Thermal Noise Calculator

Compute RMS noise voltage, available noise power, peak‑to‑peak noise, and spectral density for a resistor at a given temperature and bandwidth.

Resistor value in ohms
converted to Kelvin internally
Noise measurement bandwidth
? 50Ω, 27°C, 1 MHz
?️ 1kΩ, 27°C, 100 kHz
? 75Ω, 20°C, 10 MHz
⚙️ 10kΩ, 85°C, 500 kHz
? 200Ω, 40°C, 2 MHz
Privacy-first: All calculations run locally in your browser. No data is sent to any server.

Johnson–Nyquist Noise: Theory & Practical Relevance

Thermal noise, also known as Johnson–Nyquist noise, is an unavoidable electronic noise generated by the thermal agitation of charge carriers (usually electrons) inside an electrical conductor at equilibrium. It was first measured by John B. Johnson at Bell Labs in 1926 and theoretically explained by Harry Nyquist. The mean‑square noise voltage across a resistor is given by the fundamental formula:

Vn,rms = √(4 · kB · T · R · B)

where kB is Boltzmann's constant (1.380649 × 10−23 J/K), T is absolute temperature (Kelvin), R is resistance (Ω), and B is bandwidth (Hz). The available noise power from a resistor is independent of resistance: Pn = kBT B — a crucial insight for impedance matching and receiver design.

Key Properties

  • White noise: constant spectral density SV(f) = √(4kBTR) V/√Hz
  • Independent of frequency up to ~THz range (quantum effects at very high f)
  • Fundamental limit for sensitivity in amplifiers, radio receivers, and sensors
  • Cannot be eliminated, only mitigated by cooling or reducing bandwidth/resistance

Real‑World Applications

  • ? RF front‑end noise figure calculations
  • ? Precision low‑noise amplifiers (LNA design)
  • ?️ Radio astronomy sensitivity limits
  • ⚡ Quantum computing cryogenic electronics
  • ?️ Audio preamplifier SNR optimization

Derivation & Physical Origin

The fluctuation‑dissipation theorem links thermal fluctuations to dissipative properties. Nyquist’s original derivation considered a transmission line terminated by resistors in thermal equilibrium. The noise voltage spectral density across a resistor can be modeled as a Thevenin equivalent with series voltage source having mean‑square value ⟨V2⟩ = 4kBTR·Δf. In practical engineering, the RMS noise voltage integrates this density over the effective bandwidth: Vn = √(4kBTR·B). For most applications below 100 GHz, the classical formula holds with high accuracy.

The 174 dBm/Hz Legend: Thermal Noise Floor

At room temperature (290 K), the thermal noise spectral density in a 1 Hz bandwidth equals −174 dBm/Hz. This is the ultimate noise floor for any passive component. For a communication receiver, the minimum detectable signal is often limited by thermal noise from the antenna impedance (typically 50 Ω). This calculator computes the exact noise power in dBm so you can relate to real‑world sensitivity specifications.

Parameter Value (Typical) Significance
Room temperature (290 K) -174 dBm/Hz Standard noise floor reference
1 kΩ resistor @ 27°C, 1 MHz BW ~4.07 µVrms Measurable by sensitive oscilloscopes
kTB @ 1 kHz BW, 300K -144 dBm Typical narrowband receiver limit
Case Study: Radio Telescope Sensitivity

The Green Bank Telescope (GBT) operates at cryogenic temperatures to reduce thermal noise from receiver electronics. For a 50 Ω feed at 20 K, the noise power per Hz is only kT ≈ 2.76×10-22 W/Hz (~ -175.6 dBm/Hz). Using our calculator, doubling bandwidth improves sensitivity by √2 but also integrates more noise — the tradeoff is fundamental. This tool helps engineers quickly evaluate system noise contributions.

Step-by-Step Calculation Method

  1. Convert temperature from Celsius to Kelvin: T[K] = T[°C] + 273.15.
  2. Compute RMS noise voltage: Vn = √(4 × k × T × R × B).
  3. Compute noise power (available): Pn = k × T × B (Watts).
  4. Convert power to dBm: PdBm = 10·log10(Pn / 0.001).
  5. Peak‑to‑peak estimation using crest factor 6.6 for Gaussian noise (99.9% confidence).
  6. Spectral density √(4kTR) in nV/√Hz for quick noise comparisons.

Common Pitfalls & Misconceptions

  • “Noise voltage depends on applied voltage” – False: thermal noise is intrinsic and independent of DC bias.
  • “Larger resistors are always noisier” – Yes for voltage noise, but for current noise small resistors generate less current noise; choose based on application.
  • “Cooling eliminates noise” – Only reduces it; even at cryogenic temperatures, noise power scales with temperature.
  • “Noise disappears in a short circuit” – Instead, noise manifests as current noise; both voltage and current representations remain consistent.

Advanced Topics: Quantum Corrections & Shot Noise

At extremely high frequencies (f > kT/h ~ 6 THz at 300 K) quantum effects modify the spectrum: Vn2 = 4hfR/(ehf/kT−1) · B. At room temperature, these corrections are negligible below 100 GHz. Also, note that shot noise (due to DC current) differs from thermal noise; this calculator focuses purely on equilibrium Johnson noise.

Scientific Foundation & References
H. Nyquist, "Thermal Agitation of Electric Charge in Conductors," Phys. Rev. 32, 110 (1928).
J. B. Johnson, "Thermal Agitation of Electricity in Conductors," Phys. Rev. 32, 97 (1928).
International standard: Boltzmann constant fixed in 2019 (k = 1.380649×10−23 J/K).
Last updated May 2026. 

Thermal noise exists even without current flow and depends only on temperature, resistance, and bandwidth. Shot noise occurs when charge carriers cross a potential barrier (e.g., diode) and is proportional to DC current.

For Gaussian noise, 99.9% of instantaneous values lie within ±3.29σ; the peak-to-peak is 2×3.29σ ≈ 6.6σ. Useful for estimating voltage swing in amplifier stages.

Yes, RMS noise voltage scales with √B. Narrower bandwidth filters dramatically improve SNR, which is why lock‑in amplifiers are effective.

Up to very high frequencies (≈ THz), yes. At optical frequencies, quantum corrections appear, but for nearly all electronics applications it is perfectly flat.
References: Nyquist 1928, Pozar "Microwave Engineering", ITU-R SM.1755. This tool complies with standard electronic engineering formulas.