One of the most common metrics used to measure the forecasting accuracy of a model is the **mean absolute percentage error**, often abbreviated as **MAPE**.

It is calculated as:

**MAPE** = (1/n) * Σ(|actual – forecast| / |actual|) * 100

where:

**Σ**– A symbol that means “sum”**n**– Sample size**actual**– The actual data value**forecast**– The forecasted data value

MAPE is commonly used because it’s easy to interpret. For example, a MAPE value of 14% means that the average difference between the forecasted value and the actual value is 14%.

The following example shows how to calculate and interpret a MAPE value for a given model.

**Example: Interpret the MAPE Value for a Given Model**

Suppose a grocery chain builds a model to forecast future sales. The following chart shows the actual sales and the forecasted sales from the model for 12 consecutive sales periods:

We can use the following formula to calculate the absolute percent error of each forecast:

- Absolute percent error = |actual-forecast| / |actual| * 100

We can then calculate the mean of the absolute percent errors:

The MAPE for this model turns out to be **5.12%**.

This tells us that the mean absolute percent error between the sales predicted by the model and the actual sales is **5.12%**.

To determine whether this is a good value for MAPE depends on the industry standards.

If the standard model in the grocery industry produces a MAPE value of 2%, then this value of 5.12% might be considered high.

Conversely, if most forecasting models in the grocery industry produce MAPE values between 10% and 15%, then a MAPE value of 5.12% may be considered low and this model may be considered excellent at forecasting future sales.

**Comparing MAPE Values from Different Models**

The MAPE is particularly useful for comparing the fit of different models.

For example, suppose a grocery chain want to build a model to forecast future sales and they want to find the best possible model among several potential models.

Suppose they fit three different models and find their corresponding MAPE values:

- MAPE of Model 1:
**14.5%** - MAPE of Model 2:
**16.7%** - MAPE of Model 3:
**9.8%**

Model 3 has the lowest MAPE value, which tells us that it’s able to forecast future sales most accurately among the three potential models.

**Additional Resources**

How to Calculate MAPE in Excel

How to Calculate MAPE in R

How to Calculate MAPE in Python

MAPE Calculator

What would your intrepretation be, if MAPE is Nan?