Mean Squared Error Calculator
Calculate MSE = sum(residuals^2) / n from observed and predicted values.
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Enter your observed (actual) values in the first box and predicted (fitted) values in the second box, separated by commas or spaces. Both lists must have the same number of values. The calculator computes MSE, RMSE, and MAE instantly.
MSE is calculated by squaring each residual (observed minus predicted), summing them, and dividing by the number of data points.
About Mean Squared Error
Mean Squared Error (MSE) is a fundamental metric for evaluating regression models and predictions. It penalizes larger errors more heavily due to squaring. RMSE (root mean squared error) converts MSE back to the original units, making it easier to interpret. MAE (mean absolute error) gives equal weight to all errors and is more robust to outliers.
Frequently Asked Questions
What is a good MSE value?
There is no universal threshold. A good MSE depends on the scale of your data and the problem context. Compare MSE across different models on the same dataset to determine which performs better.
What is the difference between MSE and RMSE?
RMSE is the square root of MSE. While MSE is in squared units, RMSE is in the same units as the original data, making it more interpretable. An RMSE of 5 means predictions are off by about 5 units on average.
Should I use MSE or MAE?
MSE penalizes large errors more heavily, which is useful when large errors are especially undesirable. MAE treats all errors equally and is more robust to outliers. Many practitioners report both.