How to use the forecast accuracy calculator
- Paste the actual values in order, one per period, separated by commas, spaces or line breaks.
- Paste the forecast values for the same periods in the same order.
- Read the mean absolute deviation, MAPE, RMSE, MSE, bias and tracking signal.
- Scan the period by period table to see which periods were far off and in which direction.
Formula
error = actual - forecast
MAD = average of |error|, MSE = average of error^2, RMSE = square root of MSE
MAPE = average of |error| / |actual| x 100, left out if any actual value is 0
bias = average of error, tracking signal = sum of errors / MAD
A positive error means the forecast was too low. MAD and RMSE are in the units of your data, MAPE is a percentage and the tracking signal counts how many MADs of error have piled up in one direction.
Eight months of demand
The actual values 120, 135, 128, 150, 142, 160, 155, 170 are compared with the forecast 125, 130, 135, 140, 148, 152, 158, 162. The errors are -5, 5, -7, 10, -6, 8, -3 and 8. The absolute errors add up to 52, so MAD is 6.50, and the squared errors add up to 372, so MSE is 46.50 and RMSE is 6.82.
MAPE is 4.48%. The errors add to 10, so the bias is 1.25 (the forecast ran slightly low) and the tracking signal is 10 / 6.5 = 1.54. When the forecast runs below the actual value in every period, as in the second preset, MAD is 12.38 and the signal grows to 8.00, which clearly shows a one-sided forecast.
Which measure answers which question
MAD tells you the usual size of a miss in the units you forecast. RMSE does the same but punishes large misses harder, so it is the one to watch when a big error is costly. MAPE puts the miss on a percentage scale, which helps when you compare items of different sizes, but it breaks down for values at or near zero. Bias shows whether you lean high or low, and the tracking signal shows whether that lean is building up.
Use the measures to compare methods on the same data, for example a forecast from the Exponential Smoothing Forecast Calculator against a manual one. The Descriptive Statistics Calculator summarizes the series themselves.
Zeros and short series
If any actual value is zero, MAPE would divide by zero, so the tool shows that it is not defined and still reports the other measures. With only a few periods every measure is noisy, so use a longer history before you decide a method is better or worse.
Assumptions and limits
- Actual and forecast values are in the same units and cover the same periods.
- Errors of equal size are equally costly in both directions, which is not always true in practice.
- The tool applies no threshold. Whether a value is acceptable depends on your decisions and costs.
- Up to 1,000 values are read, and each must be below one billion in size.
Frequently asked questions
What is a good MAPE?
There is no universal answer. It depends on how volatile the item is and what a miss costs you, so compare the number with the MAPE of a simple alternative on the same data.
What does the tracking signal show?
It adds up all errors with their signs and divides by MAD. A value near zero means misses cancel out. A value that keeps growing means the forecast is consistently too high or too low.
Why are my errors defined as actual minus forecast?
It is a common convention, and it means a positive bias shows a forecast that ran low. If your organization uses the opposite sign, flip the sign of the bias and the tracking signal.
Why is MAPE missing for my data?
A MAPE needs every actual value to be non-zero because each error is divided by its actual value. The other measures do not have that limit and are still shown.