Calculate Johnson-Nyquist thermal noise voltage and current for any resistor. Includes spectral density, SNR, and noise vs. bandwidth tables.
Every resistor generates a small random voltage across its terminals — even with no current flowing. This phenomenon, known as Johnson-Nyquist noise or thermal noise, was first measured by John B. Johnson in 1926 and theoretically explained by Harry Nyquist in 1928. It is a fundamental consequence of the thermal agitation of charge carriers (electrons) inside the resistive material.
Thermal noise sets the ultimate sensitivity limit for electronic circuits. In a radio receiver, the noise floor of the front-end amplifier is largely determined by the thermal noise of its input resistance. In precision measurement systems, low-noise design starts with understanding and minimizing resistor noise. The RMS noise voltage is proportional to the square root of resistance, temperature, and bandwidth — meaning that reducing any of these three factors reduces noise.
This calculator computes Johnson-Nyquist noise voltage, noise current, available noise power, and voltage/current spectral density. It provides tables showing how noise changes with bandwidth and resistance, plus a signal-to-noise ratio chart for various signal levels. You can also analyze the combined noise of multiple identical resistors in series or parallel configurations.
Understanding resistor noise is essential for low-noise circuit design. Whether you\'re selecting components for an audio preamplifier, an RF front end, or a precision instrumentation amplifier, thermal noise sets the fundamental limit. This calculator lets you quickly quantify noise voltage, noise current, and spectral density, compare values across resistances and bandwidths, and estimate the signal-to-noise ratio for your application.
V_noise = √(4 · k · T · R · Δf), where k = 1.381×10⁻²³ J/K (Boltzmann constant), T = absolute temperature (K), R = resistance (Ω), Δf = bandwidth (Hz). Noise power P_n = k · T · Δf (independent of R).
Result: 4.07 µV RMS noise voltage
V_noise = √(4 × 1.381e-23 × 298.15 × 10000 × 100000) = √(1.652e-11) ≈ 4.07 µV. The spectral density is 12.87 nV/√Hz.
Thermal noise arises from the random Brownian motion of charge carriers inside any conductor. At thermal equilibrium, the fluctuation-dissipation theorem guarantees that any dissipative element (resistance) will produce voltage fluctuations with a white power spectral density of S_v = 4kTR V²/Hz. This is a remarkably universal result — it depends only on resistance and temperature, not on material, geometry, or construction.
In a transimpedance amplifier (e.g., for photodiode readout), the feedback resistor\'s thermal noise directly limits the minimum detectable current. A 1 MΩ feedback resistor at 25°C produces about 4 nV/√Hz, which translates to ~4 fA/√Hz of equivalent input noise current. Designers often face a tradeoff: higher resistance means more gain but also more noise (both scale as √R). Bandwidth limiting through capacitive feedback can reduce total integrated noise.
Real resistors exhibit additional noise beyond the thermal minimum. Carbon composition resistors generate significant 1/f (flicker) noise when current flows, quantified by a noise index in dB. Metal film and wirewound resistors have much lower excess noise. For the most demanding applications, bulk metal foil resistors (e.g., Vishay VHP) offer the lowest combined thermal and excess noise.
It is the random voltage generated by any resistor due to thermal motion of electrons. It was first measured by Johnson and theoretically explained by Nyquist in the 1920s. Unlike shot noise or flicker noise, thermal noise has a flat (white) spectrum.
Johnson-Nyquist (thermal) noise depends only on resistance, temperature, and bandwidth. However, real resistors also generate excess noise (1/f noise and current noise) that varies by type. Carbon composition resistors are noisier than metal film.
Available noise power P = kTΔf is independent of R because higher R produces more voltage but also limits the current proportionally. The maximum power transfer occurs when load impedance matches the source, and the result is always kTΔf.
Noise voltage scales as √T (absolute temperature in Kelvin). At room temperature (298 K), cooling to liquid nitrogen (77 K) reduces noise voltage by about half, which is why cryogenic preamplifiers are used in radio telescopes.
Series: total R increases, so V_noise increases (but I_noise decreases). Parallel: total R decreases, so V_noise decreases but I_noise increases. Paralleling n identical resistors reduces voltage noise by √n.
The noise floor is the minimum detectable signal level in a system, set by thermal noise (and other noise sources). At 25°C over a 1 Hz bandwidth, the thermal noise floor is −174 dBm regardless of resistance.