Stepper Motor Calculator — steps per mm, speed and resolution

Steps per mm, microstepping resolution, maximum RPM and torque at speed.

Example: 1.8° at 16× microstepping over 40 mm per revolution gives 80 steps/mm — 12.5 µm per step.

Inputs

Step angle(°)

Microstepping

Drive type

Leadscrew travel per turn(mm)

8 mm for a common T8 four-start screw, 2 mm for single-start.

Belt pitch(mm)

2 mm for GT2, 3 mm for GT3.

Pulley teeth

Max speed(mm/s)

Result

Steps per mm

Resolution: 12.5 µm
Steps per revolution: 3200
Travel per revolution: 40 mm
Step rate at max speed: 8 kHz
Motor speed: 150 rpm
Incremental torque per microstep: 9.8%

At 16× microstepping, the incremental holding torque of a single microstep is only 9.8% of full-step torque — it goes as the sine of the microstep angle. Microstepping buys smoothness and quiet, not accuracy: friction absorbs those last increments and the motor does not actually reach every commanded position.
Positional accuracy is limited by the motor's own step accuracy, typically ±5% of a full step, and that does not improve with microstepping. A 1.8° motor is accurate to about 0.09° regardless of whether you drive it at 1× or 256×.

Microstepping trade-off

Microsteps	Steps/mm	Resolution	Step rate at max speed	Torque/step
1×	5	200 µm	500 Hz	100%
2×	10	100 µm	1 kHz	70.7%
4×	20	50 µm	2 kHz	38.3%
8×	40	25 µm	4 kHz	19.5%
16×	80	12.5 µm	8 kHz	9.8%
32×	160	6.25 µm	16 kHz	4.9%
64×	320	3.13 µm	32 kHz	2.5%
128×	640	1.56 µm	64 kHz	1.2%
256×	1280	0.78 µm	128 kHz	0.6%

// generated by urdb.io/tools/stepper-motor
#define DEFAULT_AXIS_STEPS_PER_UNIT   { 80, 80, 80, 500 }
// 1.8° motor, 16x microstepping, 40 mm/rev

Formula

steps/mm = (360 / step angle × microsteps) / travel per revolution

Worked example

1.8° at 16× microstepping over 40 mm per revolution gives 80 steps/mm — 12.5 µm per step.

steps per revolution = 360 / angle × microsteps
360 / 1.8 × 16
3200
steps/mm = steps per rev / travel per rev
3200 / 40
80
step rate = speed × steps/mm
100 mm/s × 80
8 kHz

Frequently asked questions

How do I calculate steps per mm?

Divide steps per revolution by travel per revolution. A 1.8° motor at 16× microstepping is 3200 steps per revolution; on a GT2 belt with a 20-tooth pulley that is 40 mm of travel, giving 80 steps/mm.

Does more microstepping mean more accuracy?

No — it means more smoothness. Incremental torque per microstep falls as the sine of the microstep angle, so at 256× a single microstep has under 1% of full-step torque and friction simply absorbs it. Positional accuracy stays limited by the motor's own ±5% step error.

Why does my stepper lose torque at speed?

Back-EMF. As the motor turns faster it generates a voltage opposing the drive, so less current flows and torque falls. Raising the drive voltage is the effective fix, which is why 24 V and 36 V systems reach much higher speeds than 12 V ones.

What step rate can my controller handle?

Most 8-bit boards struggle beyond about 40 kHz across all axes combined; 32-bit boards manage several hundred kHz. Drivers with internal interpolation sidestep the problem by taking full steps from the controller and generating microsteps in hardware.

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