How to calculate stepper motor resolution

Hello everyone. Stepper motor resolution describes how finely commanded motion can be divided. A motor with a 1.8° full-step angle completes one revolution in 200 full steps. With the driver set to 1/16 microstepping, a standard pulse input requires 3200 command pulses per motor revolution. However, a small calculated motion increment does not guarantee equally fine positioning accuracy.

Understanding the stepper motor operating principle alongside driver current regulation helps explain the difference between full steps and microsteps. The stepper motor FAQ provides further background on motors, drivers and control.

Resolution, accuracy and repeatability

Resolution is the smallest command increment. Accuracy describes how close the actual position is to the target. Repeatability describes how closely repeated moves agree with one another. A 0.001 mm command increment does not automatically deliver ±0.001 mm accuracy. Backlash, load, friction and winding-current quality affect the result.

Full-step and microstep formulas

Let θ be the full-step angle, N the full steps per revolution, M the commanded microsteps per full step and P the input pulses per motor revolution. For standard STEP/DIR control, where one pulse advances one commanded microstep:

N = 360 / θ
P = N × M
Motor angle/pulse = θ / M = 360 / P

1.8° motor: 360 / 1.8 = 200 full steps/rev. Half stepping, M = 2: 400 pulses/rev and 0.9°/pulse. 1/16 microstepping, M = 16: 3200 pulses/rev and 0.1125°/pulse. Full stepping, half stepping and microstepping do not change the motor's physical full-step angle; they change the intermediate positions being commanded.

A 0.9° motor has 400 full steps/rev and requires 6400 pulses/rev at 1/16 microstepping. Therefore, “1/16” and “3200 pulses/rev” are not interchangeable for every motor. If a driver setting is specified directly in pulses per revolution, check how the manufacturer implements that setting.

Different microstep settings on the same motor

The approximately 0.098 µm/pulse at 1/256 shown in the table is a mathematical command increment. It does not establish that the mechanism positions with 0.098 µm accuracy. Likewise, the effect of microstepping on torque cannot be reduced to “more steps mean proportionally less total torque”.

Linear resolution with a gearbox and screw

Define G = motor revolutions / output revolution. For a 3:1 reduction, G = 3: the motor turns three times for one output revolution. Including the gear mechanism, output pulses/rev = P × G and output angle/pulse = 360 / (P × G).

If screw lead is L mm per revolution, travel/pulse = L / (P × G), while the controller scaling is pulses/mm = (P × G) / L. Screw lead and thread pitch are different: on a multi-start screw, lead equals pitch multiplied by the number of starts.

Example: A 1.8° motor at 1/16 microstepping, directly driving a 5 mm/rev screw, requires 3200 / 5 = 640 pulses/mm. Its theoretical travel is 5 / 3200 = 0.0015625 mm/pulse. Adding a 3:1 reduction gives 1920 pulses/mm. Enter the correct scaling into the speed and position controller.

How does finer microstepping affect speed?

Maintaining the same motor speed requires more command pulses. Required frequency: f = P × n / 60, where n is motor speed in rpm and f is input pulse frequency in Hz. At 300 rpm, 3200 pulses/rev requires 16 kHz, while 51200 pulses/rev requires 256 kHz.

If the controller and driver input support at most 100 kHz, the theoretical motor-speed ceiling imposed by pulse frequency alone is 1875 rpm at 3200 pulses/rev and 117.19 rpm at 51200 pulses/rev. These figures do not prove the motor can reach those speeds under load; torque curves, acceleration and mechanics still need evaluation.

Interpolation and electronic gearing: Some drivers convert a coarser input command into finer internal microsteps. For example, interpolating a 1/16 input to 1/256 internally does not by itself require 51200 input pulses/rev. Base calculations on the input pulse scaling, rather than confusing it with the driver's internal microstep resolution.

The calculation is correct, but the motion is wrong

Check the scaling: Verify screw lead, reduction ratio, microstep settings and electronic gearing. If measured travel is consistently wrong by the same proportion, first check pulses/mm. An error appearing after direction reversal suggests mechanical backlash, which calls for mechanical inspection and maintenance.

Check for lost motion: Missed steps and other system problems can invalidate calculated positions. Check supply voltage, the power supply, phase current and motor and driver temperatures under load. An encoder-equipped stepper with a suitable driver can monitor shaft position; measuring the motor shaft does not directly measure every error in the screw and slide.

Technical references: Analog Devices — resolution and accuracy; Oriental Motor — screw-drive calculations; Analog Devices — pulse interpolation.