SMAPE Calculator (Symmetric Mean Absolute Percentage Error)

SMAPE (Symmetric Mean Absolute Percentage Error) measures how far a set of forecasts sits from the values they were meant to predict, expressed as a scale-free percentage. It was introduced to fix two problems with plain MAPE: MAPE is undefined when an actual value is 0, and it penalises over-forecasts and under-forecasts by different amounts. SMAPE divides each error by a symmetric denominator built from both the actual and the forecast, so a single zero actual no longer breaks the metric.

There are two published definitions, and this tool supports both because different papers and competitions use different ones:

• Makridakis (1993), 0%–200%. Each point term is |Fₜ − Aₜ| / ((|Aₜ| + |Fₜ|) / 2), equivalently 2·|Fₜ − Aₜ| / (|Aₜ| + |Fₜ|). Each term lies in [0, 2], so the average ×100 lands in 0%–200%. This is the form used in the M3 and M4 forecasting competitions.
• Armstrong (1985), 0%–100%. The denominator is the full |Aₜ| + |Fₜ| rather than its half, so the result is exactly half the Makridakis value for the same data. Model rankings are identical; only the scale changes.

The calculator performs these steps:

1. Parse both boxes into numeric arrays, accepting commas, spaces, tabs, or new lines. It rejects the input if the two series differ in length or if any token is not a number, naming the exact position of the problem.
2. For each point, compute the absolute error |Fₜ − Aₜ| and the denominator for the chosen definition.
3. Apply the zero convention: when both the actual and forecast are exactly 0, the point term is defined as 0 (a perfect zero forecast) instead of the undefined 0/0.
4. Sum the point ratios, divide by n, multiply by 100, and round the headline number to two decimals. Full precision is kept internally, and the per-point ratios are shown to six decimals so you can audit the math.

For context the tool also shows MAE (mean absolute error, in the data's own units) and MAPE. When any actual value is 0, MAPE is reported as undefined — a direct demonstration of the failure mode SMAPE was designed to avoid.

• Makridakis, S. (1993). Accuracy measures: theoretical and practical concerns. Int. J. Forecasting 9(4): 527–529.
• Makridakis, Spiliotis & Assimakopoulos (2020). The M4 Competition. Int. J. Forecasting 36(1): 54–74.
• Armstrong, J. S. (1985). Long-Range Forecasting (2nd ed.), p. 348 — the adjusted-MAPE (0–100%) definition.
• Wikipedia — Symmetric mean absolute percentage error (corroboration of both definitions).

The formulas and worked examples on this page were last cross-checked against the sources above on 2026-07-12. SMAPE definitions are stable; this page is reviewed if the referenced competition guidelines change.