acalculator

How much safety stock do I need?

Type your service level, how much demand varies, and your lead time. The safety stock calculator shows the buffer to keep and the reorder point.

Your numbers

Safety stock
49.35

At a 95% service level, a demand standard deviation of 10 and a lead time of 9, keep 49.35 units of safety stock.

Safety stock in whole units
50
z for the service level
1.6449
Standard deviation over the lead time
30
Average demand over the lead time
450
Reorder point
499.35

Safety stock: 49.35. At a 95% service level, a demand standard deviation of 10 and a lead time of 9, keep 49.35 units of safety stock.

Safety stock by service level

How to calculate

Works out safety stock from the service level, the standard deviation of demand and the lead time (z × σ × √lead time), with the reorder point when the average demand is given.

Example with the default inputs (Service level 95%, Standard deviation of demand per period 10, Lead time, in the same periods 9, Average demand per period (optional) 50): At a 95% service level, a demand standard deviation of 10 and a lead time of 9, keep 49.35 units of safety stock.

Method: z = the standard normal quantile of the service level. Standard deviation over the lead time = σd × √L. Safety stock = z × σd × √L. Reorder point = average demand × L + safety stock.

  • Demand per period is normally distributed and independent from one period to the next.
  • The lead time is fixed. A lead time that varies needs more safety stock than this.
  • Demand, its standard deviation and the lead time use the same period (days, weeks or months).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Service level 90%, Standard deviation of demand per period 4, Lead time, in the same periods 1, Average demand per period (optional) 20 gives z for the service level 1.281552, Safety stock 5.126206, Safety stock in whole units 6, Reorder point 25.126206.Source: Abbas and Goosheh, Operations Management (eCampusOntario, 2024), section 13.7 Inventory Models for Uncertain Demand: σL = σd × √L, SS = Z × σL, ROP = d × L + SS, https://ecampusontario.pressbooks.pub/opsmgmt/chapter/13-7-inventory-models-for-uncertain-demand/ (with z rounded to 1.28 the book gets 5.12); NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.7.1 (standard normal quantiles: 0.90 gives 1.282, 0.95 gives 1.645, 0.99 gives 2.326), https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm
  2. Service level 95%, Standard deviation of demand per period 10, Lead time, in the same periods 9 gives z for the service level 1.644854, Standard deviation over the lead time 30, Safety stock 49.345609, Safety stock in whole units 50.Source: Abbas and Goosheh, Operations Management (eCampusOntario, 2024), section 13.7 Inventory Models for Uncertain Demand: σL = σd × √L, SS = Z × σL, ROP = d × L + SS, https://ecampusontario.pressbooks.pub/opsmgmt/chapter/13-7-inventory-models-for-uncertain-demand/; NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.7.1 (standard normal quantiles: 0.90 gives 1.282, 0.95 gives 1.645, 0.99 gives 2.326), https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm (0.95 gives 1.645)
  3. Service level 99%, Standard deviation of demand per period 25, Lead time, in the same periods 4, Average demand per period (optional) 120 gives z for the service level 2.326348, Safety stock 116.317394, Safety stock in whole units 117, Average demand over the lead time 480, Reorder point 596.317394.Source: Abbas and Goosheh, Operations Management (eCampusOntario, 2024), section 13.7 Inventory Models for Uncertain Demand: σL = σd × √L, SS = Z × σL, ROP = d × L + SS, https://ecampusontario.pressbooks.pub/opsmgmt/chapter/13-7-inventory-models-for-uncertain-demand/; NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.7.1 (standard normal quantiles: 0.90 gives 1.282, 0.95 gives 1.645, 0.99 gives 2.326), https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm (0.99 gives 2.326)
  4. Service level 50%, Standard deviation of demand per period 10, Lead time, in the same periods 9, Average demand per period (optional) 50 gives z for the service level 0, Safety stock 0, Safety stock in whole units 0, Reorder point 450.Source: NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.7.1 (standard normal quantiles: 0.90 gives 1.282, 0.95 gives 1.645, 0.99 gives 2.326), https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm (the normal median is 0); Abbas and Goosheh, Operations Management (eCampusOntario, 2024), section 13.7 Inventory Models for Uncertain Demand: σL = σd × √L, SS = Z × σL, ROP = d × L + SS, https://ecampusontario.pressbooks.pub/opsmgmt/chapter/13-7-inventory-models-for-uncertain-demand/

How it works

  • z = the standard normal quantile of the service level: the value with that probability below it (z = 0 at 50%)
  • Standard deviation over the lead time σL = σd × √L, where σd is the standard deviation of demand per period and L is the lead time in periods
  • Safety stock = z × σL = z × σd × √L
  • Safety stock in whole units = the safety stock rounded up to the next whole number
  • Average demand over the lead time = average demand per period × L
  • Reorder point = average demand × L + safety stock (shown when average demand is typed)

The service level here is the cycle service level: the chance that stock does not run out while an order is on its way.

Numbers. z, the square root and the products use 64-bit floating point; average demand × lead time is exact. z is accurate to about 1 part in 10^15. Below about 84%, where z is under 1, one Newton step on the exact (level − 50) ÷ 100 keeps that accuracy as z nears 0.

Output format. Safety stock, standard deviation over the lead time, lead time demand and reorder point show 2 decimal places; z shows 4; each is rounded half up. The whole-unit safety stock is rounded up.

Assumptions

  • Demand per period is normally distributed and independent from one period to the next.
  • The lead time is fixed (0 to 1,000,000 periods); demand, its standard deviation and the lead time use the same period.
  • The service level is from 50% to under 100%.

Worked examples by hand

The textbook's phone kiosk. 90% gives z = 1.28155; σL = 4 × √1 = 4; safety stock = 1.28155 × 4 = 5.13 phones (the book rounds z to 1.28 and gets 5.12), 6 in whole phones; reorder point = 20 × 1 + 5.13 = 25.13 phones.

95%, σ = 10 units a day, 9-day lead time. z = 1.64485; σL = 10 × √9 = 30; safety stock = 1.64485 × 30 = 49.35 units, 50 in whole units.

99%, σ = 25 units a week, 4-week lead time, 120 a week on average. z = 2.32635; σL = 25 × 2 = 50; safety stock = 116.32 units (117 whole); lead time demand = 120 × 4 = 480; reorder point = 480 + 116.32 = 596.32 units.

50%. z = 0, so the safety stock is 0 and the reorder point is the lead time demand, 50 × 9 = 450 units.

Other questions people ask

How do you calculate safety stock?

Safety stock = z × σ × √L, where z comes from the service level, σ is the standard deviation of demand per period and L is the lead time in periods. At 95% (z = 1.645), σ = 10 units a day and a 9-day lead time: 1.645 × 10 × 3 = 49.35 units.

What is the z value for a service level?

It is the point on the standard normal curve with the service level below it. 90% gives 1.282, 95% gives 1.645, 97.5% gives 1.960 and 99% gives 2.326 (NIST/SEMATECH e-Handbook). The calculator works z out for any level from 50% up.

Why is the lead time under a square root?

Demand swings in different periods partly cancel out. If each period’s demand is independent, the variances add, so over L periods the variance is L × σ² and the standard deviation is σ × √L. Four times the lead time needs twice the safety stock, not four times.

How do I find the standard deviation of demand?

Take your demand for each of the last periods, such as 12 weeks or 30 days, and work out their standard deviation. Use the same period for the lead time: a daily standard deviation goes with a lead time in days.

What is the reorder point?

Reorder point = average demand × lead time + safety stock. With 20 phones a week, a 1-week lead time and 5.13 phones of safety stock, reorder when stock falls to 25.13 phones. (The textbook’s worked answer adds the standard deviation, 4, instead of the 20 phones of lead time demand and prints 9.)

What service level should I choose?

Each step up costs more stock: going from 95% to 99% raises z from 1.645 to 2.326, about 41% more safety stock. Many businesses keep a higher level for important items and a lower one for cheap or slow ones.

What if my lead time varies too?

This calculator assumes a fixed lead time. When deliveries are sometimes late, the lead time adds its own variation and you need more safety stock than shown here.