Power, Torque & Speed

CNC Steps per mm Calculator

Calculate a controller’s command scale from your axis geometry, then compare it with measured travel. The output describes commanded increments, not a guarantee of positioning accuracy.

Declare motor/load ratio and geometry. Reverse solves produce mathematical requirements; no hardware is selected.

CALCULATION SETUP

Inputs

Preset

Axis solve

Motion mechanism

Motor step basis

Full steps per motor revolution

Driver microstep factor

Use the actual supported driver setting. Not necessarily a power of two.

Motor revolutions / load revolution

Ratio 2 means two motor revolutions for one load revolution.

Screw dimension basis

Screw lead

Calculated locally in your browser. No sign-up or input upload.

CALCULATED VALUE

Results

Command scale

640 steps/mm16,256 steps/in

Travel per load revolution

5 mm0.19685 in

Full steps per motor revolution

200 steps/rev

Integer microstep factor

Motor / load revolution ratio

Theoretical command increment

0.001563 mm0.000062 in

screw: 5 mm per load revolution, 640 steps/mm. Illustration is schematic and does not select hardware.

Calculation breakdown

Ratio convention: Motor revolutions / load revolution. A ratio of 2 means two motor revolutions per one load revolution.
Geometry: Screw lead is travel per revolution; thread pitch × integer starts only when that basis is chosen.

Only the result summary and canonical link are shared. Inputs and free-form names are excluded.

Assumptions & checks

Command/microstep resolution is not mechanical positioning accuracy or available running torque. Backlash, slip, lost steps and compliance require separate checks.

A numerical pulse limit does not prove motor/controller motion capability. Verify driver pulse width, acceleration and actual torque-speed behavior. No firmware commands are sent.

Verify inputs & continue

Driver scale and measured correction use declared motion geometry. Hardware microstep/teeth/starts remain discrete; no stocked motor or driver recommendation.

Gear Module Chart

Use data for the actual component and operating conditions. Continue with the related calculations below after reviewing the selected result.

Formula

Steps per unit, measured calibration and controller command-pulse arithmetic

S = N × μ × i / L. i = motor revolutions / load revolution. Screw L = lead = pitch × starts; belt L = pitch × teeth; standard spur rack L = π × module × teeth. Calibration Snew = Sold × commanded / measured. Pulse f = S × v; vmax = fmax / S. Consistent length units throughout.

Worked example

Using the default values shown in the calculator, the same formula gives the following result. This is a quick sanity check for the calculation, not a design recommendation.

Inputs

Axis solve: Command scale (steps per unit)
Motion mechanism: Lead screw / ball screw
Motor step basis: Full steps per motor revolution
Full steps per motor revolution: 200
Driver microstep factor: 16
Motor revolutions / load revolution: 1
Screw dimension basis: Lead — travel per screw revolution
Screw lead: 5 mm

Result

Command scale: 640 steps/mm
Travel per load revolution: 5 mm
Full steps per motor revolution: 200 steps/rev
Integer microstep factor: 16
Motor / load revolution ratio: 1
Theoretical command increment: 0.001563 mm

REAL INPUTS · CLEAR METHOD

Practical worked examples

Illustrative scenarios using this page’s calculation or verified reference model. Change the assumptions for your own job.

100 mm commanded, 98 mm measured

Given

Old command scale: 400 steps/mm
Commanded travel magnitude: 100 mm
Measured travel magnitude: 98 mm

Calculation / lookup method

Result

Corrected command scale: 408.163265 steps/mm
Scale correction: 2.040816 %
Command scale change: 8.163265 steps/mm
Measured minus commanded: -2 mm

The scale correction is 100/98. 400 steps/mm becomes 408.163265 steps/mm. This does not remove backlash, slip or lost steps.

GT2: 2 mm pitch × 20 pulley teeth

Given

Axis solve: Command scale (steps per unit)
Motion mechanism: Timing belt and pulley
Motor step basis: Full steps per motor revolution
Full steps per motor revolution: 200
Driver microstep factor: 16
Motor revolutions / load revolution: 1
Timing belt pitch: 2 mm
Pulley teeth: 20

Calculation / lookup method

Result

Command scale: 80 steps/mm
Travel per load revolution: 40 mm
Full steps per motor revolution: 200 steps/rev
Integer microstep factor: 16
Motor / load revolution ratio: 1
Theoretical command increment: 0.0125 mm

Travel per load revolution is 40 mm. 3200 command steps per motor revolution gives 80 steps/mm at ratio 1; no pulley or motor rating is approved.

640 steps/mm at 25 mm/s

Given

Pulse calculation: Pulse frequency at requested speed
Known command scale for pulse check: 640 steps/mm
Requested axis speed: 25 mm/s
Controller command-pulse limit: 20000 Hz

Calculation / lookup method

Result

Command-pulse frequency: 16,000 Hz
Command scale: 640 steps/mm
Axis speed: 25 mm/s
Maximum numerical speed at entered limit: 31.25 mm/s

The numerical command rate is 16000 Hz. At the hypothetical 20000 Hz criterion the numerical speed ceiling is 31.25 mm/s; acceleration and torque need separate checks.

Related calculators

Continue your workflow with a related calculation.

View all Power, Torque & Speed calculators

Power, Torque & Speed

Encoder Resolution Calculator

Convert encoder cycles or decoded counts into resolution, signal frequency and maximum RPM using explicit quadrature and counter-rating conventions.

Gears

Gear Ratio Calculator

Calculate ideal external gear ratio from driver and driven gear tooth counts.

Gears

Rack Travel per Pinion Revolution Calculator

Calculate rack linear travel per pinion revolution from spur-gear module and pinion tooth count.

Belts & Pulleys

Belt Speed Calculator

Calculate belt linear speed from pulley diameter and rotational speed.

Technical references for this calculation

Reference lookupGear Module Chart

Frequently asked questions

Is screw lead the same as thread pitch?

Lead is travel per screw revolution. For a multiple-start screw it is pitch × starts; enter the actual drawing’s travel basis.

Can calibration remove backlash or lost steps?

No. It corrects scale from a measurement. Reversal backlash, slip, mechanical compliance and missed command steps require separate diagnosis.

Do microsteps guarantee positioning accuracy?

No. The command increment is not a specification of actual position, repeatability or available running torque.

Which direction is the drive ratio?

Motor revolutions divided by load revolutions. A 2:1 input here means two motor revolutions for one screw/pulley/pinion revolution.

Are encoder events counted as command pulses?

No. The pulse check means step-input command events; encoder channel cycles and decoded counts are handled by the encoder tool.

Reference data & method sources

Thomson: screw lead versus pitch
Lead is linear travel/revolution; source-linked terminology, not an imported catalog.
Oriental Motor: stepper speed–torque conditions
Holding torque is not the available torque at every operating speed/driver condition.