SMAPE Calculator
Calculate symmetric mean absolute percentage error for forecast accuracy.
About SMAPE Calculator
Symmetric Mean Absolute Percentage Error (sMAPE) improves on MAPE by dividing by the average of the absolute actual and predicted values rather than the actual value alone: sMAPE = (100/n) × Σ|y_i − ŷ_i| / ((|y_i|+|ŷ_i|)/2). This bounds each term's contribution between 0% and 200% and treats over- and under-predictions more symmetrically, making it more stable than MAPE when actual values are small or the model sometimes over- and sometimes under-predicts significantly.
Formula
sMAPE = (100 / n) * sum(|y_i - y_hat_i| / ((|y_i| + |y_hat_i|) / 2))
- n
- Number of valid samples
- y_i
- Actual value for sample i
- \hat{y}_i
- Predicted value for sample i
Worked example
With the default values below, SMAPE Calculator returns sMAPE of 7.22%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Actual Values
- 100, 200, 300, 400
- Predicted Values
- 110, 190, 320, 370
Results
- sMAPE
- 7.22%
- Valid Samples
- 4
Step by step
- 1Sum of symmetric ratios: Σ[|y_i−ŷ_i| / ((|y_i|+|ŷ_i|)/2)]= 0.2890
- 2sMAPE: (100 / n) × sum of ratios= 7.22%
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does sMAPE fix MAPE's asymmetry problem?
By dividing by the average magnitude of the actual and predicted values instead of the actual value alone, sMAPE gives comparable penalties whether the model over-predicts or under-predicts by the same proportion, unlike MAPE which is skewed toward penalizing over-prediction more.
What's the maximum possible sMAPE value?
Each individual term is bounded at 200% (occurring when actual and predicted have opposite signs or one is zero and the other is nonzero), so overall sMAPE is bounded between 0% and 200%, unlike MAPE which is theoretically unbounded.
Is sMAPE always better than MAPE?
Not universally — sMAPE handles near-zero actual values more gracefully and is more symmetric, but it can behave counterintuitively when actual and predicted values have opposite signs; the best choice depends on your data's characteristics.