1 year ago Inventory Management1,042

6 Safety Stock Formulas You Can Consider in Your Next Calculation Cycle

Safety stock is a term used to describe the additional quantities of stock held by a company to mitigate the risk of running out of stock. This therefore acts as a buffer in case the supply and demand are different to what was planned or forecasted. There are many ways in which to calculate safety stock and there are plenty of Safety Stock Formulas available which you could use. Below we will go through 6 different Safety Stock formula definitions to get a comprehensive figure for safety stock. At the end we’ve given you a ‘bonus track’ of EOQ calculation!

Recommend Safety Stock Formula (s):

1.   Average SS

Safety stock = (max daily sale per unit * max LT in days) – (average daily sales per unit * average LT)

Although the above safety Stock formula is simple and gives an average amount of Safety Stock the company need to hold per unit of stock however does not take into account seasonal fluctuations (tradegecko, 2010)

2.   Heizer and Render (2013)

𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 = 𝑍𝜎𝑑𝐿𝑇


Z= number of standard normal deviations (Z-score)

𝜎𝑑𝐿𝑇 = standard deviation of demand during the lead time.

Although this approach takes into consideration standard deviation, it does not take account of time by including it as a variable in the equation (Emmanuel-Ebikake, 2015).


3.   Greasley (2013)


𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 = 𝑍 ∗( √𝐿𝑇) ∗ 𝜎𝑑


Z= number of standard deviations from the mean (Z-score)

LT = lead time

𝜎𝐷  = standard deviation of demand rate.

On the other hand, this approach takes account of lead time as a variable within the equation. This is one of favorite Safety Stock formula.


4.   King method


𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 = 𝑍 ∗( √ 𝑃𝐶 / 𝑇1) ∗ 𝜎𝐷


Z= Z-score (a statistical figure based on the cycle service level)

PC = performance cycle or total lead time (including transport time)

T1 = time increment used for calculating standard deviation of demand

𝜎𝐷 = standard deviation of demand


King (2011) safety stock formula, considers variations in demand, lead time, cycle time and fill rate. The purpose of the formula was to overcome the inaccuracies in data on demand. (Emmanuel-Ebikake, 2015)

5.   King (2011)


Safety stock = Z *√ ((PC/ T1 * σD 2) + (σLT × Davg)) 2

Z= Z-score (a statistical figure based on the cycle service level)

PC = performance cycle or total lead time (including transport time)

T1 = time increment used for calculating standard deviation of demand

𝜎𝐷 = standard deviation of demand

𝜎𝑑𝐿𝑇 = standard deviation of demand during the lead time

Davg= average demand


This safety stock formula is used when demand and lead time variability are independent and are therefore influenced by different factors whilst still having normally distribution.

But when demand and lead time are not independent of each other, this equation changes to:

Safety stock = (Z *√( PC/ T1 * σD) + ( Z * σLT * Davg)

6 McKinsey & Company Method.


In selecting to consider any safety stock formula, it is important to consider the joint impact of demand and replenishment cycle variability. This can be accomplished by gathering valid samples of data on recent sales volume replenishment cycles. Once the data are gathered, it is possible to determine safety stock requirement using this safety stock formula:

σC = √R (σS2 ) + S2 (σR2 )

σC = Units of safety stock need to satisfy 68 percent of all probabilities (one standard deviation)

R = Average replenishment cycle

σR = Standard deviation of the replenishment cycle

S = Average daily sales

σS = Stanard deviation of daily sales


How to do Economic Order Quantity (EOQ) calculation with examples

The economic order quantity is a method used to calculate when stocks need replenishing, the purpose of this method is to balance the benefits and disadvantages of holding stock, namely minimizing the cost of holding stock also mitigating the risks associated with this and reducing the ordering costs, this would then lead to the optimum quantity of goods being kept.

There is one commonly used formula used to:

EOQ= √ (2*CO *D)/CH

Co= Total cost of placing an order

D = Demand

CH= Total cost of holding a unit of stock


In this formula holding costs include:

Working capital costs

Storage costs

Obsolescence costs


Order costs are calculated using

Cost of placing the order

Price discount costs



Below is a worked example (Slack, 2016)
A construction company gets its cement from a single supplier, the demand throughout the year is constant and last year the company sold 4000 tons of cement. After some calculation, the cost of placing an order is £50 each time with the annual costs of holding the cement being at 40 % of the purchasing cost. The company purchases the cement at £120 per tonne. How much should the company order at a time?

EOQ= √ (2*CO *D)/CH

EOQ= √(2*50*4,000)/(0.4*120)

EOQ= √(400,000)/(48)

EOQ= 28.87 tons (answer in 2d. p)



Like many other statistical theories and mathematical equation, no safety stock formula can be claimed to be best. Similarly no formula can claim to be fit in all scenario. Use your knowledge and experience to find which formula best suits your business.

If you happen to know and used other safety stock formulas please do share in the comments box with me and the supply chain community.

Recommended Book:

Inventory Management Explained: A focus on Forecasting, Lot Sizing, Safety Stock, and Ordering Systems.

Recommended Course:

Supply Chain: Inventory Control & Safety Stock Calculation

Nunn Bush



Harold Averkamp , http://www.accountingcoach.com/about


King, P.L. (2011), Crack the Code, APICS magazine, July/August 2011 – http://media.apics.org/omnow/Crack%20the%20Code.pdf

Dr Oyetola Emmanuel-Ebikake , https://repository.edgehill.ac.uk/7007/1/Safety%20stock%20Paper-Final3.pdf

Heizer, J. and Render, B. (2014), Operations Management: sustainability and supply chain management, 11th ed. Pearson, England

Greasley, A. (2013). Operations Management, 3rd ed. Wiley, England

Slack, N.Brandon-Jones, A. Johnston, R. (2013) “Operations Management”  7th ed. Pearson, Harlow, UK

Robert Hammond of McKinsey and Company, Inc. as reported in Robert Fetter and Winston C. Dalleck Decision Models for Inventory Management (Burr Ridge, IL; Richard D, Irwin, 1961), pp. 105-8