Stepper Motor Steps per mm Calculator (3D Printers and CNC)
Steps per millimetre for a belt or lead-screw axis, the distance per step and the top speed your controller's step rate allows.
Results
What this tool does
The firmware of a 3D printer or CNC machine moves an axis by counting steps, so it needs to know how many make a millimetre: full steps per revolution times the microstepping, divided by how far the axis travels per turn. A standard 1.8° motor with 16 microsteps on a 20-tooth GT2 pulley gives 80 steps/mm, and on a T8 lead screw with 8 mm lead it gives 400. Check the lead, not the pitch, of the screw: a four-start T8 has a 2 mm pitch but moves 8 mm per turn. Microstepping smooths motion but does not add real accuracy in proportion, because the motor's torque between microsteps is weak.
Formula
steps/mm = full steps per rev × microsteps ÷ travel per rev · belt: travel = pitch × teeth
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sr | Full steps per revolution (1.8° = 200) | — |
ms | Microstepping | — |
dt | Drive | — |
bp | Belt pitch (GT2 = 2 mm) | mm |
pt | Pulley teeth | — |
ld | Lead of the screw (travel per turn) | mm |
fq | Highest step rate of the controller | kHz |
SM | Steps per mm | steps/mm |
TR | Travel per motor revolution | mm |
RS | Distance per microstep | µm |
FS | Distance per full step | µm |
MV | Top speed the step rate allows | mm/s |
Worked example
- Full steps per revolution (1.8° = 200)200
- Microstepping16
- Drive1
- Belt pitch (GT2 = 2 mm)2 mm
- Pulley teeth20
- Lead of the screw (travel per turn)8 mm
- Highest step rate of the controller40 kHz
- Steps per mm80.000 steps/mm
- Travel per motor revolution40.00 mm
- Distance per microstep12.50 µm
- Distance per full step200.0 µm
- Top speed the step rate allows500 mm/s
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.