Root Mean Square Error

Updated 01 Oct 2026

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What it is
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  summarizes the magnitude of prediction or approximation errors using the square root of their mean square
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Formula
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  $\mathrm{RMSE}=\sqrt{\frac1n\sum_{i=1}^{n}(\hat y_i-y_i)^2}$ .
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Interpretation
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  has the same units as the target.
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  gives larger errors more influence than smaller ones.
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  is not a percentage unless an explicit normalization is applied.
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Comparison
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  compare models using the same evaluation observations and units.
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  for sampled waveform approximations, the grid and treatment of discontinuity points affect the result.
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Related
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  Unavailable reference
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  Unavailable reference

Linked references 2