Johnson-Nyquist Noise Calculator

Find the RMS thermal (Johnson-Nyquist) noise voltage, current, and power of a resistor from its temperature, resistance, and measurement bandwidth.

🌡️ Johnson-Nyquist Noise Calculator
Temperature (T)300 K
K
1500
Resistance (R)1000 Ω
Ω
1100k
Bandwidth (B)1 MHz
Hz
1 Hz20 MHz
Noise voltage (RMS)
—
Noise current (RMS)
—
Available noise power
—
Step-by-step working

🌡️ What is Johnson-Nyquist Noise?

Johnson-Nyquist noise, also called thermal noise, is the electronic noise generated inside any resistive element by the random thermal motion of its charge carriers. Unlike shot noise or flicker noise, it requires no applied current or voltage, it exists in every resistor simply because its temperature is above absolute zero, and its RMS voltage is given by Vn = sqrt(4*kB*T*R*B).

Electrical and RF engineers rely on this calculation to set the theoretical noise floor of any circuit, size the input-referred noise budget of low-noise amplifiers, predict receiver sensitivity in communications links, and understand why cooling sensitive detectors (radio telescopes, cryogenic sensors) meaningfully reduces measurement noise.

A common point of confusion is that noise power, unlike noise voltage, does not depend on resistance value; the available noise power delivered to a matched load is simply kB*T*B, independent of R. This is the origin of the widely quoted "-174 dBm/Hz" thermal noise floor used throughout RF link budget analysis.

This calculator computes RMS thermal noise voltage, RMS noise current, and available noise power (in dBm) from your temperature, resistance, and bandwidth, and plots how noise voltage grows with resistance at your chosen temperature and bandwidth.

📐 Formula

Vn = √(4kBTRB)      Pn = kBTB
kB = 1.380649×10⁻²³ J/K (Boltzmann constant)
T = absolute temperature (K), R = resistance (Ω), B = bandwidth (Hz)
In = √(4kBTB/R), the equivalent RMS noise current
Example: T = 300 K, R = 1,000 Ω, B = 1,000,000 Hz → Vn ≈ 4.0704 µV, Pn ≈ -113.828 dBm.

📖 How to Use This Calculator

Steps

1
Enter the temperature. Type the absolute temperature T in Kelvin. Use 290 K for the standard RF reference temperature or convert from Celsius (K = C + 273.15).
2
Enter the resistance and bandwidth. Type the resistance R in ohms and the measurement bandwidth B in Hertz.
3
Read the noise voltage, current, and power. The calculator reports RMS thermal noise voltage, RMS noise current, and available noise power in dBm.

💡 Example Calculations

Example 1 — 1 kΩ Resistor at Room Temperature, 1 MHz Bandwidth

T = 300 K, R = 1,000 Ω, B = 1,000,000 Hz

1
Vn = √(4 × 1.380649×10⁻²³ × 300 × 1000 × 1,000,000) = 4.0704 µV
2
In = √(4kBTB/R) = 4.0704 nA
Pn = kBTB = -113.828 dBm
Try this example →

Example 2 — Low-Impedance LNA Source at 290 K, Wide Bandwidth

T = 290 K, R = 50 Ω, B = 20,000,000 Hz

1
Vn = √(4 × 1.380649×10⁻²³ × 290 × 50 × 20,000,000) = 4.0019 µV
2
In = 80.039 nA
Pn = -100.965 dBm
Try this example →

Example 3 — High-Impedance Sensor at 290 K, Narrow Bandwidth

T = 290 K, R = 10,000 Ω, B = 1,000 Hz

1
Vn = √(4 × 1.380649×10⁻²³ × 290 × 10,000 × 1,000) = 0.4002 µV
2
In = 0.0400 nA
Pn = -143.975 dBm
Try this example →

❓ Frequently Asked Questions

What is Johnson-Nyquist noise?+
Johnson-Nyquist noise, also called thermal noise, is the electronic noise generated by the random thermal motion of charge carriers inside any resistive element, present in every resistor regardless of applied voltage, at any temperature above absolute zero.
What is the formula for thermal noise voltage?+
The RMS thermal noise voltage is Vn = sqrt(4 * kB * T * R * B), where kB is the Boltzmann constant (1.380649e-23 J/K), T is absolute temperature in Kelvin, R is resistance in ohms, and B is the measurement bandwidth in Hertz.
Why does noise power not depend on resistance?+
The available thermal noise power delivered to a matched load is Pn = kB * T * B, independent of the resistance value. While noise voltage does depend on R, a higher-resistance source also has higher source impedance, and these effects exactly cancel when computing maximum available power to a matched load.
What does -174 dBm/Hz noise floor mean?+
At the standard reference temperature of 290 K, kB * T equals about 4.0 x 10^-21 W/Hz, or -174 dBm per Hz of bandwidth. This is the theoretical noise floor used throughout RF engineering to compute receiver sensitivity: multiply by your actual bandwidth in Hz (in dB, add 10*log10(B)) and add the system noise figure.
How does bandwidth affect thermal noise?+
Thermal noise voltage scales with the square root of bandwidth, since wider bandwidth admits more of the noise's flat (white) power spectral density. Doubling bandwidth increases noise voltage by about 41% (sqrt(2)) and noise power by exactly 2x (3 dB).
Is thermal noise the same for all frequencies?+
Yes, in the frequencies relevant to almost all electronic circuits, Johnson-Nyquist noise has a flat (white) power spectral density, meaning equal noise power per Hz of bandwidth regardless of center frequency. This flat spectrum is what makes the kB*T*B formula bandwidth-independent per Hz.
What temperature should I use, Kelvin or Celsius?+
This calculator requires absolute temperature in Kelvin, since the formula derives from statistical thermodynamics referenced to absolute zero. To convert, K = C + 273.15. Room temperature (20 C) is about 293 K; the RF industry-standard reference is 290 K.
How is thermal noise different from shot noise or flicker noise?+
Thermal noise arises purely from thermal agitation and exists in any resistance with no current flow required. Shot noise arises from the discreteness of charge carriers crossing a junction and requires current flow. Flicker (1/f) noise dominates at low frequencies and has device-specific, non-white spectral characteristics.
How do I use noise voltage to estimate signal-to-noise ratio?+
Divide your signal's RMS voltage by the noise voltage from this calculator (both across the same resistance and bandwidth) to get a linear SNR, then convert to dB with 20*log10(SNR) if desired. This gives the theoretical noise floor limit; real circuits also add active-device noise on top.
What is a typical thermal noise voltage for a 1 kilohm resistor?+
At room temperature (290 K) over a 1 MHz bandwidth, a 1 kilohm resistor produces roughly 4 microvolts RMS of thermal noise voltage. Lower resistances, narrower bandwidths, or lower temperatures all reduce this proportionally per the sqrt(4kTRB) formula.
Tags: Johnson Nyquist Noise Calculator Thermal Noise Calculator Resistor Noise Voltage Calculator Noise Floor Calculator KTB Noise Calculator Calculator Formula Free Online

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What is Johnson-Nyquist noise?

Johnson-Nyquist noise, also called thermal noise, is the electronic noise generated by the random thermal motion of charge carriers inside any resistive element, present in every resistor regardless of applied voltage, at any temperature above absolute zero.

What is the formula for thermal noise voltage?

The RMS thermal noise voltage is Vn = sqrt(4 * kB * T * R * B), where kB is the Boltzmann constant (1.380649e-23 J/K), T is absolute temperature in Kelvin, R is resistance in ohms, and B is the measurement bandwidth in Hertz.

Why does noise power not depend on resistance?

The available thermal noise power delivered to a matched load is Pn = kB * T * B, independent of the resistance value. While noise voltage does depend on R, a higher-resistance source also has higher source impedance, and these effects exactly cancel when computing maximum available power to a matched load.

What does -174 dBm/Hz noise floor mean?

At the standard reference temperature of 290 K, kB * T equals about 4.0 x 10^-21 W/Hz, or -174 dBm per Hz of bandwidth. This is the theoretical noise floor used throughout RF engineering to compute receiver sensitivity: multiply by your actual bandwidth in Hz (in dB, add 10*log10(B)) and add the system noise figure.

How does bandwidth affect thermal noise?

Thermal noise voltage scales with the square root of bandwidth, since wider bandwidth admits more of the noise's flat (white) power spectral density. Doubling bandwidth increases noise voltage by about 41% (sqrt(2)) and noise power by exactly 2x (3 dB).

Is thermal noise the same for all frequencies?

Yes, in the frequencies relevant to almost all electronic circuits, Johnson-Nyquist noise has a flat (white) power spectral density, meaning equal noise power per Hz of bandwidth regardless of center frequency. This flat spectrum is what makes the kB*T*B formula bandwidth-independent per Hz.

What temperature should I use, Kelvin or Celsius?

This calculator requires absolute temperature in Kelvin, since the formula derives from statistical thermodynamics referenced to absolute zero. To convert, K = C + 273.15. Room temperature (20 C) is about 293 K; the RF industry-standard reference is 290 K.

How is thermal noise different from shot noise or flicker noise?

Thermal noise arises purely from thermal agitation and exists in any resistance with no current flow required. Shot noise arises from the discreteness of charge carriers crossing a junction and requires current flow. Flicker (1/f) noise dominates at low frequencies and has device-specific, non-white spectral characteristics.

How do I use noise voltage to estimate signal-to-noise ratio?

Divide your signal's RMS voltage by the noise voltage from this calculator (both across the same resistance and bandwidth) to get a linear SNR, then convert to dB with 20*log10(SNR) if desired. This gives the theoretical noise floor limit; real circuits also add active-device noise on top.

What is a typical thermal noise voltage for a 1 kilohm resistor?

At room temperature (290 K) over a 1 MHz bandwidth, a 1 kilohm resistor produces roughly 4 microvolts RMS of thermal noise voltage. Lower resistances, narrower bandwidths, or lower temperatures all reduce this proportionally per the sqrt(4kTRB) formula.

📌 Quick Tips

💡Thermal noise is fundamental and unavoidable, it exists in every resistor at any temperature above absolute zero, purely from the random thermal motion of charge carriers, independent of any applied voltage or current.
💡Noise voltage scales with the square root of resistance, temperature, and bandwidth, so doubling any one of them increases noise voltage by only about 41%, not double.
💡The standard reference temperature for noise figure specifications is 290 K (about 17 degrees Celsius), use this default when comparing your result against a datasheet noise figure.
💡Available noise power kB*T*B is independent of resistance value, it depends only on temperature and bandwidth, this is the origin of the famous kTB noise floor used throughout RF and communications engineering.
💡At room temperature (290 K) with a 1 Hz bandwidth, kTB is about -174 dBm, the standard thermal noise floor reference used to compute receiver sensitivity and link budgets.