# How is RMS and Peak-to-peak of white noise calculated

I have seen some devices which specify their internal noise in RMS or Peak-to-peak value. How does one calculate RMS or p2p values for white noise?

• The answer depends on what you know about the noise process. Do you know its probability density function? Or do you have a recorded signal? – Deve Nov 14 '14 at 19:27
• @Deve I have a recorded signal (noise) and I want to measure peak to peak and RMS of that signal (noise) – zud Nov 25 '14 at 13:14

Let $r_k$ be the sequence of $N$ measured noise samples. Then
1. Peak-to-peak value $$r_\mathrm{pp} = \operatorname{max}(r_k) - \operatorname{min}(r_k)$$
2. RMS value $$r_\mathrm{RMS} = \sqrt{\frac{1}{N}\sum_k r_k^2}$$
But Robert's answer should be taken seriously, especially the comment about peaks of Gaussian random variables. If your noise source is really Gaussian, the probability of a certain peak value increases with $N$. You should also take into account the limited range of values of your measurement device.