RMSE Calculator
Calculate root mean squared error between predicted and actual values.
About RMSE Calculator
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
Worked example
With the default values below, RMSE Calculator returns Root Mean Squared Error of 0.6124. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Actual Values
- 3, -0.5, 2, 7
- Predicted Values
- 2.5, 0.0, 2, 8
Results
- Root Mean Squared Error
- 0.6124
- Mean Squared Error
- 0.3750
- Number of Samples
- 4
Step by step
- 1MSE: Σ(y_i − ŷ_i)² / n= 0.3750
- 2RMSE: √MSE= 0.6124
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.