I have been searching online on how to calculate power of a generator based on the rpm, but I cannot find anything. Is there a equation that relates rpm and power generated by a induction generator? Also, is there an equation that gives minimum force needed to turn the generate based on the strength of the magnets?
Power is calculated in Watts. Usually generators are sold on KVA. So you need to calculate your building load or your device wattage; then you can simply convert the KVA to KW by dividing KVA by 0.8 and you will get the KW. As the unit of electricity is in KWH so simply 1 KW is equal to 1 KWH. Here 0.8 is power factor.
Now moving towards your question: It looks like that you are trying to make a generator. We have made a motor in university. That was totally a trail and error method.
Else, you can visit this link for further help regarding load calculation, HP of motor, 3 phase generator. http://www.dieselserviceandsupply.com/Power_Calculator.aspx