Root Mean Squared Error (RMSE) Calculator
Calculate Root Mean Squared Error (RMSE) between actual and predicted values for a regression model.
Inputs
Comma-separated actual (true) values.
Comma-separated predicted values, same order and count as actual.
Root Mean Squared Error
0.6124
Mean Squared Error
0.3750
Number of Samples
4
Step by step
MSE: Σ(y_i − ŷ_i)² / n
1.5000 ÷ 4
= 0.3750
RMSE: √MSE
√0.3750
= 0.6124
How it works
Root Mean Squared Error (RMSE) is the square root of MSE: RMSE = √MSE = √[(1/n) × Σ(y_i − ŷ_i)²]. Taking the square root brings the error back into the same units as the target variable, making RMSE much easier to interpret than MSE while retaining the same sensitivity to large errors (since the squaring happens before the square root). RMSE is one of the most widely reported regression metrics because it balances interpretability with a meaningful penalty for large mistakes.
Formula
RMSE = sqrt((1/n) * sum((y_i - y_hat_i)^2))
- n
- Number of samples
- y_i
- Actual value for sample i
- \hat{y}_i
- Predicted value for sample i
Frequently Asked Questions
Why use RMSE instead of MSE?
RMSE is in the same units as the original target variable (since taking a square root undoes the squaring), making it directly interpretable — e.g. 'predictions are off by about $450 on average' — whereas MSE's squared units have no intuitive meaning.
Is RMSE always larger than MAE?
Yes, for the same set of errors, RMSE is always greater than or equal to MAE, because squaring disproportionately amplifies larger errors before the square root is taken — the gap between them grows when errors are inconsistent in size.
What does a large gap between RMSE and MAE indicate?
A large gap suggests the presence of some particularly large errors (outliers) in the predictions, since RMSE is much more sensitive to big mistakes than MAE is.