How to Calculate MAPE (Mean Absolute Percentage Error)

Forecasting is a common challenge for businesses and individuals, from predicting sales figures to anticipating financial market trends. Accurately measuring forecast performance is important for informed decision-making and strategic planning. Organizations frequently rely on various metrics to assess how well their forecasts align with actual outcomes. One widely recognized metric for evaluating forecast precision is the Mean Absolute Percentage Error (MAPE). Understanding MAPE helps refine predictive models and enhance operational efficiency.

Understanding Mean Absolute Percentage Error (MAPE)

MAPE quantifies the accuracy of a forecast by expressing the average error as a percentage of the actual value. This metric offers a standardized, relative measure of prediction accuracy, making it straightforward to compare forecast performance across different datasets or time periods, regardless of their scale.

Actual values represent the true, observed outcomes for a specific period, such as units sold or revenue generated. Forecasted values are the predicted outcomes for that same period. The error is the direct difference between the actual value and the forecasted value.

The absolute error is the magnitude of this difference, always expressed as a positive number, ensuring both positive and negative differences contribute equally. The percentage error converts this absolute error into a proportion of the actual value, standardizing the error for meaningful comparisons.

Calculating MAPE Step-by-Step

The Mean Absolute Percentage Error is calculated using a specific formula that aggregates individual percentage errors across multiple periods. The formula is: MAPE = (1/n) Σ (|Actual – Forecast| / |Actual|) 100%. Here, ‘n’ represents the number of periods, ‘Σ’ denotes the sum, and ‘||’ signifies the absolute value.

Consider a scenario with three periods of data to illustrate: Period 1 (Actual: 100, Forecast: 90), Period 2 (Actual: 120, Forecast: 130), and Period 3 (Actual: 110, Forecast: 105).

• Calculate individual error: Subtract the forecast from the actual value for each period. For Period 1, the error is 100 – 90 = 10. Period 2 yields an error of 120 – 130 = -10. Period 3 results in an error of 110 – 105 = 5.
• Calculate absolute error: Take the positive value of the errors. The absolute error for Period 1 is |10| = 10. For Period 2, it is |-10| = 10, and for Period 3, it is |5| = 5.
• Calculate absolute percentage error: Divide the absolute error by the actual value and multiply by 100%. For Period 1, this is (10 / 100) 100% = 10%. Period 2’s absolute percentage error is (10 / 120) 100% ≈ 8.33%. Period 3’s calculation yields (5 / 110) 100% ≈ 4.55%.
• Sum individual absolute percentage errors: Add these values: 10% + 8.33% + 4.55% = 22.88%.
• Calculate final MAPE: Divide this sum by the total number of periods (three). The MAPE for this dataset is 22.88% / 3 ≈ 7.63%. This systematic approach yields a single, interpretable percentage representing the average forecast accuracy.

Interpreting Your MAPE Results

Once calculated, the MAPE value provides a direct measure of forecast accuracy expressed in percentage terms. A lower MAPE percentage indicates a more accurate forecast, meaning predictions are closer to actual outcomes. For instance, a MAPE of 5% suggests that, on average, the forecasts deviate from the actual values by five percent. Conversely, a higher MAPE percentage implies a less precise forecast, indicating a larger average deviation. A MAPE of 20%, for example, would signal a less reliable set of predictions.

The acceptability of a specific MAPE value is not universal and depends heavily on the industry, the inherent volatility of the data being forecasted, and the specific application of the forecast. For example, a 10% MAPE might be considered acceptable for long-range economic forecasts, but unacceptable for short-term inventory planning where precise quantities are needed. Highly volatile data, such as daily stock prices, typically yields higher MAPE values compared to more stable data, like monthly utility consumption.

Businesses utilize MAPE to assess the overall reliability and effectiveness of their predictive models. A consistently low MAPE across various forecasts suggests a robust and dependable forecasting process, which can greatly aid in better resource allocation, production scheduling, and overall operational planning. Understanding this percentage allows decision-makers to gauge the potential impact of forecast errors on their operations and adjust strategies accordingly.