What is resistor thermal noise (Johnson–Nyquist noise)?

Thermal noise is the random voltage that appears across any resistor because the charge carriers inside it jiggle with thermal energy. It was measured by John B. Johnson in 1928 and explained by Harry Nyquist the same year. It exists in every resistor at any temperature above absolute zero, needs no current, and is white — flat with frequency up to hundreds of GHz.

What is the Johnson noise formula?

The RMS open-circuit noise voltage is Vn = sqrt(4 × kB × T × R × Δf), where kB = 1.380649e-23 J/K is the Boltzmann constant, T is absolute temperature in kelvin, R is resistance in ohms, and Δf is the measurement bandwidth in hertz. The noise density is en = sqrt(4 × kB × T × R), in volts per root hertz.

What is noise density in nV/√Hz?

Noise density is the noise per unit bandwidth: en = sqrt(4·kB·T·R), in V/√Hz. Multiply it by sqrt(Δf) to get total RMS noise: Vn = en × √Δf. A 10 kΩ resistor at 290 K has 12.66 nV/√Hz; over a 20 kHz audio bandwidth that integrates to 12.66 nV/√Hz × √20000 ≈ 1.79 µV RMS.

How much noise does a 10 kΩ resistor produce at room temperature?

At T = 290 K over Δf = 20 kHz: 4·kB·T·R·Δf = 3.2031e-12, so Vn = √3.2031e-12 ≈ 1.79 µV RMS, with density 12.66 nV/√Hz and noise current In = Vn/R ≈ 179 pA. That is −114.9 dBV and −112.7 dBu.

Does resistor noise depend on the current flowing through it?

No. Thermal noise is generated by the random thermal motion of charge carriers and is the same whether current flows or not. It depends only on resistance, temperature, and bandwidth. Current-dependent excess noise — 1/f flicker noise in some resistor types — is a separate effect and is not covered by this calculator.

Should I use 290 K or 300 K for room temperature?

Use 290 K when the result feeds a noise-figure calculation — 290 K (17 °C) is the IEEE standard reference temperature. For a bench at 20–25 °C, 293–298 K is physically closer. Noise voltage scales with √T, so 300 K vs 290 K differs by only √1.034 ≈ 1.7%.

How do I convert resistor noise to dBV or dBu?

dBV = 20·log10(Vn / 1 V) and dBu = 20·log10(Vn / 0.7746 V). Our worked example of 1.79 µV becomes 20·log10(1.79e-6) ≈ −114.9 dBV and −112.7 dBu. This calculator shows both automatically.

What is the available noise power kTB?

A resistor delivers maximum noise power P = kB·T·Δf into a matched load — famously independent of resistance. At 290 K over 20 kHz that is 8.01e-17 W = −131.0 dBm. Double the bandwidth and the power doubles; the resistance only sets the voltage/current split.

How do I calculate SNR against my signal level?

Enter your signal's RMS level and this calculator computes SNR = 20·log10(Vsignal / Vn) in dB. For example, a 1 mV RMS signal against 1.79 µV of noise gives 20·log10(1e-3 / 1.79e-6) ≈ 54.9 dB SNR.

Why does noise grow with the square root of resistance and bandwidth?

Thermal noise is the sum of countless independent random electron motions, and independent random sources add in power, not voltage — so the voltage grows as √N. Doubling the resistance doubles the noise power but only multiplies voltage by √2 ≈ 1.41. Same for bandwidth: ten times the bandwidth is ten times the power, √10 ≈ 3.16 times the voltage.

What about shot noise and 1/f flicker noise?

They are real, but outside this tool's scope. Shot noise (2·q·I·Δf) appears only where DC current crosses a barrier, such as a diode or transistor junction — not in a plain resistor. 1/f flicker noise dominates at low frequencies in some resistor types. This calculator covers Johnson–Nyquist thermal noise only, which is the universal baseline every resistor has.

Which resistor values are quietest for a low-noise audio preamp?

Lower resistance is quieter: density scales with √R, so a 100 Ω resistor is √100 = 10× quieter than 10 kΩ. Use the lowest resistance your circuit's biasing and loading allow, keep the bandwidth no wider than needed, and check the live table on this page, which recomputes for your temperature and bandwidth.

How much does cryogenic cooling reduce resistor noise?

Noise voltage scales with √T. Cooling from 290 K to 77 K (liquid nitrogen) cuts noise by √(290/77) ≈ 1.94×; to 4.2 K (liquid helium) by √(290/4.2) ≈ 8.3×. Try the temperature presets above — a 10 kΩ resistor drops from 12.66 nV/√Hz at 290 K to 1.52 nV/√Hz at 4.2 K.

Which nrtechstudio tool should I use for related resistor calculations?

This tool covers Johnson–Nyquist thermal noise only. For resistor networks, use our parallel resistor calculator (https://nrtechstudio.com/tools/parallel-resistor/). Resistor color-code / Ohm's-law and voltage-drop calculators are planned and will be linked here when published — this page stays focused on thermal noise so each tool does one job well.

nrtechstudio / tools / resistor-noise

Resistor Noise Calculator — Johnson–Nyquist Thermal Noise

Every resistor hisses. Compute the thermal (Johnson–Nyquist) noise voltage Vn = √(4·k_B·T·R·Δf), noise density in nV/√Hz, noise current, dBV/dBu, available power kTB, and SNR against your signal level — with cryogenic and audio-bandwidth presets. 100% client-side, no data leaves your browser.

Thermal noise calculator

Enter resistance, temperature, and bandwidth. Results update live.

Resistance R

Temperature T (kelvin)

Bandwidth Δf

Signal level (for SNR)

RMS signal voltage at the same node. SNR = 20·log₁₀(V_signal / Vn).

Noise voltage Vn (RMS)

—

Noise density en

—

Noise current In (RMS)

—

Level

—

Available power kTB

—

SNR vs signal

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k_B = 1.380649×10⁻²³ J/K (exact, SI 2019). dBu reference = 0.7746 V RMS.

Common resistor values

Noise density and total noise for standard values, recomputed live for your temperature and bandwidth.

R	Density en	Vn RMS	In RMS

Methodology

Vn = √(4 · k_B · T · R · Δf) · en = √(4·k_B·T·R) · In = Vn/R · P = k_B·T·Δf

Worked example. R = 10 kΩ, T = 290 K, Δf = 20 kHz:
4·k_B·T·R·Δf = 4 × 1.380649×10⁻²³ × 290 × 10⁴ × 2×10⁴ = 3.2031×10⁻¹²
Vn = √3.2031×10⁻¹² = 1.79 µV RMS · en = √(4·k_B·T·R) = 12.66 nV/√Hz · In = Vn/R = 179 pA

This is the Johnson–Nyquist model: white thermal noise, flat with frequency, present in every resistive element above 0 K. It is the minimum noise a resistor can have — real parts may add 1/f excess noise on top (see FAQ), which this tool intentionally does not model.

Scope boundary — what this tool is (and isn't)

This tool = Johnson–Nyquist thermal noise only. White noise from random thermal motion of charge carriers. It does not model shot noise (needs DC current across a barrier — diodes, transistors, not plain resistors) or 1/f flicker/excess noise.
Resistor networks (series/parallel, current division, power per branch) → our parallel resistor calculator.
Resistor color code / Ohm's law and resistor voltage drop calculators are planned and will be linked here once published — no placeholder links.

Frequently asked questions

Free tool by NRTechStudio

Resistor Noise Calculator — Johnson–Nyquist Thermal Noise

Thermal noise calculator

Common resistor values

Methodology

Scope boundary — what this tool is (and isn't)

Frequently asked questions

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