Capacitors for Starting Single-phase AC Motors

What does the manufacturer's information say for this motor?

By that he means (being presumptuous here), it is a complex formula that has a LOT to do with the design and construction of the motor and winding, so the calculations are something only relevant to the motor manufacturer who has access to all of the necessary data. By the time you get all of that info from an engineer at the motor mfr., you would be speaking to the person who could just tell you what size to use, and in fact it's probably printed in the owner's manual anyway.

If you have an old motor that's not supported by the manufacturer and/or where someone has removed the old capacitors so you can't see the size, you can look at a similar motor an see what size they use, then experiment with trial and error. But I would first decide if that is worth the trouble. Used 1 phase motors are cheap.

Now if you are planning to build your own 1 phase motor from scratch and you have to ask this question, you should re-think your decision to build your own motor!

And if this is a homework question for a student, shame on you! Do your proper research! Engineering school is not about simply getting someone to tell you answers, that's Management chool. Engineers need to learn how to find them yourself. And no, asking a question in a forum doesn't count until you are already an established EE and you arelooking for relative experience on a particularly perplexing issue.