Gain margin is the amount of additional gain (as a multiplicative factor or in dB) that can be applied to an open-loop system before it becomes unstable. It is evaluated at the phase crossover frequency, where the open-loop phase is exactly -180 degrees.

What is the phase crossover frequency?

The phase crossover frequency (ω_pc) is the frequency at which the open-loop transfer function's phase shift equals -180 degrees. At this frequency, a feedback loop could sustain oscillations if the gain is exactly 1 (0 dB).

What is a good gain margin?

A gain margin of at least 6 dB (a factor of 2) is commonly recommended for robust stability. Systems with margins below 3 dB may be sensitive to parameter variations.

What does a negative gain margin mean?

A negative gain margin in dB (or a GM ratio less than 1) means the system is unstable — the open-loop gain already exceeds 1 at the phase crossover frequency.

What if there is no phase crossover frequency?

If the open-loop phase never reaches -180 degrees, the gain margin is theoretically infinite, and the system is unconditionally stable for all positive gains.

Gain Margin Calculator

Name: Gain Margin Calculator
Availability: InStock
Author: Nham Vu

Calculate gain margin in dB from open-loop gain at the phase crossover frequency, with stability assessment.

System Parameters

Open-loop gain at phase crossover |G(jω_pc)|

Absolute magnitude (e.g. 0.25 means the gain is 25% of 1 at -180° phase).

— or enter gain in dB

If your Bode plot shows the gain in dB at ω_pc, enter it here (negative = below 0 dB).

Phase crossover frequency ω_pc (optional)

Enter for reference; does not affect the gain margin calculation.

Formula Reference

GM = 1 / |G(jω_pc)|

GM_dB = 20 × log₁₀(GM)

Stable: GM_dB > 0 dB (GM > 1)

ω_pc is the phase crossover frequency where ∠G(jω) = -180°.

Common Examples

\|G(jω_pc)\|	GM (ratio)	GM (dB)
0.125	8.00	+18.06 dB
0.25	4.00	+12.04 dB
0.5	2.00	+6.02 dB
1.0	1.00	0.00 dB
2.0	0.50	-6.02 dB

Click a row to load the example.

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Summary

Calculate gain margin in dB from open-loop gain at the phase crossover frequency, with stability assessment.

How it works

Find the phase crossover frequency from your Bode plot — the frequency where phase equals -180 degrees.
Read the open-loop gain magnitude at that frequency (as an absolute value, e.g. 0.25 or 2.0).
Enter the gain value into the calculator.
The gain margin is computed as GM = 1 / |G(jω_pc)| and converted to dB as 20 × log₁₀(GM).
The stability assessment shows whether the system is stable (GM > 1, i.e. GM_dB > 0 dB).

Use cases

Verify the stability margin of a PID-controlled plant before deployment.
Design a compensator with a target gain margin of at least 6 dB.
Cross-check gain margin readings from a Bode plot analysis tool.
Determine how much extra gain can be added before a stable system goes unstable.
Analyze robustness of a feedback amplifier circuit.
Quickly convert a gain ratio to decibels for a control system report.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu