CNC / machinist calculator
Steps Per Inch (CNC Motor) Calculator
Set the motion resolution on a CNC router, mill conversion or 3D printer. Enter your motor's full steps per revolution, the driver microstepping and the drive, a leadscrew lead or a belt and pulley, and this calculator gives the steps per inch or per millimetre to put in the firmware, along with the resulting positioning resolution. It is the number GRBL, Marlin and LinuxCNC need to move the right distance.
How it works
A stepper motor turns in fixed steps, most commonly two hundred full steps per revolution for a 1.8 degree motor. The driver can split each step into microsteps, multiplying the count, and the mechanical drive converts those revolutions into linear travel. Steps per unit of travel is the motor steps per revolution times the microstepping, divided by the distance the axis moves in one revolution.
For a leadscrew or ballscrew that distance is the lead, the travel per turn. For a belt drive it is the belt pitch times the number of teeth on the drive pulley, so a two millimetre GT2 belt on a twenty tooth pulley moves forty millimetres per revolution. Gearing between the motor and the screw multiplies the steps per unit by the gear ratio.
The reciprocal of steps per unit is the resolution, the smallest commanded move. More microsteps raise the count and the theoretical resolution, but they also cut torque per microstep, so very high microstepping buys smoothness more than real accuracy.
Worked example
A 200-step motor at 16 microsteps on a 0.2 in lead screw: 200 x 16 / 0.2 = 16,000 steps/in, about 0.0000625 in per step.
Frequently asked questions
How do I calculate steps per inch?
Multiply the motor full steps per revolution by the microstepping, then divide by the travel per revolution. A 200-step motor at 16 microsteps on a 0.2 inch lead screw gives 200 times 16 divided by 0.2, which is 16000 steps per inch.
What is travel per revolution for a belt drive?
It is the belt pitch times the number of teeth on the drive pulley. A 2 mm pitch GT2 belt on a 20 tooth pulley moves 40 mm per motor revolution, so steps per mm is the motor microsteps divided by 40.
Does microstepping improve accuracy?
It improves smoothness and theoretical resolution but not true accuracy, because torque per microstep falls as microstepping rises and the motor cannot reliably hit every microstep under load. It mainly reduces vibration and noise.
How does gearing change steps per unit?
A gear reduction between the motor and the screw multiplies the steps per unit by the gear ratio, raising resolution and torque at the cost of speed. Multiply the calculated steps per unit by the reduction ratio.
What is positioning resolution?
Resolution is the smallest commanded move, the reciprocal of steps per unit. At 16000 steps per inch the resolution is about 0.0000625 inch per step, though real accuracy is limited by mechanics, not just step size.
Related calculators
Sources
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.