What are the "magic numbers" people refer to regarding print resolution on the Monoprice Select Mini?

  • 1
    $\begingroup$ As an owner of the Monoprice Select Mini, I use the "Magic Numbers". It seems that any given printer design will have such magic numbers as a result of the Z-axis mechanics, but I haven not come across discussions for other printers. Are most printers designed to obtain "naturally" round numbers, i.e. multiples of (0.05 or 0.025), or fine enough stepping control that it doesn't matter if it's precise (0.0006...)? $\endgroup$
    – mbmcavoy
    Apr 21, 2017 at 22:22

3 Answers 3


The "magic numbers" are optimal values that work particularly well for the layer height. Michael O'Brien derived these numbers by reverse engineering the mechanics of the Z-axis stepper motor.

Using these values as your layer height will generally improve your print quality over using round layer heights such as 0.15, 0.2, or 0.25 by eliminating quantization errors.

To see an example of this, print a copy of 3DBenchy at 0.15 and 0.175. On the 0.15, you will see some wavy patterns on the curved bow portion compared to the 0.175. This is the result of inexact rounding.

Layer Height (mm)
0.04375 (results may vary)*

Though this approach is logical on paper, in the real world it doesnt work as well. Even if you do choose a magic number for the layer height, you cant gurentee that your print head, once homed at the beginning of a print, is using a full step of the motor. Its more common to be on a half step than a full step with a motor

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    $\begingroup$ Since your answer says "in the real world" you should provide some real world examples that back up your claim. Many owners on the Mini owners list have posted examples of how using the magic numbers improved print quality and reduced print time. I also think you're misunderstanding the claimed benefit (elimination of quantization errors). $\endgroup$ Dec 29, 2019 at 20:34
  • $\begingroup$ Wouldn't it be exactly as common to be on a half step as a full step? Or did you mean, more generically, some incremental non-full step? $\endgroup$
    – Davo
    Dec 31, 2019 at 0:44

This is an issue with homing. It is not synced to the stepper motor so it may occur on something other than a full or half or even quarter step. That said, it always does this so moving up from there, the first little bit may be off but I would expect once the motor runs freely, the error will go away. Also keep in mind with microstepping, you can have 1/16 or 1/32 steps as well. Using the magic number ensures the new position you request is within the limits of the stepper/controller to reach. Its like rounding numbers. if you don't, as you increment, the numbers will always be consistant. If you round, the numbers will dither around. At least thats my $45 (inflation) and stickin to it. Good luck everyone and have fun.


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