Mean Square Error Calculator

Calculator Input

Enter matching actual and predicted values. Use commas, spaces, semicolons, or new lines between numbers.

Actual Values

Add your observed values here.

Predicted Values

Add model or estimated values here.

Labels (Optional)

Provide matching labels for each observation.

Decimal Places

Choose output precision from 0 to 10.

Plotly Graph Type

Switch between line, scatter, and residual views.

Quick Example

Example data: 3, -0.5, 2, 7 and 2.5, 0, 2, 8

Example Data Table

This sample shows how the squared error values lead to the mean square error result.

Label	Actual	Predicted	Residual	Squared Error
A	3.00	2.50	0.50	0.25
B	-0.50	0.00	-0.50	0.25
C	2.00	2.00	0.00	0.00
D	7.00	8.00	-1.00	1.00
Total Squared Error				1.50
MSE = 1.50 / 4				0.375

Formula Used

Mean Square Error formula:

MSE = (1 / n) × Σ(actual_i − predicted_i)²

Where:

n = number of observations
actual_i = observed value
predicted_i = forecast or model value
(actual_i − predicted_i)² = squared error for each point

Related metrics shown by this calculator:

SSE = sum of all squared errors
RMSE = square root of MSE
MAE = average absolute error
Mean Error = average signed residual
R² = fit score based on actual value variance

How to Use This Calculator

Enter all actual values in the first field.
Enter matching predicted values in the second field.
Optionally add labels for each observation.
Choose decimal places and your preferred Plotly graph type.
Click Calculate MSE to generate the result block above the form.
Review the summary metrics, graph, and row-by-row error table.
Use the CSV and PDF buttons to export your calculation.

Frequently Asked Questions

1) What does mean square error measure?

Mean square error measures the average squared difference between actual and predicted values. Lower values show better prediction accuracy because the model stays closer to the observed data points.

2) Why are the errors squared?

Squaring removes negative signs and gives larger mistakes more weight. This helps highlight models that make occasional large prediction errors, not just many small ones.

3) What is a good MSE value?

A good MSE depends on your data scale. An MSE of 1 may be excellent for large values but poor for tiny measurements. Always judge it against context.

4) What is the difference between MSE and RMSE?

MSE keeps squared units, while RMSE returns the error in the original unit scale. RMSE is often easier to interpret when discussing model performance with others.

5) Can I use decimals and negative numbers?

Yes. The calculator accepts decimals, negative numbers, and mixed ranges. Separate each value with commas, spaces, semicolons, or new lines.

6) Why must the two lists have equal length?

Each actual value needs one matching predicted value. Without equal lengths, the calculator cannot build valid error pairs for the MSE formula.

7) When should I use MSE instead of MAE?

Use MSE when large errors should matter more. Use MAE when you want a simpler average error measure that treats all mistakes more evenly.

8) What does the residual chart show?

The residual chart shows the signed difference between actual and predicted values for each point. It helps you spot bias, outliers, and changing error patterns.