MAPE & Forecast Error Calculator
MAPE is the average absolute error as a percentage of the actual values: actuals 100, 110, 120, 130 against forecasts 98, 115, 118, 125 give MAPE = 3.01457 %.
3.01456876456876 %
Full answer, then cut to fewer decimals (not rounded):
- 3.01456876456876 %
- 3.0145687645687 %
- 3.014568764568 %
- 3.01456876456 %
- 3.0145687645 %
- 3.014568764 %
- 3.01456876 %
- 3.0145687 %
- 3.014568 %
- 3.01456 %
- 3.0145 %
- 3.014 %
- 3.01 %
- 3.0 %
- MAE
- 3.5
- MSE
- 14.5
- RMSE
- 3.80789
- Mean error (bias)
- 1
| t | Actual | Forecast | Error | |Error| ÷ Actual |
|---|---|---|---|---|
| 1 | 100 | 98 | 2 | 2 % |
| 2 | 110 | 115 | -5 | 4.5455 % |
| 3 | 120 | 118 | 2 | 1.6667 % |
| 4 | 130 | 125 | 5 | 3.8462 % |
Step-by-step solution
- MAE = Σ|Aₜ − Fₜ| ÷ n = 3.5
- MSE = Σ(Aₜ − Fₜ)² ÷ n = 14.5; RMSE = √MSE = 3.80789
- MAPE = (100 ÷ n) Σ|(Aₜ − Fₜ) ÷ Aₜ| = 3.01457 %
MAPE & Forecast Error Formula
MAPE = (100 ÷ n) Σ |(Aₜ − Fₜ) ÷ Aₜ|
MAE = Σ|e|/n, MSE = Σe²/n, RMSE = √MSE, with eₜ = Aₜ − Fₜ
Worked Example
Actuals 100, 110, 120, 130 against forecasts 98, 115, 118, 125:
- MAE = Σ|Aₜ − Fₜ| ÷ n = 3.5
- MSE = Σ(Aₜ − Fₜ)² ÷ n = 14.5; RMSE = √MSE = 3.80789
- MAPE = (100 ÷ n) Σ|(Aₜ − Fₜ) ÷ Aₜ| = 3.01457 %
MSE: 14.5 · RMSE: 3.80789 · Mean error (bias): 1
| t | Actual | Forecast | Error | |Error| ÷ Actual |
|---|---|---|---|---|
| 1 | 100 | 98 | 2 | 2 % |
| 2 | 110 | 115 | -5 | 4.5455 % |
| 3 | 120 | 118 | 2 | 1.6667 % |
| 4 | 130 | 125 | 5 | 3.8462 % |
MAD, MSE and MAPE
MAD averages the absolute errors in the data’s own units, MSE squares them so large misses count more, and MAPE expresses the average error as a percentage of the actual values. MAPE is easy to compare across products but is undefined when an actual value is zero and exaggerates errors on small values. A tracking signal that keeps drifting above +4 or below −4 suggests the forecast is biased, not just noisy.
Frequently asked questions
What is a good MAPE?
It depends on the data. As a rough guide, under 10 % is very good, 10–20 % good, 20–50 % reasonable and above 50 % poor. Compare against a simple benchmark such as the naive forecast.
Why is MAPE undefined for zero actual values?
It divides by each actual value. With zeros, use MAE, RMSE or a scaled error such as MASE instead.
MAE or RMSE: which should I use?
RMSE squares errors, so it penalises large misses more; MAE treats all errors equally. Report both in the same units as the data.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). MAPE & Forecast Error Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/forecast-error-calculator/
IEEE
Scientific Converters, "MAPE & Forecast Error Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/forecast-error-calculator/