VFD Power Savings

Changing pulleys is going to be more efficient, since you're going to have them anyway. VFD's are not 100% efficient, and therefore the combination of pulleys and VFD will use more power. No calculations needed.

There are two issues in here, that you needs to take in to consideration.

The 1^st issues is, that, if your existing motor is couple to a pulley, then you can change the pulley ratio to reduce your RPM. No point to install the VFD to reduce the RPM. Of course, this option does not save any energy for you since your motor will run at full load.

2^nd issues is to install the VFD and remove out all the pulley, which means that your motor will be couple directly to your load. This option will able to help you to save some energy since you do not need to run your motor at full speed or full load. How much saving will depend upon your require motor load. Never or less, there will be about 15 to 20 % saving of energy.

If your load is somewhat steady (i.e. not idling too much not much variations in torque demand) and if your motor stressing goes near it's max capacity, definitely changing pulley dia is your solution. Reducing RPM will also increase your usable torque. If the above criteria does not apply to you and cost is not much of an issue VFD is your preferable choice considering it will give you somewhat lower max torque, considerably lower than normal driven motor could (forget advertisements, read small letters on VFD's AppNotes) but then control is much better. Not much power saving to expect though because ther's a lossy conversion applied, except maby on idling intervals or high inertia loads' regenarative braking and that not with all VFD's .

Calculations? What's to calculate? T2=T1*D1/D2 for pulley or P2=n*P1 : n<1 for VFD