Resistor Noise Calculator (Johnson–Nyquist thermal noise √4kTRB)

Understanding the resistor noise calculator — concept and principle

This calculator finds the thermal (Johnson–Nyquist) noise of a resistor: the RMS noise voltage and current over a bandwidth, the noise density, the level in dBV and the available noise power in dBm. Electronics designers use it to set the noise floor of amplifiers, sensors and audio circuits.

Thermal jiggling of electrons makes noise in any resistor; it grows with the square root of R, T and bandwidth.

How it is calculated

v_n = √(4 k T R B)

Noise density = √(4 k T R) per √Hz

i_n = √(4 k T B ÷ R)

Available noise power = k T B (in dBm)

k = 1.380649 × 10⁻²³ J/K; T in kelvin (°C + 273.15); R in Ω; B in Hz.

The principle

The electrons in any resistor jiggle randomly with thermal energy. That motion produces a tiny fluctuating voltage across the resistor even with no current applied. Johnson measured it and Nyquist explained it in 1928: the noise power in each hertz of bandwidth is set by temperature alone, and the voltage grows with the square root of resistance, temperature and bandwidth. It is the physical minimum noise of a resistor; real parts can add extra noise.

Worked example

Default inputs: R = 10 kΩ, 25 °C, bandwidth 20 kHz (audio).

T = 298.15 K.
v_n = √(4 × 1.380649 × 10⁻²³ × 298.15 × 10,000 × 20,000) = 1.815 µV RMS.
Noise density = √(4kTR) = 12.83 nV/√Hz; current = 1.815 µV ÷ 10 kΩ = 181.47 pA.
In dBV: −114.8 dBV; available power kTB = −130.8 dBm.

Each point is the calculator re-run with only “Resistance (kΩ)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Resistance (kΩ)	Noise voltage (µV RMS)
2.5	0.907
5	1.283
7.5	1.572
10	1.815
12.5	2.029
15	2.223
20	2.566

How to read the result

Compare the noise voltage with the smallest signal you need to measure. Lower resistance, lower temperature or narrower bandwidth reduce noise. About 4 nV/√Hz for 1 kΩ at room temperature is a handy benchmark: noise scales with √R.

Common mistakes

Using °C instead of kelvin.
Adding noise voltages directly instead of in quadrature.
Forgetting that bandwidth is the effective noise bandwidth of the circuit.

Keep in mind: Real resistors also have excess (1/f) noise depending on their construction, and amplifiers add their own noise. This is the physical minimum.

Frequently asked questions

Does a resistor make noise with no current?

Yes; thermal noise exists whenever the resistor is above absolute zero.

Why does cooling reduce noise?

Noise power is proportional to temperature.

How do I combine several noise sources?

Add their powers (squares of RMS voltages) and take the square root.

What is noise density?

Noise voltage per square root of bandwidth, nV/√Hz.

Sources: J. B. Johnson and H. Nyquist, Phys. Rev. 32 (1928) · Agilent (Keysight) Application Note 57-1, chapter 1 "Sources of Noise"

Checked 9 Nov 2026. Johnson–Nyquist thermal noise (J. B. Johnson and H. Nyquist, Phys. Rev. 32, 1928): v_n² = 4kTRB; available power kTB as in Agilent (Keysight) Application Note 57-1, ch. 1 “Sources of Noise”. k = 1.380649 × 10⁻²³ J/K (SI 2019, exact).

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