There are plenty of instructables on youtube videos out there about how to convert a bicycle into an eBike. I wont repeat this here but just cover the basics.

What you need

• motor (($50-$500)
• battery (($100-$1000)
• controller ($40-$200)
• throttle, pedal sensor, speed sensor, brake lever with sensor

Motor

The easiest conversion is done with a hub motor. They come in two varieties: as direct drive motor which is gearless and as geared motors. Here is a picture of a geared hub motor:

You can use a 36V motor also on 48V and even higher. It is not the volts that destroy a motor but the amps. Technically a motor is nothing but a copper wire. When too many amps are pushed through for too long then the insulation of the wires will melt causing short circuits and subsequently havoc. Also the magnets will loose their force once being heated over the curie temperature.

Battery

There are plenty out there and the more capacity you want the more expensive it will be. To calculate how much battery you need there is a calculator here. As a rule of thumb 100W of assistance will give you already a nice boost. Thus with a battery of 500Wh you can have five hours of 100W of assist. That's good for cruising on the flat at 25km/h or 16mph. However when going uphill fast you may need 1000W and your battery will last only 30 minutes.

In general if you continue to use the bicycle as such and use the motor only as assist then a small battery can bring you pretty far. If you want to use the bicycle as an electric motorcycle then you will need many more times of battery.

Controller

The controller must fit the battery voltage. A battery voltage too high will destroy it. A battery voltage too low and the controller will cut off believing the battery is empty.