3D Printing Calculators
PID Tuning (Ziegler–Nichols)
https://www.3dsizing.com/calculators/pid-tuning/
Estimate only — not firmware, a slicer profile or a shop quote. Confirm on a test print.
PID Tuning (Ziegler–Nichols)
When a heater sits at the edge of oscillation, Ku is that gain and Tu is the period in seconds. Classic Ziegler–Nichols turns those two numbers into Kp, Ki and Kd. Firmware choice here is documentation — the three gains are the same math.
Inputs
Results
- Kp
- 18.0000
- Ki
- 1.8000
- Kd
- 45.0000
Calculation method
Classic Ziegler–Nichols PID from the ultimate-sensitivity experiment: Kp = 0.6 × Ku, Ki = 2 × Kp / Tu, Kd = Kp × Tu / 8, with Tu in seconds. The firmware dropdown does not alter the numbers; Marlin and Klipper simply expect different G-code or config keys. Invalid if Ku or Tu is not positive. There is no unit conversion — these gains are dimensionless in the usual printer firmware convention.
Exact formula
Kp = 0.6 × Ku. Ki = 2 × Kp / Tu. Kd = Kp × Tu / 8. Marlin M301/M304 and Klipper pid_kp/pid_ki/pid_kd use these symbols with different command syntax. Limits: Classic Ziegler–Nichols is aggressive and can overshoot. Prefer firmware PID_CALIBRATE / M303; never leave a heater unattended hunting Ku.
Where to paste the numbers
Marlin: M301 for hotend, M304 for bed, then M500. Klipper: pid_Kp, pid_Ki, pid_Kd under the heater section, then SAVE_CONFIG after a real PID_CALIBRATE if you can.
Frequently asked questions
How do I find Ku and Tu?
Raise Kp (others zero) until the temperature oscillates at constant amplitude. Ku is that Kp. Tu is the time between peaks. Then come here. Or skip this and run M303 / PID_CALIBRATE.
Marlin vs Klipper values differ on forums.
Firmware auto-tune uses different algorithms. This page is only classic ZN from Ku and Tu, identical for both.
Bed Tu is huge compared with the hotend.
A 300 mm bed is a slow plant. Tu of tens of seconds is normal. Do not paste hotend PID onto the bed.
My bed overshoots 10 °C.
ZN classic is snappy. Lower Kp a bit or use the firmware autotune, which often damps more.
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