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Root Mean Squared Error Calculator

The root mean squared error (RMSE) or root mean squared deviation (RMSD) is a metric that tells you how close your predicted values are to your observed values in a regression analysis. It is the square root of the mean squared error, the sum of the squares of the distance between the predicted and observed values.

The equation for the RMSE is as follows:

RMSE = √( Σ(Pi – Oi)2 / n )


  • Σ = Sum over all considered values
  • Pi = ith Predicted value
  • Oi = ith Observed value
  • n = sample size

We can also describe RMSE as how concentrated the observed data is around the line of best fit.

You can use the RMSE calculator below by entering a list of observed and predicted values in the boxes below, then click Calculate RMSE.