RMSE (Root Mean Square Error) Calculator
Compute RMSE, MSE, MAE and R² between predicted and observed values from two paired lists.
How it works
RMSE = √[ (1/n) Σ (predicted − observed)² ]
RMSE is the standard deviation of the prediction errors, in the same units as the data. Squaring before averaging punishes large misses more than MAE does, so a gap between RMSE and MAE signals a few big outlier errors. R² compares the squared error to simply predicting the mean.
Worked example
The default six pairs have squared errors summing to 0.94 → MSE 0.157 → RMSE 0.396; MAE 0.35.
Frequently asked questions
RMSE or MAE?
MAE is easier to interpret and robust; RMSE is preferred when large errors are disproportionately bad or when errors are roughly normal.
Can R² be negative here?
Yes — if the predictions are worse than just guessing the mean of the observed values.
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