About the Safety Stock Calculator
Safety stock is the extra inventory you hold to cover the gap between average and actual conditions — weeks when customers buy more than forecast, or deliveries that arrive late. This calculator uses the standard statistical formulas: it combines the standard deviation of demand and the standard deviation of lead time into the uncertainty over the replenishment lead time, then multiplies by the z-score for your target cycle service level.
Choose the formula that matches your situation: demand variability only (reliable supplier), lead-time variability only (steady demand), the combined formula for independent variation (the most common choice), or the more conservative additive formula when demand and lead time tend to move together. Demand and lead time can be measured in days, weeks or months, as long as both use the same period.
The result shows the safety stock, the reorder point (lead-time demand plus safety stock), the z-score and — if you enter a unit cost and carrying rate — what it costs per year to hold the buffer. Use it for supply chain planning, purchasing and S&OP reviews, or to show the cost of moving from a 95% to a 99% service level.
With the default inputs, the safety stock is 341 units. Change any value above to recalculate instantly.
How to use the safety stock calculator
- 1Pick the time period you measure demand and lead time in.
- 2Enter average demand and its standard deviation per period.
- 3Enter the average lead time and its standard deviation in the same period.
- 4Set the target cycle service level and choose a formula.
- 5Add unit cost and carrying rate to see the yearly cost of the buffer.
Formula and method
The combined formula treats demand and lead time as independent random variables: over an average lead time L the variance of demand is L × σ_D², and lead-time uncertainty adds D² × σ_L². The square root is the standard deviation of demand during the lead time, and z — the inverse standard normal value for the service level (1.645 for 95%) — scales it into safety stock. With demand variation only it reduces to z × σ_D × √L, and with lead-time variation only to z × D × σ_L.
The dependent version adds the two standard deviations instead of their variances, giving a larger, more conservative buffer. The reorder point is the average lead-time demand plus safety stock. Safety stock is rounded up to whole units. The service level here is the cycle service level (probability of no stockout per cycle), not the fill rate.
- SS
- Safety stock (units)
- z
- Service factor from the standard normal distribution
- D, σ_D
- Average demand per period and its standard deviation
- L, σ_L
- Average lead time in periods and its standard deviation
- ROP
- Reorder point
Worked examples
100 units/day, 7-day lead time, 95% service
Lead-time variance is 7 × 20² + 100² × 2² = 2,800 + 40,000 = 42,800, so σ over the lead time is 206.9 units. Multiplying by z = 1.645 gives 340.3, rounded up to 341 units. The reorder point is 700 + 341 = 1,041, and holding 341 units at $12 with a 25% carrying rate costs about $1,023 a year.
Weekly demand, reliable supplier, 98% service
With demand variability only, σ over the lead time is 120 × √3 = 207.8. z for 98% is 2.054, so safety stock is 426.9, rounded up to 427 units, and the reorder point is 3 × 500 + 427 = 1,927.
Dependent formula for a cautious planner
The additive formula sums the two standard deviations: 20 × √7 + 100 × 2 = 52.9 + 200 = 252.9. At 90% service z = 1.2816, so safety stock is 324.1, rounded up to 325 units.
Frequently asked questions
What is the safety stock formula?+
The most widely used formula is SS = z × √(L × σ_D² + D² × σ_L²), where z is the service factor, L the average lead time, σ_D the standard deviation of demand, D average demand and σ_L the standard deviation of lead time. Simpler versions drop either term.
What z-score should I use for safety stock?+
The z-score comes from your target cycle service level: 1.282 for 90%, 1.645 for 95%, 2.054 for 98%, 2.326 for 99% and 3.090 for 99.9%. Higher service levels need disproportionately more stock.
What is the difference between safety stock and reorder point?+
Safety stock is the buffer held for variability. The reorder point is the inventory level that triggers a new order, equal to the average demand during the lead time plus safety stock.
How do I find the standard deviation of demand?+
Take at least 12 periods of actual demand (or forecast errors, which is better if you forecast), and calculate the sample standard deviation with a spreadsheet STDEV function. Use the same period length as your lead time.
Is cycle service level the same as fill rate?+
No. Cycle service level is the probability of no stockout during a replenishment cycle; fill rate is the share of demand filled from stock. Because a stockout usually affects only the end of a cycle, a 95% cycle service level often gives a fill rate well above 95%, especially when order quantities are large relative to lead-time demand.