# Thermal Noise Power Calculator

Thermal noise power (also known as Johnson-Nyquist Noise) is a function of

• Temperature T
• Bandwidth B
• Boltzmann’s Constant k = 1.380649 × 10-23 m2 kg s-2 K-1

This calculator goes by different names

• kTB Calculator
• Noise Power Calculator

## kTB Noise Power Formula

Thermal noise power is calculated using the following:

Pn = 10 * log10 (kTB/1mW)

The units are dBm.

If the bandwidth selected is 1 Hz, then the noise power in dBm is actually dBm/Hz. This is also called the noise spectral density.

Note: The temperature T has to be higher than 0 Kelvin

## Noise Power Example Calculation

At room temperature 27o Celsius, the noise power in a 1 Hz bandwidth is -173.83 dBm/Hz.

It’s typically rounded to -174 dBm/Hz.

Noise power increases with temperature and bandwidth.

🔎 Consider a Radio Receiver or Spectrum Analyzer that is set to 1 Hz resolution bandwidth (RBW). The noise power level is the threshold below which no signal can be detected. In practice, the threshold is higher by about 10 dB or more depending on the noise figure (NF) of the receiver. This calculator uses the NF to determine the Noise floor of a radio receiver.

The noise figure provides an estimate of the detection threshold. If we want to demodulate a signal, the minimum signal-to-noise ratio for that signal type has to be taken into account. In general, the more complex the modulation type, the higher the required minimum SNR.

As examples, these two posts discuss the sensitivity of

## What is Thermal Noise?

Thermal noise is the electronic noise generated when the electrons inside an electrical conductor at equilibrium are thermally agitated. A state of equilibrium implies that the charge distribution is fixed.

Thermal noise exists in all electrical circuits. It has a detrimental impact in receivers which have to be sensitive in order to detect weak signals. As the thermal noise increases, the ability of the receiver to detect signals decreases.

Thermal noise impacts the receiver sensitivity. The lower the value in dBm, the more sensitive the receiver.

## Can the Thermal Noise Power be reduced?

Yes it can.

The equation

Pn = 10 * Log10 (kTB/1mW)

shows that there are two variables that impact Noise Power. Temperature of operation, T and bandwidth, B.

### Reducing T reduces the Noise Power

Receivers for example those used in radio astronomy, have to be very sensitive in order to detect very weak signals. At the NRAO for instance, receivers are cryogenically cooled to reduce the temperature and therefore the noise power.

### Reducing B reduces the Noise Power

Reducing the bandwidth requires high quality analog filtering followed by digital filtering. However the limit to this is the bandwidth of the actual signal being observed. The receiver has to have a bandwidth higher than the signals of interest.

## Noise Power for Everyday Signals

The table below shows the noise power at room temperature (300 K) for many of the wireless signals around us.

The noise power is at its highest for the widest bandwidth signal mmWave 5G and lowest for 2G as would be expected from the formula above.