Mean Absolute Percentage Error CalculatorFree online math calculator — instant results, no sign-up
Calculate mean absolute percentage error using nonzero actual values.
Sign in to save results and favorites.
About the Mean Absolute Percentage Error Calculator
The Mean Absolute Percentage Error Calculator measures the average absolute percentage difference between actual values and their paired predictions. It uses the Values list as nonzero actual values and the Paired values or weights list as predictions, not weights. With the default lists 2, 4, 6, 8, 10 and 1, 2, 3, 4, 5, the MAPE is 50%.
- Values
- Enter the nonzero actual observations, defaulting to 2, 4, 6, 8, 10, in the same measurement units as the paired predictions.
- Paired values or weights
- Enter the predictions in matching order, defaulting to 1, 2, 3, 4, 5, in the same units as the actual values; this calculation treats them as paired values rather than weights.
Formula and method
MAPE (%) = (100/n) × Σᵢ₌₁ⁿ |(Aᵢ − Pᵢ)/Aᵢ|. For the defaults: (100/5) × (|2−1|/2 + |4−2|/4 + |6−3|/6 + |8−4|/8 + |10−5|/10) = 50.
- MAPE (%)Mean absolute percentage error, expressed as a percentage.
- nNumber of actual–prediction pairs; n = 5 for the default inputs.
- iPosition of a pair in the two input lists.
- AᵢActual value at position i, taken from Values; it must not be zero.
- PᵢPrediction at position i, taken from Paired values or weights.
- ΣSum across all pairs, from i = 1 through n.
- | |Absolute value, which makes each relative error nonnegative.
Match the lists by position and verify that they have equal lengths and no actual value is zero. For each pair, subtract the prediction from the actual value, divide by the actual value, and take the absolute value. Average these relative errors and multiply by 100. In the default example, every relative error is 0.5, so their average is 0.5 and MAPE is 50%.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Values2, 4, 6, 8, 10
- Paired values or weights1, 2, 3, 4, 5
Results
- MAPE (%)50
How to use the Mean Absolute Percentage Error Calculator
- 1Enter the actual values in Values; use 2, 4, 6, 8, 10 to reproduce the default example.
- 2Enter the corresponding predictions in Paired values or weights; use 1, 2, 3, 4, 5 for the default example.
- 3Check that the lists have the same number of entries, that each prediction matches the actual value in its position, and that all actual values are nonzero.
- 4Run the calculation to average the absolute relative errors and convert the result to a percentage.
- 5Read the MAPE (%) output; the default inputs give 50.
Reading your result
The MAPE (%) row reports the average absolute error relative to the actual values, in percent. A displayed value of 50 means the predictions differ from the actual values by 50% on average; for the default inputs, every prediction is exactly half its actual value. Lower MAPE indicates smaller relative errors, and 0% indicates exact matches throughout. MAPE does not indicate whether predictions are too high or too low and should not be interpreted as an accuracy score of 100 minus MAPE.
Limitations
MAPE is undefined when any actual value is zero, and actual values near zero can produce extremely large percentage errors. It assumes correctly aligned, equally long lists and gives each pair equal weight in the average of relative errors. Percentage comparisons are most meaningful for quantities with a meaningful zero; negative actual values are mathematically usable when nonzero but can make interpretation less intuitive. MAPE can exceed 100%, hides error direction, and has no universal cutoff for acceptable performance.
Common questions
Does Paired values or weights accept weights for MAPE?+
For this calculator, the second list supplies predictions paired with the actual values by position. It does not supply observation weights; each pair contributes equally to the average relative error.
Why do the default inputs produce a MAPE of 50%?+
The pairs are (2, 1), (4, 2), (6, 3), (8, 4), and (10, 5). Each absolute error divided by its actual value equals 0.5, so the average percentage error is 50%.
Can I include zero in the Values list?+
No. Each actual value is a denominator in the MAPE formula, so zero makes that pair's percentage error undefined. Do not silently remove zero-valued observations, because doing so changes the set being evaluated.
Will swapping the two default lists change MAPE?+
Yes. If 1, 2, 3, 4, 5 become the actual values and 2, 4, 6, 8, 10 become the predictions, every absolute error equals its actual value, giving a MAPE of 100%. MAPE depends on which list is used as the actual-value denominator.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
You might also like
Standard Deviation Calculator
Sample and population standard deviation of a data set.
Number Sequence Calculator
Terms and sums of arithmetic and geometric sequences.
Sample Size Calculator
Sample size for a survey at a confidence level.
Probability Calculator
Combined probabilities of two independent events.
Statistics Calculator
Summary statistics for a data set.
Mean, Median, Mode, Range Calculator
Central tendency and spread of a list.
Results are estimates for informational purposes and are not financial, medical or legal advice.