How to use the steps per mm calculator
- Choose Find steps per mm, then the drive type: belt and pulley, lead screw, or a known travel per turn.
- Enter the full steps per motor turn (200 for a 1.8 degree motor, 400 for a 0.9 degree motor), the driver microsteps and the gear ratio.
- Enter the pulley teeth and belt pitch, the screw lead, or the travel per output turn, depending on the drive type.
- To fix a setting after a test, choose Correct a setting, enter the current value, the distance you asked for and the distance you measured.
Formula
steps per mm = full steps x microsteps x gear ratio / travel per output turn
travel per turn (belt) = pulley teeth x belt pitch
travel per turn (lead screw) = screw lead
new value = current value x distance asked / distance measured
The gear ratio is the number of motor turns for one turn of the output. A 3:1 reduction is 3. Firmware that asks for a rotation distance wants the travel per motor turn, which is the travel per output turn divided by the gear ratio.
A belt axis and a screw
A 200-step motor at 16 microsteps drives a 20-tooth pulley on a 2 mm belt. Travel per turn is 20 x 2 = 40 mm and steps per mm is 200 x 16 / 40 = 80. One microstep moves the axis 0.0125 mm.
The same motor on a screw with an 8 mm lead gives 200 x 16 / 8 = 400 steps per mm, a move of 0.0025 mm per microstep. For an extruder set to 93 steps per mm that pushes 103 mm when asked for 100 mm, the new value is 93 x 100 / 103 = 90.2913.
Where the numbers come from
Every step of a stepper motor is a fraction of a turn, and the driver splits each full step into microsteps. Multiplying the two gives the number of microsteps in one motor turn. Dividing by how far the axis travels in one turn gives steps per millimeter. A belt moves one pitch per tooth, so a pulley moves teeth times pitch per turn. A lead screw moves its lead per turn, where the lead is the thread pitch times the number of starts.
If a geared extruder or a reduction sits between the motor and the output, multiply by the gear ratio. For related drive math, the gear ratio calculator compares gear sets, and the filament length to weight calculator helps with the material you push.
Checking on the machine
Computed values assume the mechanics are exact. Belt stretch, pulley tolerance and slipping change the real travel by a small amount. Mark the filament or move an axis a known distance, measure with calipers or a ruler, and use the correction mode. One correction usually gets close, and a second test confirms it. Save the setting in your firmware after you check it. Check your driver and firmware documentation before changing any motor current or limits; this page only does arithmetic.
Assumptions and limits
- Full steps per turn, microsteps, gear ratio and travel per turn are exact values for your parts.
- The driver really uses the microstep setting you enter, including any interpolation your driver does internally, which does not change steps per mm in firmware.
- The belt pitch is the tooth spacing of the belt (for example 2 mm), not the belt width.
- Corrections assume the error is proportional to distance, which is true for scale errors but not for backlash.
Frequently asked questions
What are full steps for a stepper motor?
A 1.8 degree motor makes 200 full steps per turn and a 0.9 degree motor makes 400. The step angle is on the motor label or data sheet. Use the full-step count, not the number after microstepping.
Does interpolation in the driver change the number?
No. Some drivers interpolate to 256 microsteps internally while the firmware uses a lower number. Enter the microstep setting that the firmware counts, which is what steps per mm refers to.
How do I find the lead of a screw?
Lead is the travel per turn. For a screw with several starts it is the thread pitch times the number of starts. A common product with an 8 mm lead has a 2 mm pitch and 4 starts, for example.
What if the correction makes things worse?
Check the measurement and the units first. If the machine moved more than asked, the new value must be smaller; if it moved less, larger. Repeat the test once to confirm, and look for slipping or looseness if it still disagrees.