How to use
- Enter the two lists in matching order: the first number in one list belongs with the first number in the other. Keep each list in one consistent unit and remove headings or unit symbols.
- Use spaces, commas or semicolons between numbers, and a dot for decimals, such as 1.5. A comma always starts another value, even when your display language uses decimal commas. Scientific notation such as 2e-3 is accepted.
- Results and charts update as soon as both lists are valid. Incomplete or mismatched input leaves the results empty. Press Calculate if you want to see an explanation of an input error.
- Copy results copies the numerical summary as text. Clear empties the inputs and results. The chart is an on-screen explanation; this tool does not export an image or data file.
Example
How far off were the predictions? Error = actual − predicted. Above zero means the prediction was too low; below zero means too high.
e = Actual values − Predicted values · RMSE = √(Σe² / n)
Actual values: 3 5 7 · Predicted values: 2 5 9
Errors: 1, 0, −2 · RMSE ≈ 1.29 · MAE = 1
The input fields start with this example. Edit them to use your own data, then calculate.
What the results mean
Use this calculator when you already have observed values and matching predictions. It summarizes their differences without training or selecting a model. It is useful for checking a worksheet, comparing forecasts on the same held-out observations, or understanding which large misses drive an error score.
The signed error is e = actual − predicted. A positive error means the prediction was too low; a negative error means it was too high. SSE = Σ(e²), MSE = SSE / n, RMSE = √MSE, and MAE = Σ|e| / n. Every pair receives equal weight.
SSE measures total squared error and normally grows when more imperfect predictions are included. MSE divides that total by the number of pairs, while RMSE returns to the original measurement unit. MAE is the average absolute miss in the same unit and gives large errors less emphasis than squaring does.
The error chart shows one point per pair and a stem to the zero line. The horizontal axis is the order you entered, not a time scale. Alternating positive and negative errors can average to zero without any prediction being accurate; the four nonnegative metrics avoid that cancellation.
Worked examples
Actual = 3, 5, 7 and predicted = 2, 5, 9 give errors 1, 0, −2. SSE = 5, MSE ≈ 1.67, RMSE ≈ 1.29 and MAE = 1. The first forecast is too low and the third is too high. Only the second pair lies on the zero line.
Actual = 10, 20 and predicted = 12, 18 give errors −2 and 2. Their signed average is zero, but SSE = 8, MSE = 4, RMSE = 2 and MAE = 2. If the predicted list exactly matches the actual list instead, all four scores are zero.
Input, precision and output
Compare model scores using the same observations, units and evaluation period. A lower score is better for that chosen metric on that dataset, but is not a universal quality threshold. Changing units changes the scores; adding easier observations can improve an average. Use data that were not used to fit the model when estimating its performance on new cases.
Both lists need the same 2–200 values. Missing entries, text, NaN and infinity are rejected. Zero, negative numbers and repeated values are allowed. Remove a missing observation from both lists, rather than shifting only one list.
Nonzero input magnitudes must be between 1e-100 and 1e100. Calculations use browser floating-point numbers, with about 15–16 significant digits. Distinct entries that collapse to the same stored number are rejected; reduce an offset or choose more suitable units before retrying.
Most displayed results use at most two decimal places. Small nonzero values use scientific notation, and calculations keep unrounded intermediate values. Offset/scaled axes explicitly show how to recover the original values, so tiny differences remain visible beside a large baseline.
Frequently asked questions
Why is MSE divided by n rather than n − 2?
This page evaluates supplied predictions using the mean of squared errors. An estimate of regression noise variance may use residual degrees of freedom instead; that is a different statistical task and is not this MSE.
Can I compare SSE between lists of different lengths?
Usually not directly. SSE adds every squared miss, so sample size affects it. Average metrics reduce that size effect, but fair comparison still requires equivalent cases, units and weighting.
Why can RMSE be much larger than MAE?
Squaring gives larger misses more influence before the square root is taken. A large gap can signal a few substantial errors. Inspect the plot and the original pairs rather than relying on one summary alone.
Are zeros, negative actuals or constant lists valid?
Yes. None of these formulas divides by an actual value, so zero and negative actuals are supported. There is no MAPE, percentage error, model fitting, CSV upload or automatic missing-value imputation.