3D Printer Magic Numbers: Getting the Best Quality Prints


Put simply, magic numbers in 3D printers are layer heights which align with the Z-axis motor and lead screw properties, to give a smoother printing process. Rather than your layer heights being unaligned with the points on your motor, you can use these magic numbers to your benefit.

To get the best 3D print quality using magic numbers, you should first determine the operational numbers

What are 3D Printer Magic Numbers?

When it comes to 3D printers, you may have heard of magic numbers, which are very useful to a successful 3D printing journey.

Magic numbers for a 3D printer refers to a series of layer heights that work towards giving you higher quality prints. It works by taking into account the mechanical logistics of your stepper motor.

Stepper motors don’t have a feedback system, so your printers only option is to direct your stepper motor to go to a location and hope it goes there. Steppers move in steps, mainly being a full-step and a half-step.

A full-step is a magnet which is aligned with an electromagnet, while a half-step is two electromagnets pulling the magnet to align half-way through the rotation of the motor.

Your stepper motor moves in a series of steps and rotations, so you want your stepper motor to move in full steps rather than partial steps.

If you aren’t getting either a full-step or half-step, your stepper has to move in between steps, which is called a micro-step, and these are basically guesses as to where the shaft of the stepper aligns to a step.

The accuracy of these micro-steps aren’t ideal for 3D printing quality and aren’t equal, so we implement layer heights where we can avoid these micro-steps.

Once we properly incorporate magic numbers, we can remove the need for micro-steps in our 3D printing for some smooth, high quality 3D prints.

I’ve seen many instances where people have continuously tried printing a model, ending up with print imperfections, then once they implement magic number layer heights, produce a nice quality print with little to no imperfections.

How to Determine Magic Numbers for Your 3D Printer

You can either do some research for your 3D printer to determine the magic numbers, since many people have happily calculated and given out the information, or you can use the Prusa Magic Number Calculator.

You’ll need to know the following:

  • Motor step angle
  • Leadscrew pitch
  • Gear ratio
  • Pitch presets
  • Then your desired layer height

As mentioned in the calculator, they are best suited for 3D printers that implement imperial leadscrews, but still work for metric leadscrews where you are using an unusual layer height.

After putting in these parameters, the calculator will tell you whether your desired layer height gives you an optimal layer height, or returns a red highlighted layer height which should be changed to one of the green highlighted layer heights.

Magic Numbers Calculator Prusa - 3D Printerly
Source: RepRap Calulator – Prusa Printers

Ender 3 & Creality Machine Magic Numbers

For Creality machines, the magic number is 0.04, so layer heights of:

  • 0.04
  • 0.08
  • 0.12
  • 0.16
  • 0.20
  • 0.24
  • 0.28mm and so on are going to give proper steps for better quality prints.

Cura has started to use these magic numbers as the default setting now.

The Ultimaker brand also has the 0.04mm magic number.

Monoprice Select Mini Magic Numbers

For the Monoprice Select Mini it is 0.04375, as discovered by Michael O’Brien in this Hackaday article. So you would use the following values:

  • 0.04375
  • 0.0875
  • 0.13125
  • 0.175
  • 0.21875
  • 0.2625
  • 0.30625

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