Resistor Noise Calculator - Johnson-Nyquist Thermal Noise

A resistor noise calculator applies the Johnson-Nyquist thermal noise equation to any resistor you specify, returning the RMS noise voltage, the noise current, the spectral densities in V/√Hz and A/√Hz, and the available noise power k_B T Δf in a single result panel.

• • Audio preamp noise floor: Estimate the Johnson-Nyquist noise of a 10 kΩ source resistor at 290 K across a 20 kHz audio band before adding a microphone preamp on top.
• • RF front-end budget: Pick the smallest source resistance that still meets a −90 dBm noise floor at 20 MHz IF bandwidth and 300 K.
• • Sensor interface design: Compare the thermal noise of a 1 MΩ feedback resistor to the leakage current of a transimpedance amplifier at room and cryogenic temperatures.
• • Teaching the Johnson-Nyquist equation: Plug any R, bandwidth, and temperature into the formula and read back the same answer a textbook derivation produces.

Every resistor produces a small but unavoidable noise voltage that grows with resistance, absolute temperature, and the bandwidth of the measurement. The Johnson-Nyquist equation captured this behaviour in 1928 and is still the foundation of every low-noise analogue design today.

Because the noise is white - meaning the spectral density is flat up to frequencies where quantum effects appear - the only parameters you need are the resistance R, the noise-equivalent bandwidth Δf, and the absolute temperature T. The resistor noise calculator handles the unit conversions and the square roots so you can compare circuit options quickly.

Before sizing a noise budget, confirm the bias point with the Ohm's Law calculator so the chosen R is consistent with the operating voltage and current.

The calculator runs the Johnson-Nyquist equation in four lines: it converts R, Δf, and T to SI base units, evaluates 4 k_B T R Δf, and returns the square root as the open-circuit noise voltage. The short-circuit noise current uses the same constant divided by R.

• R: Resistance in ohms (converted from kΩ, MΩ, or GΩ by the input prefix).
• Δf: Noise-equivalent bandwidth in hertz (converted from kHz, MHz, or GHz).
• T: Absolute temperature in kelvin (273.15 K = 0 °C, 290 K ≈ 17 °C, 300 K ≈ 27 °C, 77 K liquid-nitrogen, 4 K liquid-helium).
• k_B: Boltzmann constant, exactly 1.380649 × 10^-23 J/K in the 2019 SI redefinition.

The prefactor 4 k_B T carries the temperature dependence of the equation; at the conventional 290 K noise reference used by Analog Devices the prefactor evaluates to about 1.60 × 10^-20 J. At the more common 300 K room-temperature reference the prefactor grows to about 1.66 × 10^-20 J, which is why a 10 °C warmer resistor is about 3% noisier.

Noise voltages from individual resistors are usually much smaller than the signal of interest, so the calculator reports results in V, mV, µV, nV, or pV depending on the magnitude, and similarly for noise currents and noise power.

According to Wikipedia (Johnson–Nyquist noise), RMS noise voltage equals sqrt(4 k_B T R Δf) and noise current equals sqrt(4 k_B T Δf / R)

If the resistance came off a through-hole part, the resistor color code calculator decodes the bands into ohms before the noise formula runs.

Four ideas show up in every Johnson-Nyquist calculation; once they click, the formula reads itself.

When the noisy resistor sits inside an LM317 feedback divider, the LM317 calculator sets R1 and R2 so the regulator noise stays well above the resistor's own floor.

Six quick steps take you from a resistor part number to a complete noise budget in V, A, V/√Hz, A/√Hz, and W.

1. 1 Pick the resistance value: Read the resistor value off the part (use the colour-code calculator if you have a through-hole part) and enter the number plus a unit from Ω to GΩ.
2. 2 Set the bandwidth: Enter the noise-equivalent bandwidth of the system that follows the resistor: the audio band, the IF filter width, or the FFT bin size you plan to use.
3. 3 Choose the operating temperature: Enter the resistor's absolute temperature in kelvin. 290 K is the standard noise reference, 300 K is room temperature, and 77 K covers liquid-nitrogen-cooled designs.
4. 4 Read the RMS noise voltage: The black result panel shows v_n in the prefix (V, mV, µV, nV, pV) that keeps the value between 1 and 999.
5. 5 Check the noise current: Use i_n when the resistor drives a low-impedance load such as a 50 Ω RF stage or a transimpedance amplifier input.
6. 6 Note the spectral densities: S_v and S_i tell you how the noise scales as you change the bandwidth of the next stage, which is essential for cascade noise calculations.

A 1 MΩ feedback resistor at 300 K feeding a 100 kHz low-pass filter: enter R = 1 MΩ, Δf ≈ π/2 × 100 kHz ≈ 157 kHz, T = 300 K. The result panel shows v_n ≈ 4.5 µV and i_n ≈ 4.5 pA, so the op-amp needs an input current noise below 4.5 pA / √Hz to stay close to the resistor noise floor.

Once the resistor noise is known, the Op Amp Gain calculator tells you how much the next op-amp stage amplifies it before it reaches the ADC input.

Six practical reasons this resistor noise calculator beats hand calculation or a generic spreadsheet.

• • Benefit: Instant Johnson-Nyquist output: enters R, Δf, and T and returns v_n, i_n, S_v, S_i, and P_n in one panel without manual unit juggling.
• • Benefit: Auto-selected prefixes: shows the result in V, mV, µV, nV, or pV so the printed number stays between 1 and 999.
• • Benefit: Supports Ω through GΩ and Hz through GHz: covers everything from a 10 Ω RF source to a 1 GΩ photodiode load.
• • Benefit: Covers cryogenic temperatures: accepts any temperature from a fraction of a kelvin up to 1000 K, so the same calculator handles liquid-helium sensors and hot-filament resistors.
• • Benefit: Uses the exact 2019 SI Boltzmann constant: k_B = 1.380649 × 10^-23 J/K with zero measurement uncertainty, so the result matches every NIST-traceable reference.
• • Benefit: Pairs cleanly with the resistor colour-code and Ohm's law calculators: keep the value lookup, circuit context, and noise estimate in the same workflow.

When a series resistor sets the RC bandwidth of the next stage, the capacitor charge time calculator converts the corner frequency to the noise-equivalent Δf the noise formula needs.

Four factors decide whether the calculator's number matches what the bench shows, and two limitations tell you when to look beyond the simple Johnson-Nyquist equation.

• • The calculator assumes a passive, linear resistor at thermal equilibrium; active devices such as op-amps and diodes add shot noise, flicker noise, and popcorn noise that the Johnson-Nyquist equation does not model.
• • Below about 4 K the quantum zero-point fluctuation term (hf / (exp(hf / k_B T) - 1) + hf / 2) replaces the classical k_B T formula; the calculator still works as an upper bound, but the true noise floor is roughly half the classical value.

According to NIST CODATA, Boltzmann constant exact 2019 SI value and derived 4 k_B T

Two resistors in series both contribute noise, and the voltage divider calculator confirms whether Thevenin-equivalent R replaces them in the Johnson-Nyquist equation.