Prusa Calculator
Calibrate your X, Y, Z, and Extruder steps with precision.
Most NEMA 17 motors used in Prusa-style printers are 1.8°.
Standard RAMPS/Einsy boards usually use 1/16.
GT2 belts (standard) have a 2.0mm pitch.
Common sizes are 16 or 20 teeth.
Distance moved per single rotation (e.g., T8x8 = 8mm).
Effective diameter where the filament touches the gear.
X/Y Steps per mm
400.00
139.63
3200
Steps/mm Comparison Chart
Visualizing the difference in resolution across axes.
| Axis | Formula Components | Target Value |
|---|---|---|
| X Axis | Belt + Pulley | 80.00 |
| Y Axis | Belt + Pulley | 80.00 |
| Z Axis | Leadscrew Pitch | 400.00 |
| Extruder | Gear Diameter | 139.63 |
What is a Prusa Calculator?
A prusa calculator is an essential tool for 3D printing enthusiasts and engineers using Fused Deposition Modeling (FDM) technology. It is designed to calculate the precise motor movements required to move a printer’s toolhead or build plate by exactly one millimeter. This value is known as “Steps per mm.”
Whether you are building a RepRap machine from scratch or upgrading your Prusa i3 MK3S+ with new stepper motors or different pulleys, the prusa calculator ensures your dimensions remain accurate. Using an incorrect prusa calculator value can lead to prints that are too small, too large, or suffering from severe extrusion issues. Experts use this to calibrate the firmware (like Marlin or Repetier) to match the physical hardware of the machine.
Prusa Calculator Formula and Mathematical Explanation
The math behind the prusa calculator varies depending on the axis. Belt-driven axes (X and Y) use different mechanics than screw-driven axes (Z) or the filament drive (Extruder).
The Core Formulas
- X/Y Axis Steps/mm:
(Steps per Revolution * Microstepping) / (Belt Pitch * Tooth Count) - Z Axis Steps/mm:
(Steps per Revolution * Microstepping) / Leadscrew Lead - Extruder Steps/mm:
(Steps per Revolution * Microstepping) / (Drive Gear Diameter * π)
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Steps/Rev | Full steps in one 360° turn | Steps | 200 or 400 |
| Microstepping | Division of full steps | Integer | 1 to 256 |
| Belt Pitch | Distance between belt teeth | mm | 2.0 (GT2) |
| Leadscrew Lead | Travel per rotation | mm | 2.0 to 8.0 |
Practical Examples (Real-World Use Cases)
Example 1: Standard GT2 Calibration
A user has a standard motor (1.8°), 1/16 microstepping, and a 20-tooth pulley.
The prusa calculator logic: (200 * 16) / (2.0 * 20) = 3200 / 40 = 80 steps/mm. This is the gold standard for most hobbyist printers.
Example 2: High-Resolution Leadscrew Upgrade
Upgrading a Z-axis with a 0.9° motor and a 2mm lead screw.
The prusa calculator logic: (400 * 16) / 2 = 6400 / 2 = 3200 steps/mm. This provides incredible vertical precision, crucial for fine detail work.
How to Use This Prusa Calculator
- Select your Motor Step Angle. Most standard motors are 1.8 degrees.
- Choose your Microstepping level. This is usually set via jumpers or software on your control board.
- Input the Belt Pitch. For almost all modern printers, this is 2.0.
- Enter the Pulley Tooth Count. Count the teeth on the gear attached to your X or Y motor.
- For the Z-axis, check your Leadscrew Lead. T8x8 screws have an 8mm lead.
- The prusa calculator will automatically update the values. Copy these into your Marlin configuration.h or send them via G-code (M92).
Key Factors That Affect Prusa Calculator Results
- Motor Precision: Even a 1.8° motor has a tolerance (usually +/- 5%). The prusa calculator assumes perfect geometry.
- Belt Tension: While the formula is static, loose belts cause “slop,” which makes the theoretical prusa calculator value feel inaccurate during actual prints.
- Microstepping Stability: High microstepping (like 1/256) sounds better, but drivers may not have the torque to hold those positions accurately under load.
- Effective Gear Diameter: In the extruder, the “bite” of the gear into the filament changes the effective diameter, requiring a prusa calculator adjustment.
- Thermal Expansion: In extreme environments, the expansion of belts or screws might slightly shift the required steps/mm.
- Firmware Limits: Ensure your CPU (8-bit vs 32-bit) can handle the step frequency generated by high prusa calculator values at high speeds.
Frequently Asked Questions (FAQ)
Leadscrews provide mechanical advantage. A small rotation results in very little vertical movement, requiring more steps to cover 1mm compared to a belt and pulley system.
Yes! The math behind the prusa calculator applies to almost all FDM printers including Ender 3, Voron, and Anycubic machines.
If the prusa calculator value is too high, your parts will be larger than intended. If too low, they will be smaller.
Usually, the X, Y, and Z steps stay the same. However, you might want to re-run the prusa calculator for E-steps if the filament hardness changes significantly.
0.9 degree motors have twice the native resolution (400 steps per rev), which the prusa calculator accounts for to double your steps/mm.
Use the M92 X80 Y80 Z400 E140 command followed by M500 to save to EEPROM.
Microstepping makes movement smoother and quieter, but it doesn’t always increase absolute positioning accuracy due to torque loss.
The prusa calculator provides a theoretical start point, but “Extruder Calibration” (measuring 100mm) is needed to account for filament grip.
Related Tools and Internal Resources
- 3D Print Time Estimator – Calculate how long your print will take based on speeds.
- Filament Cost Calculator – Determine the price per gram for your specific prusa calculator settings.
- Acceleration and Jerk Tuner – Fine-tune the motion dynamics of your calibrated printer.
- Nozzle Size Guide – Match your extrusion width to your prusa calculator outputs.
- Shrinkage Compensation Tool – Adjust your steps to account for plastic cooling.
- Stepper Motor Torque Chart – Ensure your motors can handle the prusa calculator resolutions.