Calculators
Mean Absolute Scaled Error Calculator
Calculate MASE, mean absolute error, and the naive one-step benchmark from chronological actual and predicted pairs in your browser.
Compare forecast errors with a naive one-step benchmark.
Mean absolute scaled error (MASE) = MAE / [(1 / (n − 1)) × Σ|actualₜ − actualₜ₋₁|]. The numerator averages |actual − predicted| across all n pairs. The denominator is the mean absolute error of a one-step naive forecast over the n − 1 consecutive actual values, so rows must be entered in chronological order. For actuals 100, 110, 120 and predictions 105, 108, 118, MAE is 3, the naive MAE is 10, and MASE is 0.3. A MASE below 1 beats the naive benchmark, 1 matches it, and above 1 is worse. Unlike MAPE, MASE has no percentage denominator per observation and is finite when actual values are zero; unlike RMSE, it is unit-free. The scaled result depends on the series used for the naive benchmark and is not an accuracy percentage. Constant consecutive actuals make the denominator zero and MASE undefined, so the calculator reports an error rather than dividing by zero. Signed values and zero are accepted. Enter 2 to 10000 pairs, one pair per line, separating actual and predicted with a comma, semicolon, or space. Scientific notation is supported; omit thousands separators. Nonzero magnitudes must be between 1e-100 and 1e100. Scaled absolute differences and compensated summation reduce overflow and rounding error; browser floating-point limits still apply. Results show up to 12 significant digits. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is MASE calculated?
Divide the mean absolute forecast error by the mean absolute one-step naive forecast error. For actuals 100, 110, 120 and predictions 105, 108, 118, MAE is 3, the naive MAE is 10, and MASE is 0.3.
What does a MASE below 1 mean?
A value below 1 means the forecasts have smaller absolute errors than a one-step naive forecast on the same series. A value of 1 matches the benchmark and values above 1 are worse. Lower is better.
Why must the rows be in time order?
The denominator compares each actual value with the previous one. Reordering rows changes those consecutive differences and therefore changes the benchmark, even though the forecast errors themselves are unchanged.
What happens when actual values stay constant?
If every pair of consecutive actual values is identical, the naive forecast error is zero and MASE is undefined. The calculator reports an error instead of dividing by zero.
Can I use zero or negative values?
Yes. MASE scales by the naive error rather than dividing by each actual value, so zeros and signed values are accepted. The result is unit-free. All processing stays in your browser.