# 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.