Calculation reviewed: 4 October 2026 · Engineering Desk Tools
How to use the Ziegler–Nichols PID tuning calculator
Calculate starting P, PI or PID controller settings from the ultimate gain and ultimate period. Start with measurements or documented values for the equipment and reporting period you actually want to assess. The calculator does not fill in a typical installation for you. Its blank fields help keep a demonstration value from being mistaken for your own operating data.
Choose the required options, enter the values in the labelled units and select Calculate. If a field is rejected, check its range and unit before changing it. The result is accompanied by the equation and assumptions so you can decide whether it answers your engineering question.
Inputs and measurement basis
- Controller type. Choose the controller structure you plan to use. PID responds fastest but is the most sensitive to noise.
- Ultimate gain Ku. The proportional gain at which the loop first oscillates steadily. The value must be greater than zero.
- Ultimate period Pu (seconds). The time of one complete oscillation at that gain, in seconds. The value must be greater than zero.
Record the measurement source and operating condition. Retain unrounded values for verification.
Method and interpretation
In the closed-loop Ziegler–Nichols method the controller is set to proportional-only and the gain is raised until the process oscillates steadily. That gain is the ultimate gain Ku and the oscillation period is Pu. Fixed multipliers then give Kp, Ti and Td. They aim at quarter-amplitude decay, which is fast but oscillatory, so most plants need a gentler setting.
P: Kp = 0.5 Ku. PI: Kp = 0.45 Ku, Ti = Pu / 1.2. PID: Kp = 0.6 Ku, Ti = Pu / 2, Td = Pu / 8. Ki = Kp / Ti and Kd = Kp × Td.
These are the classic closed-loop Ziegler–Nichols starting values. They often give an aggressive response with overshoot, so treat them as a starting point and tune down. Finding Ku and Pu means driving the loop to sustained oscillation, which is not safe or acceptable on every process. Gain may be expressed as proportional band in some controllers, and time units differ between vendors.
Worked example
This example does not populate the form. Enter your own installation data.
Calculated result: 4.8 proportional gain Kp. Starting values only. Check the controller documentation for the algorithm form, units and any proportional-band convention, then tune cautiously.
Check the arithmetic independently using the displayed equation. Retain intermediate precision and compare the final value with your equipment documentation.
Quick-reference table
These illustrative rows retain the worked example assumptions except for the varied input. They are not certified ratings or manufacturer data. Use the form for intermediate values.
Common mistakes
Driving a process to sustained oscillation where that is unsafe; reading Pu in the wrong time unit; mixing proportional band with gain; entering Ti in minutes when the controller expects seconds; leaving the starting values untouched on a loop that must not overshoot. Before relying on the output, check the decimal format, unit scale and source of each value. Recheck unusual results against the formula.
Frequently asked questions
Are the example values used automatically?
No. Inputs remain blank when the tool opens or when you clear them. The worked example and table are reading material below the calculator. Enter the actual values you want to check each time, and label saved reports so their context is not lost.
What does the result mean?
The result is a set of starting controller settings, not a finished tuning. Apply them cautiously, watch the response and reduce the gain if the loop overshoots or oscillates.
Can I use a zero or a negative value?
The allowed range follows the meaning of each input. A divisor needs a positive value; other fields may allow zero. Check the form labels and error message rather than forcing an invalid value. A rejected input must be corrected before a result can be shown.
Is this a final design or equipment approval?
No. These are the classic closed-loop Ziegler–Nichols starting values. They often give an aggressive response with overshoot, so treat them as a starting point and tune down. Finding Ku and Pu means driving the loop to sustained oscillation, which is not safe or acceptable on every process. Gain may be expressed as proportional band in some controllers, and time units differ between vendors. Use the calculation as support for a checked decision, and review equipment documentation and applicable requirements before changing an installation or operating setting.
How can I save or share a calculation?
Calculate first, then use Copy result or Print report. Some maintenance tools also provide a CSV summary. Reports contain your own entered data, so review them before sharing. You can share the public page URL without including plant records or confidential measurements.
How do I report an unexpected result?
Use the Contact page and include the tool URL, input values, units, expected output and the reference you used. Explain the measurement basis. Exclude confidential information.
Related tools and records
Use related calculations with consistent units, periods and equipment scope.
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