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September 06, 2016

Safety Stock Formula: What It Is and How to Use It

safety stock formula: Z  × σLT × D avgImagine that you are an entrepreneur celebrating your third year of business selling candles. Sales have been increasing, and profits are higher than ever. However, you start to notice that you are having trouble keeping an accurate inventory due to the sudden change in demand. Some candles are selling out before new shipments arrive while some are overstocked taking up valuable inventory space, and it is costing you money. After doing research, you decide the best way to improve inventory operations is begin factoring safety stock into your ordering process.

Determining inventory level is one of the most challenging tasks faced by entrepreneurs and Operations Managers. When managing inventory, the goal is to satisfy product demand while maintaining an efficient stock supply. Too much inventory incurs extra holding and capital cost (money tied up in inventory that cannot be used for anything else). Not having enough inventory impacts the ability to manufacture goods or provide customers with product. In order to successfully manage inventory levels, learning how to use the safety stock formula is essential.

learn how to use safety stock with our free white paperWhat is Safety Stock?

Safety stock is simply extra inventory beyond expected demand. Entrepreneurs and Operations Managers carry safety stock to prevent stockouts, caused by changes in customer demand, incorrect forecast, and variability in lead times for raw materials. Calculating all of these variables can become a bit complex, partially because there are multiple formulas for determining safety stock and how to factor it into order quantities. However, in this article, I will provide the most comprehensive explanation the safety stock formula and how it fits in the ordering process.


Why Use Safety Stock formula?

Factoring the cost of inventory stockout is important for understanding the role safety stock plays in the ordering process. It is not uncommon for managers to rely on gut instinct or an educated guess to determine how much extra inventory to keep. Without properly calculating safety stock, the likelihood of a stockout drastically increases.

Over time, stockouts result in loss of revenue, gross profit, customers, and market share. If you can not meet the demand of your customers they will find someone else who will. Taking the time to use the safety stock formula not only saves you from these costs, but also increases the efficiency of your storage space. The result: increased revenue and higher service level. Service level is the probability that the amount of inventory on hand during the lead time is sufficient to meet expected demand - that is, the probability that a stockout will not occur.

The uncertainty of supply and demand makes it difficult to calculate the amount of stock needed to satisfy customers needs while avoiding stockouts. When dealing with uncertainties and multiple variables, the best way to calculate safety stock is to use standard deviation for determining variations in supply and demand.

Calculating Safety Stock

The definition of standard deviation is a quantity calculated to indicate the extent of deviation for a group as a whole. Which, in layman's terms, means you: first find the average of a set of data, second calculate the sum of the average and the data set, third take the sum and divide it by the sample proportion to get the variance, then fourth add the variance to the average. The sum amount will be your standard deviation.

With this definition in mind, the formula for calculating safety stock is given by the equation.

Z  × σLT × D avg,

where Z is the desired service level, σLT is the standard deviation of lead time, and D avg is demand average. Don’t be intimidated, the simplest method for calculating safety stock only requires a four-step process to calculate these variables.

1 | Calculating Lead Time

Lead time is the time between initiation and completion of a production process, or the time it takes in total to replenish stock. The total time it takes between submitting a purchase requisition, approval time, emailing vendors, delivery time from vendor, incoming inspection time, and the time it takes to put on the shelf determine lead time.

Depending on the vendor service used, lead times can be constant or variable. Lead times are considered constant if the total time to reorder and restock is always the same. If lead time is constant, you have an established lead time and can move on to the next stage in calculating safety stock. However, having such stability in lead time is rare. More often the lead time is variable, meaning that products production or delivery time are not always the same. It is because of this lack of consistency that we have to find the standard deviation of lead time to gain an accurate measurement. Let's take a look at the table shown below.

calculating lead time in safety stock formula

As you can see, the table is broken down into three categories: Expected Time, Actual Time, and Variance. The expected time is the expected lead time of a product. Actual time is the real time it took to replenish each order in the sample portion provided. In this example, the expected lead time to restock is 6 days while the actual time is varied. The variance column is the difference between actual time and the expected time. Positive numbers are the number of days over the expected time and negative numbers mean that the delivery arrived earlier than the expected time. With this information, we can find the standard deviation in lead time.

To find the standard deviation, first add up the variances,

5 + 3 + 5 + -1 + -2 = 10.

The sum of the variances, in this example, equals 10. Next, divide the sum of the variances by the sample portion (in this case, the lead time of the past 5 shipments)

10 ÷ 5 = 2.

Finally, add this number to the average expected time


After this step, you will have the standard deviation for the lead time (σLT). In this example, we have just discovered that the standard deviation for lead time is 8 days. 8 days signifies the average amount of time it takes to restock, after taking into account the variability in the actual time that orders have been received in the past. This is also the amount of time that our safety stock will have to hold us over until new product arrives. Now that we have the first part of the equation it's time to move on to the second step.

2 | Calculating Demand

To calculate demand average, you have to begin by determining what time frame you want to account for. The time it takes between reorders is usually a good time frame. If a product is reordered once every two weeks then demand should be calculated in two-week increments. If product is reordered once a month, the time frame will account for one month’s worth of sales. Let’s take a look at the table below:

Calculating demand for safety stock

This table is expressed by two columns, Weeks and Sales Volume. The time frame of this example is one month broken down into weekly increments. Sales Volume highlights the number of units of the product is sold each week.

To determine the demand average, simply take the sum of the total Sales Volume that month and divide it by the number of buying days. In this example, the sum of sales volume is 2550 units and the number of buying days is 30.

2550 ÷ 30 = 85 units

Now that we know that the average demand is 85 units per day, it is time calculate safety stock.

3  | Establishing Service Level

When calculating safety stock, you have to also consider the service level (Z). Deciding the correct service level for a certain product is basically balancing inventory costs vs. the cost of a stock out. Therefore, the service level is an important variable for calculating the appropriate amount of safety stock. The higher the desired service level, the more safety stock needs to be held.

Unfortunately, the cost functions highlighting this problem are very business specific. While inventory costs can often be determined easily, the cost of stock outs are much more complicated. However, in the retail industry the typical service level is 90% with higher priority items reaching 95%. Keep in mind, increasing a products service level will increase the amount of inventory held as safety stock, which will increase cost associated with this product. So, make sure that your service level is realistic and meets business model needs.  

For a more in depth look into calculating an optimal service level click here

In order to convert your desired service level into a more concise value, you will need to use a normal distribution chart. (See chart below)

service level within the safety stock formula

Looking at the normal distribution chart we can determine what our service factor is according to the service level we want to reach. For example, If you are trying to maintain a service level of 90% your service factor will be 01.28. This number will serve as your service factor, or (Z), in the equation.

So continuing with this example, if you calculate for a 90% service level  the equation looks more like

Safety Stock = 01.28 × 8 days × 85 units.



After calculating the lead time, the average demand for your product, and establishing your service level, we now have all of the pieces needed to complete the formula. Remember the formula for safety stock is Z × σLT × D avg. To determine safety stock, simply multiply these three numbers.

01.28 x 8 days × 85 units = 870.4 units

Your inventory is now at 870.4 units. Of course, you can not sell 0.40 of a product so when dealing with safety stock calculations always round your numbers. So, 870 is the amount of safety stock you will need during the month to satisfy demand.

This equation tells us that we need 870 units of safety stock on hand to meet the demand of sales over an average lead time of eight-day, while maintaining a service level of 90%. 870 units can also be used as your reorder point, because we know that it is only enough to last the eight days. Once inventory reaches this level it is time to place another order which decreases the possibility of a stockout.

Implementing Safety Stock Formula

Overall, this formula is great for forecasting inventory and calculating variable changes in supply and demand. Understand that safety stock calculations are designed to help Operations Managers avoid stockouts when ordering inventory. Remember, there are more variables that go into the ordering process than just safety stock. Safety stock simply calculates the amount extra stock that should be added to overall inventory and gives an indication on when to reorder.

Calculating safety stock correctly can save considerable amounts of money otherwise missed from stockouts or wasted in overstocked inventory. Using a software management system, such as SkuVault, to keep detailed accounts of sales and ordering process increases the accuracy and ease of calculating safety stock. Entrepreneurs and Operation Managers who understand their product and have data on past sales can expect higher inventory efficiency and higher revenue returns. Use this chart to reference your products and calculate your safety stock today.

a break down of the safety stock equation

Dominique Robinson is a content marketer who works at SkuVault, a warehouse management systems software company. Dominique's passion for helping people discover better ways to improve their business manifest in his coverage of management operations. His ability to relay the most up to date coverage of news and trends in the industry has helped provide readers with a targeted platform to meet their needs.

FILED UNDER: eCommerce, efficient warehouses, Inventory management, Inventory Tips and Tricks, Marketing, out of stocks