I’m building a belt grinder but I am deciding to use a 1phase motor with a vfd but someone has said to me that you need a 3phase motor to use a vfd but when I looked on eBay it said I can wire it to for a 1phase input and output. This is probably a stupid question but is it possible to run a vfd with a one phase motor if wired correctly. I want to use a 1phase motor because I am using household electrics. 

As far as I know, you use a single:three phase converter VFD to run a 3 phase motor off your single phase house current.   Personally I'm in favor of using dual pole/single phase, if possible, but I"m not sure if you have that over there.   I believe there is a reduction in torque available at the shaft, but may be wrong on that.  I'm sure someone with better info will be along to elaborate further.

There are single-phase VFDs out there, but there's some reason they're not good in this application (I can't remember what it is, but I'll see if I can track it down).

Update: found it.

 

So you can for certain run a multi phase motor on regular house electricity.  I run a 3 phase 1.5 hp dayton motor on a kbac 27 VFD. It just plugs into a regular outlet. 

Technically you are not running a 3ph motor from single phase power,  you are running a converter with the single phase, which in turn operates the motor.  This is not 100% efficient either, there are conversion losses to account for