Nichols Chart Calculator

• •Use the Nichols Chart Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Nichols Chart Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Plot the Nichols chart of a transfer function and read gain margin, phase margin, and closed-loop resonant peak Mr All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

A Nichols chart plots open-loop magnitude in decibels on the vertical axis against open-loop phase in degrees on the horizontal axis, with frequency as the parameter tracing the curve. It combines the information Bode splits across two plots into a single locus, which makes the distance from the critical point (−180°, 0 dB) directly visible. Gain margin is the vertical distance from the locus to 0 dB where it crosses −180°; phase margin is the horizontal distance from −180° where it crosses 0 dB. The chart's historical advantage was the overlaid M and N contours, which let an engineer read closed-loop magnitude and phase straight off the open-loop curve without recomputing the feedback algebra. Two subtleties matter more here than on a Bode plot. First, phase must be UNWRAPPED: atan2 returns values confined to (−180°, 180°], so a locus built from raw principal values folds back on itself and a phase margin computed from it can be wrong by a multiple of 360° — reporting a large positive margin for a loop that is actually unstable. This calculator anchors the unwrap to the analytic low-frequency phase and wraps the MARGIN rather than the locus, so a type-3 plant such as 1/s³ correctly reports −90° rather than +270°. Second, gain and phase margins alone are only a valid stability test for open-loop-stable, minimum-phase plants. For anything else the margins can look healthy while the closed loop has right-half-plane roots, so this tool also runs an independent Routh test on 1 + G(s) and reports the closed-loop verdict separately from the margins.

• •Loop shaping for servo drives: read gain and phase margin together while adjusting compensator gain, without switching between two Bode axes.
• •Verifying a design against a margin specification: many aerospace and industrial specs state a required gain margin in dB and phase margin in degrees, both of which are single distances on this chart.
• •Diagnosing conditionally stable loops: a locus that approaches the critical point more than once shows immediately that both raising AND lowering gain can destabilise the system.
• •Reading closed-loop resonant peak: the highest M contour the locus touches gives Mr directly, which sets the expected overshoot of the closed-loop step response.
• •Teaching the relationship between open-loop and closed-loop behaviour: the chart makes the mapping from one to the other geometric rather than algebraic.

• !Reading a phase margin from a wrapped phase locus, which can be off by 360° and turn an unstable loop into an apparently healthy one.
• !Treating positive margins as proof of stability on a non-minimum-phase or open-loop-unstable plant.
• !Entering coefficients in ascending powers. Both fields expect the highest power first, matching the other transfer-function tools on this site.
• !Assuming a missing margin means a good one. If the locus never crosses 0 dB or never crosses −180° within the swept band, the margin is undefined, not infinite.
• !Quoting Mr from an unstable closed loop, where the peak is a numerical artefact rather than a resonance.