Mean Squared Error Calculator
Penalizing Big Misses More Than Small Ones
Mean Squared Error squares every prediction error before averaging, which means a single large miss contributes disproportionately more to the score than several small ones. That property makes MSE sensitive to outliers — useful when large errors are especially costly, less useful when you want a metric that treats all errors proportionally.
The Formula
This calculator also reports RMSE (the square root of MSE, back in the original units) and MAE (mean absolute error, which weights all errors linearly instead of squaring them) alongside MSE for comparison.
Where This Matters
- Regression model training — MSE is the most common loss function minimized during model fitting.
- Forecast accuracy reporting — RMSE is often preferred for reporting because it's back in the same units as the original data, unlike MSE.
- Outlier sensitivity checks — comparing MSE against MAE on the same data reveals how much a few large errors are driving the score.
Worked Example
| Metric | Value |
|---|---|
| MSE | 0.025 |
| RMSE (√MSE) | 0.158 |
| MAE | 0.15 |
MSE = Σ(actual−predicted)² / n = 0.10 / 4 = 0.025; RMSE = √0.025 ≈ 0.158.
How to Use This Calculator
- Enter the Actual values as a comma-separated list.
- Enter the Predicted values as a comma-separated list of the same length.
- Select Calculate to get MSE, RMSE, and MAE.
Related Calculations
See how much of the underlying variance the model explains with the R-Squared Calculator, or measure distance between individual points with the Euclidean Distance Calculator.