# Forecast Error Metrics Reference: MAPE, WMAPE, sMAPE, RMSE, MASE > Source: https://netray.co/tools/forecast-error-metrics-reference-mape-wmape-rmse > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer A searchable lookup of the common forecast accuracy and bias metrics, their formulas, how to read them and where each one misleads. ## Category supply-chain ## Audience - Demand planner - Supply chain analyst - S&OP lead ## Tool **Kind:** worksheet **Mode:** reference **Columns:** #### Metric **Key:** metric **Type:** text #### Formula **Key:** formula **Type:** text #### Unit **Key:** unit **Type:** text #### How to read it **Key:** reads **Type:** text #### Main weakness **Key:** weakness **Type:** text #### Best used for **Key:** use **Type:** text **Rows:** **Metric:** Error (E) **Formula:** Actual - Forecast **Unit:** Units **Reads:** Positive means under-forecast, negative means over-forecast **Weakness:** Positive and negative errors cancel when summed **Use:** Building block for every other metric **Metric:** Percentage error (PE) **Formula:** (Actual - Forecast) / Actual **Unit:** Percent **Reads:** Signed error relative to demand **Weakness:** Undefined when actual is zero **Use:** Single item, single period review **Metric:** Absolute error (AE) **Formula:** |Actual - Forecast| **Unit:** Units **Reads:** Size of the miss, direction ignored **Weakness:** Not comparable across items of different volume **Use:** Input to MAE and WMAPE **Metric:** MAE (mean absolute error) **Formula:** Sum of |A - F| / n **Unit:** Units **Reads:** Average miss per period in units **Weakness:** Scale dependent, cannot compare SKUs **Use:** One item over time, safety stock inputs **Metric:** MAPE **Formula:** Sum of (|A - F| / A) / n x 100 **Unit:** Percent **Reads:** Average percent miss, lower is better **Weakness:** Fails on zeros, overweights low volume periods, penalises over-forecast less than under-forecast **Use:** Stable, high volume items **Metric:** WMAPE (weighted MAPE) **Formula:** Sum of |A - F| / Sum of A x 100 **Unit:** Percent **Reads:** Total absolute error as a share of total demand **Weakness:** Dominated by high volume items in a mixed portfolio **Use:** Family or portfolio accuracy reporting **Metric:** Forecast accuracy **Formula:** 100% - WMAPE (floored at 0) **Unit:** Percent **Reads:** Headline accuracy figure used in S&OP packs **Weakness:** Definition varies by company, always state it **Use:** Executive reporting **Metric:** sMAPE **Formula:** Sum of (|A - F| / ((A + F) / 2)) / n x 100 **Unit:** Percent **Reads:** Percent error scaled by average of actual and forecast **Weakness:** Several definitions exist, still unstable near zero **Use:** Comparing models across items with a zero-safe variant **Metric:** MSE **Formula:** Sum of (A - F)^2 / n **Unit:** Units squared **Reads:** Penalises large misses heavily **Weakness:** Units are hard to interpret **Use:** Model fitting and selection **Metric:** RMSE **Formula:** Square root of MSE **Unit:** Units **Reads:** Typical miss in units with large misses weighted up **Weakness:** Sensitive to outliers **Use:** Safety stock sigma when errors are roughly normal **Metric:** MASE **Formula:** MAE of forecast / MAE of naive forecast **Unit:** Ratio **Reads:** Below 1 beats the naive forecast, above 1 is worse **Weakness:** Needs a clean in-sample history **Use:** Comparing accuracy across different SKUs fairly **Metric:** Bias (mean error) **Formula:** Sum of (F - A) / n **Unit:** Units **Reads:** Positive means consistent over-forecast **Weakness:** Hides large offsetting errors **Use:** Spotting systematic optimism or sandbagging **Metric:** Percent bias **Formula:** Sum of (F - A) / Sum of A x 100 **Unit:** Percent **Reads:** Net over or under forecast as a share of demand **Weakness:** Sign convention differs between companies **Use:** Bias reporting by family or region **Metric:** MPE (mean percentage error) **Formula:** Sum of ((A - F) / A) / n x 100 **Unit:** Percent **Reads:** Average signed percent error **Weakness:** Undefined at zero actual **Use:** Bias on stable items **Metric:** Tracking signal **Formula:** Running sum of errors / MAD **Unit:** Ratio **Reads:** Beyond about plus or minus 4 suggests persistent bias **Weakness:** Threshold is a rule of thumb, not a law **Use:** Automatic bias alerts per SKU **Metric:** MAD (mean absolute deviation) **Formula:** Sum of |A - F| / n **Unit:** Units **Reads:** Same as MAE in forecasting use **Weakness:** Name is used for other statistics in other fields **Use:** Tracking signal denominator **Metric:** Forecast value add (FVA) **Formula:** Error of baseline - Error of step **Unit:** Percentage points **Reads:** Positive means the step improved accuracy **Weakness:** Needs a stored baseline forecast **Use:** Judging manual overrides against the statistical forecast **Metric:** Coefficient of variation **Formula:** Standard deviation / mean demand **Unit:** Ratio **Reads:** How volatile demand is before any forecast **Weakness:** Unstable on intermittent items **Use:** Setting realistic accuracy targets by segment **Notes:** Always state the forecast lag and the aggregation level when you quote a metric. The same data gives very different MAPE at SKU-week and at family-month. ## Content **Intro:** Forecast accuracy numbers are only comparable when everyone uses the same definition. This reference lists the metrics demand planners meet most, with the formula, the unit, how to read the result and where each one breaks down. **Sections:** #### How to use this reference **Body:** Search by metric name or by the problem you have, for example zero demand or bias. Each row gives the formula in plain text so you can reproduce it in Excel, SQL or your planning tool. Export the table to Excel and add it to your KPI definition document so finance, sales and operations quote the same measure. Agree one headline accuracy metric, one bias metric and one fairness metric such as MASE, rather than reporting everything. #### Choosing between MAPE and WMAPE **Body:** MAPE averages percent errors, so a miss on a ten unit month counts as much as a miss on a ten thousand unit month. WMAPE divides total absolute error by total demand, so volume sets the weight. For a portfolio view WMAPE usually reflects business impact better. For judging a model on one stable item MAPE is fine. If any actuals are zero, avoid plain MAPE. **Bullets:** - Use WMAPE for family and company level - Use MAPE only when actuals are rarely zero - Use MASE to compare across items - Report bias beside accuracy, never instead of it #### Worked example **Body:** Three months of actuals are 100, 120 and 80 against forecasts of 110, 100 and 90. Absolute errors are 10, 20 and 10, so MAE is 13.3 units. WMAPE is 40 divided by 300, which is 13.3%. Bias is (110 + 100 + 90) minus 300, which is zero, so the forecast looks unbiased even though each month missed. That is why you need both an absolute and a signed measure. #### Common mistakes **Body:** Teams compute accuracy against the latest forecast instead of the frozen one that supply used. Others average SKU-level MAPE and call it the company number. A third error is flooring accuracy at zero in one report but not another. Document the definition, the lag, the level and the treatment of zeros next to the figure every time. **Cta:** If you compute these metrics by hand each cycle, Netray can build them from your ERP shipment and forecast history and show the query behind every number. **Faq:** #### Which forecast accuracy metric is the best? **Answer:** There is no single best one. WMAPE suits portfolio reporting, RMSE suits safety stock, MASE suits comparing items, and bias or tracking signal suits detecting systematic error. Most teams track one accuracy metric and one bias metric. #### Why is MAPE a problem when demand is zero? **Answer:** MAPE divides by actual demand. A zero actual makes the percent error undefined or infinite, and tiny actuals produce huge percentages. Use WMAPE, MASE or a zero-safe sMAPE variant for intermittent items. #### Is forecast accuracy just 100 minus MAPE? **Answer:** Many companies define it as 100 minus MAPE or WMAPE, floored at zero, but this is a convention. Always write the definition beside the number, because a competitor or another plant may define it differently. #### What is a good WMAPE? **Answer:** It depends on demand variability and aggregation. Family level monthly figures are usually far better than SKU-week figures. Set targets by segment using volatility, and judge improvement against a naive baseline rather than a universal number. ## Search terms forecast accuracy metrics, MAPE vs WMAPE, wmape formula, smape formula, forecast error metrics list, mean absolute scaled error, forecast bias formula, which forecast accuracy metric to use --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json