Ever heard the term “magic numbers”. What are they and why are they important for getting the best quality prints? I Would like to explain what magic numbers are, how to calculate them for your 3D printer, and how to use them in your slicer settings.

Magic numbers are layer heights that are multiples of the minimum height that your Z-axis can move. For example, if your Z-axis can move in increments of 0.04 mm, then your magic numbers are 0.04 mm, 0.08 mm, 0.12 mm, and so on. By choosing one of these magic numbers as your layer height, you can ensure that your printer moves in full steps or half steps, which are more accurate and consistent than micro steps.

Micro steps are fractions of a full step that are achieved by activating two electromagnets on the stepper motor. However, micro steps are not precise and can vary depending on the current and torque of the motor. This can lead to inaccuracies and inconsistencies in your prints, especially if your layer height does not match the steps of your motor.

To avoid micro stepping, you need to know the magic numbers for your 3D printer. You can find them online for popular models like the Ender 3, or you can calculate them yourself using a simple formula or a calculator. The formula is:

Magic number = (motor step angle / 360) * leadscrew pitch * gear ratio

The motor step angle is usually 1.8 degrees for most 3D printers, but you can check your specifications to be sure. The leadscrew pitch is the distance that the leadscrew moves per rotation, which is usually 8 mm for metric leadscrews or 2 mm for imperial leadscrews. The gear ratio is the ratio between the number of teeth on the pulley and the number of teeth on the motor shaft, which is usually 1:1.

For example, if you have a printer with a 1.8 degree motor step angle, an 8 mm leadscrew pitch, and a 1:1 gear ratio, then your magic number is:

Magic number = (1.8 / 360) * 8 * 1 = 0.04 mm

Once you know your magic number, you can choose a layer height that is a multiple of it in your slicer settings. For example, if your magic number is 0.04 mm, you can choose a layer height of 0.08 mm, 0.12 mm, 0.16 mm, etc. This will ensure that your printer moves in full steps or half steps and produces smoother and more accurate prints.

However, there are some limitations and trade-offs to consider when using magic numbers. First of all, not all layer heights are suitable for all models. Some models may require finer details or sharper angles that can only be achieved with lower layer heights. In this case, you may have to sacrifice some quality for accuracy or vice versa.

Secondly, using magic numbers does not guarantee perfect prints every time. There are many other factors that affect print quality, such as temperature, speed, flow rate, cooling, retraction, etc. You still need to calibrate and optimize these settings for your printer and filament.