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All calculatorsMethodology

Safety Stock Calculator

Estimate safety stock and a reorder point from daily demand variation, lead time and an explicit normal-model service factor.

Interactive calculator · Method SAFETYSTOCK-1.1 · Last reviewed: 2026-10-05

Calculate your scenario

Lead-time demand variance = E[L] × σd² + μd² × σL², derived by conditional variance for independent daily demand and independent lead time. Safety stock = z × √variance, rounded up to whole units. Reorder point = ceiling(mean daily demand × mean lead days + whole safety stock). Fixed lead time has σL = 0.

Your inputs

Try an example

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Whole safety stock 25 units
Reorder point 205 units
Unrounded buffer 24.672804 units
Mean lead-time demand 180 units
Lead-time demand variance 225 units²
Entered service factor z 1.644854

Entered z × square root of 225 = 24.672804 buffer units. Round up to 25; add mean lead-time demand and round up for a 205-unit reorder point.

How to use the calculator

Use daily mean demand and daily demand standard deviation from one consistent history. Use lead-time observations counted in complete daily periods. Fixed lead time must be whole days; fractional means require variation possible for integer period counts. Enter the mean and standard deviation of those counts, then the z factor for your chosen one-sided normal-model cycle-service target. Compare the unrounded buffer, whole safety stock and reorder point.

What the result means

For mean 20 units/day, daily standard deviation 5, fixed nine-day lead time and z = 1.64485, unrounded buffer is about 24.673 units. Order 25 buffer units and use a 205-unit reorder point under the declared model.

Formula and units

Daily observations are nonnegative quantities over one complete day, and L is a nonnegative integer count of complete daily periods. A fractional mean E[L] is allowed only with enough lead-time variance to be possible for integer L; fixed lead time must be whole days. Lead-time demand variance = E[L] × σd² + μd² × σL², derived by conditional variance for independent daily demand and independent lead time. Safety stock = z × √variance, rounded up to whole units. Reorder point = ceiling(mean daily demand × mean lead days + whole safety stock). Fixed lead time has σL = 0. For fractional mean a + f, the entered lead-time variance must be at least f × (1 − f). This model does not interpolate part of a day.

Worked examples

Fixed nine-day replenishment: Mean daily demand: 20 units/day; Daily demand standard deviation: 5 units per one-day observation; Mean replenishment lead time: 9 days; Lead-time standard deviation (0 = fixed): 0 days; Normal-model service factor z: 1.644853626951 dimensionless.
Example result: Whole safety stock: 25 units; Reorder point: 205 units; Unrounded buffer: 24.672804 units; Mean lead-time demand: 180 units; Lead-time demand variance: 225 units²; Entered service factor z: 1.644854.

Variable four-day replenishment: Mean daily demand: 40 units/day; Daily demand standard deviation: 10 units per one-day observation; Mean replenishment lead time: 4 days; Lead-time standard deviation (0 = fixed): 1 days; Normal-model service factor z: 1.281551565545 dimensionless.
Example result: Whole safety stock: 58 units; Reorder point: 218 units; Unrounded buffer: 57.312728 units; Mean lead-time demand: 160 units; Lead-time demand variance: 2,000 units²; Entered service factor z: 1.281552.

Limitations and common mistakes

Assumes independent identically distributed complete-day demand quantities, independent nonnegative whole-day lead-time counts, consistent day units and a continuous-review normal approximation. Correlation, seasonality, intermittent demand, order constraints and lost-sales feedback violate this model. z = 1.64485 is approximately a 95% one-sided normal quantile; this is a modeled cycle-service assumption, not a measured fill rate or a guarantee.

Variance and standard deviation are different inputs: enter standard deviations here. A daily demand standard deviation cannot be replaced directly with a weekly value, and a cycle-service target is not a fill-rate guarantee.

Sources and assumptions

Method SAFETYSTOCK-1.1; last formula review 2026-10-05. Sources and their supported claims. Calculation methodology.

National Institute of Standards and Technology: Normal distribution. Normal distribution and quantiles support the declared z interpretation; the lead-time variance is derived on this page.