Why is this higher than the simple z × σ × √lead time formula?

Because that formula assumes every delivery arrives on time. Here a lead time σ of 2 days on a 12-day lead time is 89% of the variance, lifting safety stock from 205 to 627 units. Zero lead time σ gives the simple formula.

Is cycle service level the same as fill rate?

No. Cycle service level is the share of replenishment cycles without a stockout; fill rate is the share of demand shipped from stock. Fill rate usually runs higher at the same buffer.

How much stock does each extra point of service cost?

More with every point, because z climbs steeply toward 100%. At these inputs 95% needs 627 units, 98% needs 783 and 99% needs 886.

Where do I find the lead time standard deviation?

In receiving history. Take the days from order release to usable stock for recent receipts, including inspection and put-away, and compute their standard deviation. Leave out orders you deliberately deferred.

Planning calculator

Safety Stock Calculator

Size safety stock from consumption and receiving history, then test the buffer in your ERP against your service target. You need daily demand, lead time and the spread of each.

What this calculator does

Buffer stock that meets a target cycle service level when demand and supplier lead time both vary.

Formula used

Lead-time demand σ = √(lead time × demand σ² + average daily demand² × lead time σ²)
z = inverse normal of the service level (A&S 26.2.23); safety stock = z × lead-time demand σ
Reorder point = average daily demand × lead time + safety stock; buffer days = safety stock ÷ average daily demand
Service level at current stock = normal probability of (current safety stock ÷ lead-time demand σ), A&S 7.1.26
Gap = safety stock − current safety stock; lead-time share = average daily demand² × lead time σ² ÷ lead-time demand σ²

Inputs explained

Average Daily Demand: Mean daily usage from consumption or shipment history.
Daily Demand Standard Deviation: Standard deviation of the same daily usage history.
Lead Time: Average days from order release to usable stock on the shelf.
Lead Time Standard Deviation: Standard deviation of order-to-receipt days in receiving history.
Target Cycle Service Level: Share of replenishment cycles that must end without a stockout.
Current Safety Stock: Safety stock in your ERP item master now.

How to use the result

Best suited to resetting ERP safety stock after a supplier change, pricing a higher service target in buffer units.
With periodic review, add the review period to lead time. Seasonal or trending demand needs σ recomputed for each season.

Current U.S. benchmarks

U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).

Common questions

Why is this higher than the simple z × σ × √lead time formula? Because that formula assumes every delivery arrives on time. Here a lead time σ of 2 days on a 12-day lead time is 89% of the variance, lifting safety stock from 205 to 627 units. Zero lead time σ gives the simple formula.
Is cycle service level the same as fill rate? No. Cycle service level is the share of replenishment cycles without a stockout; fill rate is the share of demand shipped from stock. Fill rate usually runs higher at the same buffer.
How much stock does each extra point of service cost? More with every point, because z climbs steeply toward 100%. At these inputs 95% needs 627 units, 98% needs 783 and 99% needs 886.
Where do I find the lead time standard deviation? In receiving history. Take the days from order release to usable stock for recent receipts, including inspection and put-away, and compute their standard deviation. Leave out orders you deliberately deferred.

Related guides

What 99.10 Says About Recession Risk: Reading Factory Output as a Leading Indicator

Last reviewed 2026-10-01.