Advanced MSE Calculator

Measure prediction error with clear steps and instant summaries. Test multiple input pairs easily today. Export detailed outputs for reports, audits, and classroom practice.

MSE Input Panel

Use aligned lists of actual and predicted values. Add weights for weighted error analysis.

Actual values

Separate values with commas, spaces, or new lines.

Predicted values

The count must match the actual series exactly.

Optional weights

Use weights in weighted metrics

Decimal places

Computed outputs

MSE, SSE, RMSE, MAE, mean error, weighted metrics, R² approximation, and a row-by-row error table are generated after submission.

Example Data Table

Index	Actual	Predicted	Weight	Squared Error
1	12	10	1	4
2	18	20	1	4
3	25	24	1	1
4	31	29	2	4
5	40	41	1	1

For these values, SSE = 14 and unweighted MSE = 14 ÷ 5 = 2.8.

Formula Used

Mean Squared Error: MSE = Σ(actual − predicted)² ÷ n

Sum of Squared Errors: SSE = Σ(actual − predicted)²

Root Mean Squared Error: RMSE = √MSE

Weighted Mean Squared Error: WMSE = Σ(weight × error²) ÷ Σ(weight)

MSE penalizes larger misses more strongly because every residual is squared before averaging.

How to Use This Calculator

Enter actual values in the first field.
Enter predicted values in the second field using the same order.
Optionally enter weights and enable weighted metrics.
Choose the number of decimal places for displayed outputs.
Click Calculate MSE to show the result section above the form.
Use the CSV or PDF buttons to export the detailed results.

FAQs

1. What does MSE measure?

MSE measures the average squared difference between actual and predicted values. Lower values indicate better fit, while larger values show bigger prediction errors overall.

2. Why square the errors?

Squaring makes all errors positive and gives larger mistakes more influence. This helps reveal models that occasionally miss badly, even when average signed error seems small.

3. What is the difference between MSE and RMSE?

MSE is in squared units, while RMSE is the square root of MSE. RMSE returns to the original data scale, making interpretation easier in many practical settings.

4. When should I use weighted MSE?

Use weighted MSE when some observations matter more than others. Common cases include sample importance, confidence weighting, uneven frequency, or cost-sensitive evaluation.

5. Can MSE ever be negative?

No. Squared errors are never negative, and their average cannot be negative either. The minimum possible MSE is zero when every prediction exactly matches reality.

6. Why does the calculator require equal list lengths?

Each actual value must pair with one predicted value. If lengths differ, the calculator cannot compare observations correctly, so it stops and asks for matching inputs.

7. Is a lower MSE always better?

Lower MSE usually means better predictions on the same scale and dataset. Comparing across very different datasets requires caution because scale strongly affects the value.

8. Can I use decimals and negative values?

Yes. The calculator accepts decimals, negative values, and scientific notation, provided all entries are numeric and the actual and predicted series remain aligned.