Resistor Noise Calculator (Johnson-Nyquist Thermal Noise)
Enter the resistance, temperature, and bandwidth to find the RMS thermal noise voltage generated by the resistor. You also get the noise spectral density (nV per root-Hz), the available noise power in dBm, and the noise level in dBV. Results update instantly as you type, and the chart shows how noise voltage scales with resistance across common component values.
Formula
Worked example
A 10 kOhm resistor at 25 C over a 1 kHz bandwidth: Vn = sqrt(4 * 1.381e-23 * 298.15 * 10000 * 1000) = sqrt(1.649e-13) = 0.406 uV RMS. Spectral density = 0.406 uV / sqrt(1000 Hz) = 12.84 nV/rtHz.
What is resistor thermal noise?
All resistors generate electrical noise purely because of random thermal motion of electrons. This phenomenon was first measured by John B. Johnson at Bell Labs in 1928 and theorized by Harry Nyquist the same year, giving rise to the names Johnson noise, Johnson-Nyquist noise, and thermal noise. It is also called Nyquist noise. Unlike other noise sources, thermal noise is a fundamental consequence of thermodynamics: any conductor in thermal equilibrium with its environment generates a noise voltage across its terminals. The only way to eliminate it entirely is to cool the resistor to absolute zero, which is physically impossible. Reducing temperature, resistance, and the bandwidth of the circuit are the only practical methods for minimizing it.
Johnson-Nyquist noise formula
The RMS noise voltage across a resistor is given by Vn = sqrt(4 * kB * T * R * B), where kB is the Boltzmann constant (1.380649e-23 J/K, exact since the 2019 SI redefinition), T is the absolute temperature in Kelvin, R is the resistance in Ohms, and B is the noise bandwidth in Hertz. The noise spectral density (en = sqrt(4 * kB * T * R)) is the noise voltage per square root of frequency bandwidth, expressed in nV/rtHz (nanovolts per root-Hertz). Because spectral density is independent of bandwidth, it is the most useful quantity for comparing noise sources and specifying low-noise amplifiers. The available noise power, Pn = kB * T * B, depends only on temperature and bandwidth, not on resistance: this represents the maximum noise power that can be transferred to a matched load.
How to use this calculator
Enter the resistance value, select the unit (Ohm, kOhm, or MOhm), then set the operating temperature (Celsius, Kelvin, or Fahrenheit) and the noise bandwidth (Hz, kHz, or MHz). The calculator instantly returns the integrated RMS noise voltage in microvolts, the spectral density in nV/rtHz, the available noise power in dBm, the noise level in dBV, and the internal Kelvin temperature used in the calculation. The chart below the results shows how noise voltage changes with resistance across common component values at the same temperature and bandwidth, which helps you see how much a change in source impedance affects your noise floor.
Noise in circuit design
Thermal noise is the fundamental limit for the signal-to-noise ratio (SNR) of any electronic circuit. In audio, instrumentation, RF, and sensor interfaces the source resistance is often the dominant noise contributor. Low-noise operational amplifiers specify their voltage noise in nV/rtHz: to find the total noise at the amplifier input you combine the op-amp noise density with the thermal noise density of the source resistance in quadrature (sqrt of sum of squares), then integrate over the noise bandwidth. For source resistances above roughly 100 kOhm, current noise from bipolar-junction transistor (BJT) input stages begins to dominate, and FET-input amplifiers are preferred because their gate current is negligible. At radio frequencies, the noise figure of an amplifier in dB directly relates to how much noise it adds above the thermal noise floor at room temperature (kTB into a 50 Ohm source at 290 K gives approximately -174 dBm/Hz).
Common resistors at 25 C and 1 kHz bandwidth
| Resistance | Noise Voltage (uV) | Spectral Density (nV/rtHz) | Noise Level (dBV) |
|---|---|---|---|
| 100 Ohm | 0.0406 | 1.28 | -147.8 |
| 1 kOhm | 0.1283 | 4.06 | -137.8 |
| 10 kOhm | 0.4058 | 12.83 | -127.8 |
| 100 kOhm | 1.2832 | 40.58 | -117.8 |
| 1 MOhm | 4.0578 | 128.32 | -107.8 |
Typical thermal noise figures for standard resistor values at room temperature (298.15 K) over a 1 kHz noise bandwidth.
Frequently asked questions
What is the difference between thermal noise, Johnson noise, and Nyquist noise?
They are three names for the same phenomenon. Thermal noise describes the physical cause (thermal agitation of electrons). Johnson noise honors John B. Johnson, who first measured it experimentally in 1928. Nyquist noise honors Harry Nyquist, who derived the theoretical formula the same year. All three terms refer to the noise voltage generated by any resistive element at a temperature above absolute zero.
Does the type of resistor affect thermal noise?
For thermal (Johnson) noise, only the resistance value and temperature matter, not the material or construction. A carbon-film, metal-film, wire-wound, or thin-film resistor with the same resistance at the same temperature produces identical Johnson noise. However, some resistor types generate additional excess noise (also called current noise or 1/f noise) when direct current flows through them. Carbon-composition resistors are notably noisy in this regard, while metal-film and wire-wound types are much quieter. This calculator covers only thermal noise; excess noise depends on the resistor type and the current through it.
How does bandwidth affect the total noise voltage?
Total RMS noise voltage scales with the square root of bandwidth. Doubling the bandwidth increases the noise voltage by a factor of sqrt(2), approximately 41%. Limiting bandwidth to the minimum needed by your signal is one of the most effective ways to reduce noise. This is why anti-aliasing filters before ADC inputs and narrow-band detection techniques dramatically improve SNR.
What is noise spectral density and why is it useful?
Noise spectral density (en) is the noise voltage per square root of frequency, expressed in nV/rtHz. It is independent of bandwidth, which makes it the standard way to characterize and compare noise sources and amplifiers. To find the total RMS noise over a bandwidth B, multiply en by sqrt(B). For example, if a source has en = 10 nV/rtHz and your circuit bandwidth is 10 kHz, the total noise is 10e-9 * sqrt(10000) = 10e-9 * 100 = 1 uV RMS.
What is the noise floor at room temperature?
At room temperature (290 K, approximately 17 C, the standard reference temperature for RF noise), the available thermal noise power per unit bandwidth is kB * T = 1.38e-23 * 290 = 4.0e-21 W/Hz, which is -174 dBm/Hz. This is the absolute minimum noise floor for any system operating at room temperature, regardless of the resistance or circuit design. Real circuits always exceed this floor due to amplifier noise figures and excess noise.
How does cooling a resistor reduce its noise?
Because thermal noise voltage is proportional to sqrt(T), cooling directly reduces noise. Cooling from 300 K (room temperature) to 77 K (liquid nitrogen) reduces noise voltage by sqrt(300/77), approximately 1.97, nearly halving it. Cooling to 4 K (liquid helium) reduces it by sqrt(300/4), approximately 8.7 times. This is why the input stages of radio telescopes and quantum computers are cooled to cryogenic temperatures to minimize thermal noise.