How to get noise percentage?

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So I don't really know if this is the right place to ask, but I hope so..

Let's say I have a function $h$ and I want to make a test on the influence of noise over this function. What I have done is having

$\tilde{h} = h + n$

where $n \sim N(0, \sigma)$. The amount of noise added is changed by varying the value of $\sigma$.

Now how do I represent this in a form of percentage noise i.e. like how much noise is added to the data? Is there a way to calculate this percentage from $\sigma$?

Many thanks,