Root Mean Squared Error (RMSE)
Square root of MSE, in the same units as the target variable.
Formula
Variables
Example
If MSE = 4.67, RMSE = 2.16
How it works
RMSE measures the typical size of prediction errors by squaring each residual, averaging those squared errors, and then taking the square root. The squaring step makes larger mistakes count more heavily, while the square root brings the result back to the same units as the target variable, so it is easy to interpret. It comes directly from the mean squared error (MSE) and is useful when you want a single number that summarizes both the frequency and severity of prediction errors.
When to use it
Use RMSE when evaluating regression models, such as predicting house prices, temperatures, sales, or demand, especially when larger errors should be penalized more. It is a common metric for comparing models on the same dataset and target scale.
Worked example, step by step
Actual values: 10, 12, 14, 16 Predicted values: 9, 13, 15, 15 Errors: 10-9 = 1, 12-13 = -1, 14-15 = -1, 16-15 = 1 Squared errors: 1^2 = 1, (-1)^2 = 1, (-1)^2 = 1, 1^2 = 1 Mean squared error: (1 + 1 + 1 + 1) / 4 = 1 RMSE = sqrt(1) = 1 Final answer: RMSE = 1 unit
Common mistakes to avoid
- Forgetting to square the errors before averaging them
- Using RMSE to compare models on different target scales without standardizing
- Assuming a lower RMSE is always better without checking whether the scale is acceptable for the problem
Did You Know?
RMSE is preferred when you want the error in the original units.
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More in Data Science & ML
View allMean Squared Error (MSE)
BasicAverage of squared differences between predicted and actual values.
Mean Absolute Error (MAE)
BasicAverage of absolute differences between predictions and actual values.
Coefficient of Determination (R²)
IntermediateProportion of variance in the target explained by the model.
Classification Accuracy
BasicFraction of predictions that are correct.
Precision
IntermediateOf all positive predictions, the fraction that were correct.
Recall (Sensitivity)
IntermediateOf all actual positives, the fraction correctly identified.