# nV/SQRT Hz to dBm/Hz Calculator

Use this tool to convert nanovolt-per-root Hz (nV/√(Hz)) to dBm per Hz (dBm/Hz)

Enter the value and use the drop down menu to select one of the following units:

• nV/√Hz
• uV/√Hz
• mV/√Hz
• V/√Hz

🔄 dBm/Hz to nV/√(Hz)

## Formula

PdBm/Hz = 10*Log10((V/(√Hz))2 / Z*0.001)

## Example Calculation

• 5 nV/√Hz is equivalent to -153 dBm/Hz
• 5 V/√Hz is equivalent to +27 dBm/Hz

That’s a difference of 180 dB on account of the ‘square’ relationship within the logarithm. 1V = 109nV and therefore 20*Log(109) gives 180. A quick way to confirm that the unit conversion from nV to V works 🤓

The default impedance value of 50 ohm is used above, but it can be changed to any value.

## Background

dBm stands for deciBel referenced to 1 milliwatt. It is an absolute unit of power and there’s an easy conversion from Watt to dBm.

The Power expressed per unit frequency (Hz) is referred to as Power Spectral Density. Units are dBm/Hz or Watt/Hz. The use of Hz normalizes the power to 1 Hz. Applications for dBm/Hz are specifying the thermal noise power.

The input noise voltage is measured in V/(√Hz). The voltage noise of of an operational amplifier may vary from under 1 nV/√Hz to 20 nV√Hz or greater.

The noise also depends on frequency. It is referred to as Johnson-Nyquist noise ( also known as thermal noise floor) and an important consideration when modeling the effect of the op-amp in a receiver circuit.

Minimizing this noise is important as it can have a significant impact on sensitivity. The higher the level of noise, the harder it is to discern and extract weak signals.

Use this tool to convert from nV/√Hz to RMS Voltage or VRMS.

## Notes

• dBm/Hz can be converted to dBm by integrating over a specified bandwidth. The calculator assumes that the value is constant with frequency. However, as seen in the plot for noise associated with different opamps, it is not flat. The noise is higher at lower frequencies.