How to use this calculator
- Enter or choose actual values.
- Enter or choose forecast values, same order.
- The mAPE updates as you type. Use Copy result or Share to keep it.
Method
MAPE = 100% ÷ n × Σ|Aᵢ − Fᵢ| ÷ |Aᵢ| (Aᵢ ≠ 0); sMAPE = 100% ÷ n × Σ 2|Aᵢ − Fᵢ| ÷ (|Aᵢ| + |Fᵢ|); WAPE = 100% × Σ|Aᵢ − Fᵢ| ÷ Σ|Aᵢ|
- Aᵢ
- actual value
- Fᵢ
- forecast value
- n
- pairs included in each measure
Worked example
- Percentage errors: 10/100 = 10%, 20/200 = 10%, 0%, 10/50 = 20%.
- MAPE = (10 + 10 + 0 + 20) ÷ 4 = 10%.
- WAPE = (10 + 20 + 0 + 10) ÷ 600 = 6.67%, lower because the large-volume items were forecast well.
The forecasts have a MAPE of 10% and a volume-weighted error (WAPE) of 6.7%.
What the result means
MAPE treats a 10-unit miss on a small item as worse than the same miss on a big one. That suits comparing items, but small actual values can blow it up, and it punishes over-forecasts more than under-forecasts. WAPE weights by volume and is usually the better single number for totals such as inventory.
Assumptions and limits
- Errors are measured on actual values: MAPE skips pairs where the actual is 0 and reports how many were skipped.
- sMAPE uses the 0–200% definition with (|A| + |F|) ÷ 2 in the denominator, skipping pairs where both are 0.
- MAPE is unstable when actual values are close to zero, and meaningless for data that can be negative or have an arbitrary zero (such as temperatures).
- “Accuracy = 100% − MAPE” is a reporting convention, not a statistical measure.
Questions
What is a good MAPE?
It depends on how predictable the series is. Compare against a simple benchmark, such as last period’s value, rather than a fixed threshold.
Why do MAPE and WAPE differ?
MAPE averages percentages, so every item counts equally. WAPE divides total error by total volume, so big items count more.