PID Tuning Calculator | PrintCalcLab

Calculate hotend PID parameters using Ziegler-Nichols method.

A hotend that overshoots, oscillates, or sags ten degrees when the part-cooling fan kicks in usually needs its PID gains retuned, not new hardware. This assistant computes hotend PID parameters with the classic Ziegler-Nichols method from two measurements of your heater's natural oscillation — the ultimate gain and the oscillation period — and emits the exact M301 G-code line that applies them in Marlin-family firmware.

How It Works

Ziegler-Nichols classic tuning sets the proportional gain Kp to 0.6 × Ku, the integral gain Ki to 2Kp ÷ Tu, and the derivative gain Kd to Kp × Tu ÷ 8, where Ku is the ultimate gain at which the temperature oscillates steadily and Tu is that oscillation's period in seconds. With the default inputs of Ku = 2.5 and Tu = 12 s, the result is Kp = 1.50, Ki = 0.25, and Kd = 2.25, delivered as M301 P1.50 I0.25 D2.25. Zero or negative inputs are rejected outright, so an invalid measurement can never produce a G-code line with undefined gains.

FAQ

What are Ku and Tu, and how do I find them?

Ku is the proportional-only gain at which your hotend temperature settles into steady, constant-amplitude oscillation, and Tu is the period of that oscillation in seconds. They are found experimentally by raising the proportional gain until sustained oscillation appears, then timing one full cycle.

How is this different from M303 autotune?

M303 has the firmware run its own oscillation experiment and report gains automatically. This calculator is for when you already know Ku and Tu — or want to understand and sanity-check what an autotune produced — by applying the Ziegler-Nichols arithmetic transparently.

What does each PID term actually do?

The proportional term reacts to the current temperature error, the integral term accumulates persistent error to eliminate steady-state droop, and the derivative term damps the rate of change to curb overshoot. Ziegler-Nichols balances all three from just your two oscillation measurements.

Do I need to retune after hardware changes?

Yes — a new heater cartridge, thermistor, nozzle, or silicone sock changes the thermal response, and so does a significantly different part-cooling airflow. Retune whenever sustained oscillation or persistent over- or undershoot appears at printing temperature.