# MAD to Safety Stock Forecast Error Calculator > Source: https://netray.co/tools/mad-to-safety-stock-forecast-error-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Use your measured mean absolute deviation of forecast error to set safety stock and reorder point instead of a guessed buffer. ## Category supply-chain ## Audience - Demand planner - Inventory planner - Supply planner ## Tool **Kind:** calculator **Inputs:** #### Forecast MAD per period **Key:** mad **Type:** number **Default:** 85 **Min:** 0 **Step:** 1 **Unit:** units **Help:** Mean absolute deviation of forecast error at lag equal to your lead time, in one period. #### Average demand per period **Key:** demand **Type:** number **Default:** 600 **Min:** 0 **Step:** 10 **Unit:** units #### Replenishment lead time **Key:** lead **Type:** number **Default:** 3 **Min:** 0 **Step:** 0.5 **Unit:** periods #### Review period **Key:** review **Type:** number **Default:** 1 **Min:** 0 **Step:** 0.5 **Unit:** periods **Help:** Zero for continuous review. #### Cycle service level **Key:** service **Type:** select **Default:** 0.95 **Options:** ##### 90% **Value:** 0.9 ##### 95% **Value:** 0.95 ##### 97.5% **Value:** 0.975 ##### 99% **Value:** 0.99 ##### 99.9% **Value:** 0.999 **Outputs:** #### Forecast error sigma per period **Key:** sigma **Expr:** 1.25 * mad **Format:** decimal **Description:** For roughly normal errors, sigma is about 1.25 times MAD. #### Z score **Key:** z **Expr:** normsinv(service) **Format:** decimal #### Sigma over protection interval **Key:** sigma_p **Expr:** sigma * sqrt(lead + review) **Format:** decimal #### Safety stock **Key:** ss **Expr:** z * sigma_p **Format:** integer **Primary:** true #### Reorder point or order-up-to level **Key:** rop **Expr:** demand * (lead + review) + ss **Format:** integer **Primary:** true **Chart:** #### Safety stock vs lead time **Type:** line **X:** lead **From:** 0.5 **To:** 12 **Steps:** 24 **Series:** - ss **Disclaimer:** Assumes forecast errors are independent and roughly normal and unbiased. Correlated errors, bias and intermittent demand need other methods. ## Content **Intro:** Safety stock should protect against forecast error, not just against demand variation. Many planners track MAD, and the standard shortcut converts it to a standard deviation by multiplying by 1.25. This calculator turns that into a safety stock and a reorder point. **Sections:** #### How to use it **Body:** Measure MAD as the average of the absolute forecast errors in a period, using the forecast made one lead time earlier so that you capture the error that matters. Enter average demand, lead time, review period and the service level you want. The result is safety stock over the protection interval, which is lead time plus review period, and the reorder point or order-up-to level. **Bullets:** - Keep lead time and MAD in the same period unit - Use error at the lag of lead time - Use zero review for continuous review - Re-measure MAD every month #### The method **Body:** For normally distributed errors, standard deviation is about sqrt(pi/2) times MAD, which is close to 1.25. Errors accumulate over the protection interval with the square root of time when they are independent, so sigma over the interval is sigma times the square root of lead plus review. Safety stock is the service level Z score times that sigma, and the reorder point adds expected demand over the interval. #### Worked example **Body:** MAD 85, so sigma is 106. Lead time 3 and review 1 give a protection interval of 4 periods, so sigma over the interval is 212. At 95% service, Z is 1.645, safety stock is 349 and the reorder point is 600 times 4 plus 349, which is 2,749. Raising service to 99% lifts Z to 2.326 and safety stock to 493, which shows the price of the last few points of service. #### Common mistakes **Body:** Using the standard deviation of demand rather than of forecast error double-counts the part you already forecast. Using error at lag 1 when the lead time is three months understates the risk. Applying the formula to intermittent items fails because errors are far from normal. Finally, a biased forecast needs a bias correction before any buffer can work. **Cta:** Netray can read forecast and actual history from your ERP, compute error by item at the right lag, and propose safety stock changes for planner review. **Faq:** #### Why multiply MAD by 1.25? **Answer:** For a normal distribution the mean absolute deviation equals about 0.8 times the standard deviation, so sigma is roughly 1.25 times MAD. It is a convenient approximation when you track MAD. #### Which forecast error should I use? **Answer:** The error of the forecast made one lead time before the demand period, because that is the information you had when the order decision was made. #### Does this replace the standard safety stock formula? **Answer:** It is the same Z times sigma idea, but built on forecast error rather than raw demand variation, which is usually the more relevant uncertainty when a forecast drives replenishment. #### What if lead time is variable? **Answer:** Add the lead time variability term: combine demand error variance over the average lead time with the variance of lead time times average demand squared. This calculator assumes a fixed lead time. ## Search terms mad safety stock calculator, mean absolute deviation safety stock, forecast error safety stock, sigma from mad 1.25, safety stock from forecast error, reorder point forecast error, service level z score safety stock, forecast error standard deviation --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json