 1A (ma milliAmp)
so a battery(like listed on the links) that is 3.7v and 2500maH, translates into 2.5aH.
The Pi 3, disregarding the usb ports, the quad core at idol usually is around 250ma and at peak between 700-800ma. the hdmi port pulls about 200ma, bluetooth and wifi(if i remember double check this) between 60-120 ma range. Hence at peak proformance, + bluetooth +wifi +all four USB +hdmi the power consumption is a little over 2amps(2000ma) hence the reason for the 2.5amp(2500mA) requirement for power source. at 2 amps being pulled, the pi produces 10 watts of heat.
Also remember, in DC your Volts is your constant and your amps alter, where in AC your Volts alter and your amps are the constant. (AC 110 is the bottom of the wave and 120 is the top, U.S. at 60hertz(how many times the volts bounces between 110 to 120 per second)