It's very easy if you spell out the units for each parameter. Then you can just look at the units and figure out whether you need to multiply or divide.
Using Techgraphix's example:
Belt pitch: 5 mm/tooth
Drive pulley: 20 tooth/rev
Stepper motor: 200 step/rev
Driver microstepping: 8 pulse/step
We want microns, and there are 1000 um per mm.
Now just chain them together so that the units cancel out:
1000
um/
mm * 5
mm/
tooth * 20
tooth/
rev * 1/200
rev/
step * 1/8
step/
pulse = 62.5
um/
pulseHere's another example: your axis is screw-driven with a 12 tpi, four-start screw. You use a 0.9°/step motor. Yeah, absurd for a laser (or maybe it's your Z table), but bear with me, it's just an example to show how the units work.
Screw pitch: 12 thread/inch
Screw starts: 4 thread/rev
Motor: 0.9 degree/step
Microstepping: 8 pulse/step
We want microns, but the length unit we have is inch, so we start with the conversion factor:
25,400 um/inch * 1/12 inch/thread * 4 thread/rev * ...
What now? We don't have revs, but we have degrees, and one rev is 360 of those. That's 360 degree/rev. Keep going:
... * 1/360 rev/degree * 0.9 degree/step * 1/8 step/pulse = 2.645833 um/pulse. Ta-da!