Converting Noise Spectral Density (V/√Hz) to RMS Voltage

Updated May 16, 2026

This document explains how to convert a noise spectral density value expressed in volts per square root hertz (V/√Hz) into an RMS voltage over a specified measurement bandwidth. This calculation is commonly used to estimate total input‑referred noise when working with measurement devices that specify noise as a spectral density.

  1. Identify the noise spectral density value of the signal in V/√Hz from the device specifications or measurement data.
  2. Determine the measurement bandwidth in hertz over which the noise is being evaluated.
  3. Calculate the RMS voltage using the following formula:
     Vrms = Noise Spectral Density × √Bandwidth
  4. Use the calculated Vrms value to represent the total RMS noise voltage over the specified bandwidth.

The result is a single RMS voltage value that represents the total noise contribution across the specified measurement bandwidth.

The following plot shows a noise spectral density measurement where the red horizontal line highlights a representative noise floor of approximately 100 nV/√Hz across the measurement bandwidth. The effective bandwidth of the measurement extends to 25.6 kHz.

Using a noise spectral density of 100 nV/√Hz and a bandwidth of 25,600 Hz, the RMS noise voltage can be calculated as follows:
 
Vrms = 100 nV/√Hz × √25,600 Hz
Vrms = 100 nV/√Hz × 160
Vrms = 16 µV RMS
 
This value represents the total RMS input‑referred noise voltage over a 25.6 kHz bandwidth.

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