Safety Stock Formulas and Safety Stock Calculation- The Ultimate Guide

28 Mar

Before we talk about safety stock formula and safety stock calculation we need to understand the use of safety stocks.

Why we need Safety Safety Stock Calculation or Safety Stock Formula

According to Brown et. al (1996), safety stocks are a quantity of stock that needs to be calculated and maintain in inventory to buffer again demand variation and supply lead time variation. In other words, it is the type of insurance policy to cover fluctuation in unpredicted and unforeseen events. Whether those events an erratic sudden demand, poor supplier delivery performance or force majeure.

Get Excess and Obsolete Inventory Policy

Sharing personal experience, once, I have to build 3 months of safety stock as we want to exit a sole distributor in a country who carries safety stock of our products. So to ensure we can supply the products to that specific market I was tasked to perform safety stock calculation in the very erratic market, in case we have a sudden divorce with the specific distributor and we should continue to serve the market via 3PL.

However, due to high inventory carrying the cost we need to mindful as the use of safety stock can be very expensive, and businesses always look to deploy inventory reduction strategies.

Using adequate safety stock formulas are also must for any inventory planning methods you are using. Be it Kanban, MRP, Re-order Point and so on.

Importance of Using Safety Stock Calculation on Lower Level SKU’s

As we know if we set-up a safety stock for high-level item it will generate the demand for lower level dependents items. DeBodt and Van Wassenhove (1983) made an important comment on this:

“From our analysis….we concluded that, no matter what forecasting technique is being used, forecast errors are considerable…it follows that, in order to maintain a good customer service level. However, it is also necessary to protect the production departments against stockouts. Therefore, it may also be necessary to have safety stock on (some) components levels….”

Disadvantages of Safety Stocks

Whilst we are talking here about safety stock calculations, we must consider the disadvantages which comes with high safety stocks!

  • High safety stock may cover poor quality of manufacturing problems.
  • It may also hide the supplier poor delivery performance
  • High safety stock also hide inefficient production process (long setup times, machine capacity issues, machine breakdown etc.)
  • It can also high the skills shortage and inadequate manning
  • In some cases high safety stock hide transportation delays

To address above mentioned disadvantages of safety stock we should consider JIT System and Supply Chain Management- 5 Salient Features.

There are many ways in which to safety stock calculation are done 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. In 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 a 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)

Simple Safety Stock Calculation Example

Let’s assume we are buying a widget with the demand of 1440 over a 10-week period, which averages 144 per week. The lead time for this item is 2 weeks. Our safety stock might be to cover 25% of the lead time, i.e. maintain one half of week’s demand in stock as safety stock. This suggests a safety stock of 36. A more conservative and, of course, the expensive policy might be to cover 50% of the lead time and hold one week’s stock or  144 pcs as safety stock of this widget.

A similar margin of the buffer could also be maintained by the use of safety lead time, whereby an additional safety lead time is added to the planning lead time to allow for unforeseen events.


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 or safety stock calculations please do share in the comments box with me and the supply chain community.

[button url= size=15 icon_size=32]Excess and Obsolete Inventory Policy Guide [/button]

Recommended Book:

The Definitive Guide to Inventory Management: Principles and Strategies for the Efficient Flow of Inventory across the Supply Chain (Council of Supply Chain Management Professionals)


Essentials of Inventory Management

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


Recommended Course:

Supply Chain: Inventory Control & Safety Stock Calculation

Ultimate Guide to Love



King, P.L. (2011), Crack the Code, APICS magazine, July/August 2011 –

Dr Oyetola Emmanuel-Ebikake ,

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

Browne. J., Harhen. J. and Shivnan. J., (1996). Production Management Systems. 2nd editon. Addison Wesley. Harlow, England

DEBodt, M. and Van Wassenhove, L. 1983. “Lot sizes and safety stock in MRP”,  Production and Inventory Management, 24(1)


  • Richard Watkins

    I am not sure I can see in your formulae where it is based on the difference between forecast per period (at the cumulative lead time) and the actual demand per period.

    I also do not see a safety stock for unreliability of supply which looks ar std dev of lead time and demand over the lead time.

    Safety stock shoukd then manage the combination of both of these.

    Thus demand safety stock = k*sd(forecast error)*sqr rt(lead time)

    k = factor for number of std deviations required for given service level

    Supply safety stock = k*std dev lead time

    Total safety stock = sqrt( demand safety stock + supply safety stock)

  • Jaffer

    Thank you for the above formulas, I need an help, can we take an example for the each of the above formulas in the real life scenario it would be of great help.


  • Faisal Aqeel Farooqui

    Thanks for the formulas. Please advise if we can use minimum sales figures instead of maximum in calculating average SS.

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  • edward

    great post big up for posting

  • Malyala Vinod Kumar

    Hello Dr. Muddassir Ahmed Saab,

    This is Malyala Vinod Kumar from Hyderabad, Telangana, I am a Graduate in B.Com, I have 5+ years of experience in procurement, I want to do courses related to Supply Chain Management.

    Can you please suggest me what are the courses i can do related to SCM as i want to build my career in SCM.

    Kindly suggest me with your valuable suggestions.

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