Knowing how far your bicycle can travel is very important to make sure you do not get stuck somewhere :) It is difficult to know what the realistic range of your bike is when different companies advertise completely different numbers for similar bikes. Here is an easy way to know how far your bike will travel!
Determine Watt Hours of Battery
Multiply the battery voltage by the amp hours
48V * 13Ah = 624 Watt Hours
Watt hours determines how much energy your bike has which will determine how far it can take you. By electric assist only (aka throttle) it takes between 350 and 400 watt hours to travel 20 miles. So 624 / 400 * 20 = 30 Miles by throttle for the above example.
With pedal assistance you can increase the range by almost double if you exert the same amount of energy as the motor. So for the above example you can get up to 60 miles of range!
What are the other factors?
Wind resistance increases cubically, for example you will get 30% more range if you travel at 16 mph instead of 20mph
2) Stopping & Starting
Electric motors are not very efficient at low speeds. If you stop and start a lot your range will get cut down significantly!
3) Battery Assembly
Depending on how your battery is built, you may not get as much range as you should. Battery capacities are usually tested at very low outputs and not with the high demands of an electric bicycle. A 14Ah battery may not give you any more range than a 13Ah battery. A 11Ah battery may not give you more range than a 10Ah battery. I would not worry about the small differences between a 13 and 14Ah battery, but a 13/14 will definitely give you more range than a 10/11Ah battery.