How this calculator works
A battery rating in watt-hours is energy: volts times amp-hours. Range is that energy divided by the energy used per kilometre. Consumption on a pedal-assist bike usually falls between roughly 5 and 30 Wh per kilometre depending on assist mode, terrain, speed, temperature and load. The three scenarios here use 8, 16 and 30 Wh per kilometre as planning values. They are not a model of your motor; they are a way to bracket the likely range from a capacity you know.
Formula
Range (km) = battery watt-hours / consumption in Wh per km. Battery watt-hours = kilowatt-hours x 1,000. Capacity needed = planned range in km x consumption in Wh per km. One kilowatt-hour is 3.6 million joules.
Worked example
A 500 Wh battery at an average 16 Wh per km gives 500 / 16 = 31.25 km. The same battery in the efficient scenario gives 62.5 km, and in the extreme scenario 16.7 km. A planned 40 km ride at the average rate needs 40 x 16 = 640 Wh.
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Frequently asked questions
Why is the range so different between scenarios?
The electric assist has to supply more energy on hills, at high speed and in the cold. A 30 Wh per km ride uses nearly four times the energy of an 8 Wh per km ride, so the range shrinks by the same factor.
Does the rider still pedal?
Yes. This is a pedal-assist estimate: the motor adds to your effort rather than replacing it. A throttle-heavy ride, a heavier rider or a loaded cargo bike will sit above these figures.
How does cold weather affect range?
Lithium batteries deliver less usable capacity when cold, and higher rolling resistance in snow adds load. A cold-weather ride can lose 10 to 30 percent of the warm-weather range even before the terrain is considered.