How this calculator works
Stock has to cover demand until the next delivery arrives. If demand were perfectly steady, the reorder point would be the daily demand times the lead time: order when 700 units remain and the shelf reaches zero exactly as the truck arrives. Demand is not steady, so an extra buffer, the safety stock, covers the days when sales run above average. The buffer scales with the variability of demand, the square root of the lead time and the service level. A high service level means stocking more to make stockouts rare; a 95 percent service level leaves a five percent chance of running out during a lead time.
Formula
reorder point = average daily demand x lead time in days + safety stock. safety stock = z x standard deviation of daily demand x square root of the lead time. The z value is the one-sided normal quantile for the service level: 1.2816 at 90 percent, 1.6449 at 95 percent, 1.96 at 97.5 percent, 2.3263 at 99 percent and 3.0902 at 99.9 percent.
Worked example
Average demand is 100 units a day, the lead time is 7 days, the standard deviation of daily demand is 20 units and the service level is 95 percent. Demand during the lead time is 100 x 7 = 700 units. Safety stock is 1.6449 x 20 x square root of 7 = 87.04 units. The reorder point is 787.04, so place an order when stock falls to about 787 units.
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Frequently asked questions
Why does safety stock use the square root of lead time?
Daily demand variations partly cancel over a longer period. If each day is independent, the standard deviation of the total over L days grows with the square root of L, not L. That is why doubling the lead time increases safety stock by about 41 percent, not by 100 percent.
Should I also vary the lead time?
If supplier delivery dates move around, the lead time variability adds to the buffer. The combined formula uses the variance of demand during the lead time including both demand and lead-time variation. This page covers demand variability only, so add a margin if your supplier is unreliable.
What service level should I choose?
It is a cost trade-off. Higher service levels need more stock but reduce lost sales. Many retailers use 90 to 95 percent for ordinary goods and 97 to 99 percent for high-margin or critical items. The right figure depends on the cost of a stockout compared with holding cost.
Does this include the order quantity?
No. The reorder point says when to order, not how much. Use an economic order quantity or a fixed lot size to set the quantity, and make sure the order arrives before the reorder point is reached again.