Resistor Noise Calculator

What Is Johnson-Nyquist Resistor Noise?

Every resistor at finite temperature produces tiny random voltage fluctuations called thermal noise or Johnson noise. This noise sets a fundamental limit on how small a signal you can measure through a resistive front end. It is not a defect in the component; it comes from thermal agitation of charge carriers.

Johnson Noise Formula

The RMS noise voltage across a resistor over bandwidth \(\Delta f\) is:

where \(k = 1.38 \times 10^{-23}\,\mathrm{J/K}\) is Boltzmann's constant, \(T\) is absolute temperature in kelvin, \(R\) is resistance in ohms, and \(\Delta f\) is measurement bandwidth in hertz.

Noise Spectral Density

The voltage noise power spectral density is \(S_v = 4kTR\) in units of \(\mathrm{V^2/Hz}\). Wider bandwidth integrates more noise, so RMS voltage grows with \(\sqrt{\Delta f}\). Lowering temperature, resistance, or bandwidth all reduce thermal noise.

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