# Formula for computing RMSE percentage

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I want to find the percentage error from Root Mean Square Error (RMSE). What should be the correct formula for RMSE normalization so that I get correct percentage value.

Should I normalize RMSE with L2 norm of original data or the mean value of original data ?
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It's the L2 norm of the original data.

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Dear Alvaro

I have one more question regarding the formula for RMS error when there are more than one entities involved.
Like I have 20 images and each image has 1000 pixels and three color channels so in this setting when computing the RMS error between the original and estimated points should I compute it as option A or option B in the formulas attached with this post.

The issue is whether I should compute the mean of all 20 images only or should I compute the mean of each image pixels first and then compute the final mean.

I later want to divide it by L2 norm of 20 images to get percentage error.
Which formula among these is correct ?

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The issue is whether I should compute the mean of all 20 images only or should I compute the mean of each image pixels first and then compute the final mean.

I later want to divide it by L2 norm of 20 images to get percentage error.
Which formula among these is correct ?

Those formulas are the same up to a constant, and that constant will cancel out when you divide by the L2 norm of the original data, as long as you use an analogous formula to compute the L2 norm.

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Dear Alvaro

Now I have attached the complete formula that I intend to use for finding the ratio with this post.
RMS as well as the L2 norm formula.

Which of the two options is practically correct options A or option B formula ?

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Neither. As I said, you need to use an analogous formula for the L2 norm. That means using the same constants, but it doesn't matter which. I personally don't use any of those constants, and simply compute the square root of the sum of the squares.

The way I think about this type of situation is that you are dealing with a Euclidean vector space of dimension (M*N*C). Your given data rho_org is a vector in that space and so is rho_estimated. You are computing the distance between them, and dividing by the length of rho_org.

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