Safety Stock Calculator
Safety stock and reorder point by the King formula (demand and lead-time variability), demand-only, lead-time-only, max − average or days-of-cover methods — any service level, periodic review, fill rate, stockouts a year, holding cost, or the service level a given buffer delivers.
How it works
σ_LTD = √(LT × σ_d² + d̄² × σ_LT²); safety stock = z × σ_LTD; reorder point = d̄ × LT + safety stock; periodic review: replace LT with LT + R; max − average: SS = d_max × LT_max − d̄ × LT; days of cover: SS = days × d̄; service level of a stock: CSL = Φ(SS ÷ σ_LTD); fill rate = 1 − σ_LTD × G(z) ÷ Q; average inventory = Q/2 + SS
Safety stock is the buffer that absorbs demand arriving faster than average or a supplier delivering later than promised during the replenishment lead time. The combined (King) formula treats daily demand and lead time as independent normal variables, so the standard deviation of demand over the lead time grows with the square root of lead time for demand noise but linearly with average demand for lead-time noise — which is why an unreliable supplier is so expensive to buffer. The z-score converts the service level you want (the probability of not stocking out in a cycle) into multiples of that standard deviation; going from 95% to 99% costs 41% more buffer, and 99.9% almost doubles it. You can also pick a simpler method: demand variability only, lead-time variability only, the max − average rule (worst day × worst lead time minus the average case) or a fixed number of days of cover; for those the calculator shows the service level the buffer implies. If you order on a fixed schedule rather than at a reorder point, enter the review period: the buffer then has to cover lead time plus the review period. The fill rate — the share of units shipped from stock — uses the normal loss function and is usually higher than the cycle service level. Since every unit of safety stock is held all year, its carrying cost is the real price of the service level. Switch to “Service level of my stock” to see what an existing buffer actually delivers.
Worked example
Demand 100 ± 30 per day, lead time 10 ± 2 days, 95% service: σ_LTD = √(10 × 900 + 10,000 × 4) = 221 units; safety stock 1.645 × 221 = 364 units (3.6 days), reorder point 1,364. With orders of 2,000 units the fill rate is about 99.8% and you expect about 0.9 stockouts in 18 cycles a year. At $20 a unit and 25% holding, the buffer costs about $1,820 a year; 99% service would need 515 units. The max − average rule with a worst day of 150 and a worst lead time of 14 days gives 150 × 14 − 100 × 10 = 1,100 units — three times as much, an implied service level above 99.99%.
Sources: Omni Calculator — Safety stock (basic and statistical formulas) · NIST/SEMATECH e-Handbook — Normal distribution
Frequently asked questions
Cycle service level vs fill rate?
Cycle service level is the chance of no stockout during a replenishment cycle; fill rate is the share of demand met from stock, which is usually higher for the same safety stock. The calculator shows both — the fill rate also depends on the order quantity, because bigger orders mean fewer cycles in which a stockout can happen.
Which safety stock method should I use?
Use the King formula when you have the standard deviations of both demand and lead time; it is the standard statistical method. Demand-only suits reliable suppliers, lead-time-only suits steady demand. The max − average rule needs no statistics but usually overstocks, and days of cover is a quick policy for new items. The calculator shows the service level each simpler method implies so you can compare.
What if demand is not normal (slow movers)?
For intermittent demand the normal assumption overstates or understates the buffer; use a Poisson or empirical approach, or set safety stock in days of cover.
I have weekly sales data — can I use it?
Yes. Choose “Week” (or “Month”) and enter the average and standard deviation for that period. The calculator converts them to daily figures — the mean divides by 7, the standard deviation by √7 — assuming the days are independent.
How does a periodic review change safety stock?
If you only check and order every R days, demand during the review period is also uncovered, so the protection interval is lead time + R and the order-up-to level replaces the reorder point. With a weekly review on a 10-day lead time, the demand part of the buffer grows by √17 ÷ √10 ≈ 30%.
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