Milling calculators (HSMAdvisor, FSWizard, G-Wizard etc) often tell you the expected cutting force based on work material, tool material, spindle speed, feed rate and stepover. They need this number to calculate tool deflection anyway.
FSWizard is telling me (for example) that a 1/4" two flute HSS cutter running flat out (8881 RPM) in 6061-T6 with a stickout of 16mm, DOC 11mm, WOC 2.78mm, feed rate of 1200mm/min will use 500W, 0.54Nm and cutting force of 17.5 kg (172N).
From there, it's just maths and basic principles - torque is force times distance from axis, reduction in speed almost equals increase in torque, etc.
Following the example, worst case, that 172N applied across transverse to the axis at full radius of 3" (say 75mm) from a diameter of 6" is going to generate 172*0.075 = 12.9Nm of torque. If it's along the axis it'll be zero. But for that example I'd want the 4th to be able to deal with at least 25Nm (or in stepper terms, 3500 oz-in). This is achievable with a 5:1 reduction pulley and 700 oz-in NEMA 34 stepper, for example.
Then, as Roger mentions, resolution becomes an issue. Again working on the max radius, if you had 6" (150mm) diameter pieces that's pi*150 = 470mm circumference. If you want a resolution of a thou at that size workpiece ie 0.025mm, you need at least 470/0.025 = 18,800 steps per revolution. Which in this example is going to be a bigger ask than the torque requirement.
Whether you're going encoders or steppers, you need the resolution. And nigh on 20k divisions or steps per rev is going to need some reduction. Can you get away with a belt? Do you need something like a harmonic drive?
You can say "Ok, I don't want to go nuts, give me a 1.8º step and run microstepping at 4" ie 800 steps per rev, means you need a reduction of 18800/800 = 23.5:1 or call it 25:1 which is in the realm of a 30:1 HD or a two stage 5:1 pulley and belt rig. At that kind of ratio, your 3500oz-in torque requirement becomes 140 oz-in and any old NEMA 23 stepper can run it.
Or, if you want to stay at a single 5:1 belt rather than two stages, you'd need to run 18800/5 = 3760 steps per rev which is a squeak over 16 microsteps on a 1.8º stepper or 8 on a 0.9º stepper - doable if it and its driver can manage 700 oz-in per step at 8 microsteps.
Don't forget that stepper torque seriously drops off as
- the speed goes up: what might be fine for holding indexed work might be rubbish for continuous fast work, and this gets worse the higher your gear/belt reduction ratios are; and
- the microstep count goes up.
So you'll need to do some iterations working out feedrates - in the example FSWizard gives us a linear feed of 1201.4mm/min which, at 150mm diameter, is 2.5rpm - or 62.5rpm on the stepper if you're running 25:1 reduction.
Get the idea? Calcs are a PITA but you only need to do them twice. Once, now, when you're planning your build and purchases. Then once again, when you put it all together and it skips like a kangaroo and lacks sufficient torque to pull the skin off custard and you need to work out what you got wrong the first time so you can do it again
Damn, you went and made me do maths over my first coffee on a Saturday morning. So the numbers are probably wrong.