The Mean Absolute Percentage Error (MAPE) is a point forecast accuracy measure. As a percentage, it can be compared between forecasts for time series on different scales, and it is easily interpreted. However, it is asymmetric (underforecasts' MAPEs are bounded at 100%, while overforecasts' are unbounded), potentially leading to biased forecasts. The MAPE is undefined if any actual is zero.
For forecasts $\hat{y}_1, \dots, \hat{y}_N$ and corresponding actuals $y_1, \dots, y_N >0$, the MAPE is defined as
$$\text{MAPE} := \frac{1}{N}\sum_{i=1}^N\frac{|\hat{y}_i-y_i|}{y_i}.$$
The MAPE is typically expressed as a percentage.
The MAPE has some shortcomings that should be kept in mind.
Variants on the MAPE (Tashman & Green, 2009, Foresight) include using the forecast instead of the actual in the denominator, or using the average of the forecast and the actual, yielding the so-called "symmetric MAPE" (sMAPE), which has a different kind of asymmetry (Goodwin & Lawton, 1999, IJF).
Alternatives to the MAPE as a point forecast accuracy measure include the mase, the mae and the mse.
