Often times power ratings are misleading. The problem is that manufacturers don’t use the same standards to label their motors, and consumers often don’t understand the differences.
A “watt” is a unit of power, named for Scottish Engineer James Watt.
Watts measure the instantaneous power output (or input) of a machine, such as the electric motor on your ebike. The number of watts used by an electric motor at any moment equal the voltage supplied by the battery multiplied by the current flowing from the battery to the motor. So an ebike motor connected to a 24V battery being supplied with 10 amps of current would be powered at 24*10=240 watts.
calculating the peak power of an ebike is simple. You just multiply the voltage of the battery by the maximum current the ebike can handle. The maximum current is determined by the ebike’s controller, and is usually somewhere between 15-30 amps. An ebike with a 48V battery and a 20 amp peak controller would theoretically be capable of a nominal 960 watts of instantaneous power.
Many manufacturerers under rate the bikes power for legal and shipping reasons. An example of a standard 250 watt electric bicycle conversion kit is rated at 250w. But looking at the specifications, you’ll see the 36V controller has a peak current limit of 15A. Doing the math shows us that 36V * 15A = 540 peak watts.
This is very common in the industry. Ebikes sold with “250 watt” motors often come standard with 36V batteries and 15 or 20 amp controllers. So a 15 amp controller would mean the actual peak power supplied to the motor is closer to 540 watts and a 20 amp controller would be over 700 watts.
How do ebike manufacturers get away with this? One way is to rate the motor for “continuous power” instead of “peak power”. The difference between continuous power and peak power is that continuous power essentially means the power a motor can safely handle for an indefinite amount of time without damage or overheating the motor. A “250 watt continuous” motor, theoretically, could run forever at 250 watts without overheating, but any more power would cause it to eventually overheat. Most of the time a “250 watt continuous” motor can handle more than 250 watts continuously, meaning the numerical naming convention is inaccurate and misleading.
A 500 watt electric bicycle conversion kit may be listed as a 500 watt kit, yet a closer inspection could show that the kit comes with a 48V battery and a 20 amp peak controller. The math shows us that this kit is in fact capable of putting out 48V x 20A=960 watts, essentially a 1,000 watt kit.
Limiting the wattage of ebike motors doesn’t necessarily limit how powerful they can be. Even though a motor is marked as 250 watts (and even if it may actually be a true 250 watt motor), anyone could connect it to a 48V battery and run 20 amps through the motor to achieve 1,000 watts of power. Of course this could eventually damage or destroy the motor, but it is still demonstrates how it is entirely possible from a practical standpoint.