# How much safety stock do I need?

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.

- Page: https://www.acalculator.org/logistics/safety-stock-calculator
- JSON spec: https://www.acalculator.org/logistics/safety-stock-calculator.json
- Version: 08eb0100f40d

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| level | Service level | The chance of not running out during one lead time (the cycle service level), from 50% to under 100%. |
| sd | Standard deviation of demand per period | How much demand swings from one period to the next, in units, for one day, week or month. |
| lead | Lead time, in the same periods | Periods from placing an order to having the goods, counted in the same period as the demand. |
| demand | Average demand per period (optional) | Average units used or sold per period, for the reorder point. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| safety | Safety stock | z × standard deviation of demand × √lead time, in units. |
| whole | Safety stock in whole units | The safety stock rounded up to the next whole unit, so the service level is at least met. |
| z | z for the service level | The standard normal value with the service level below it. |
| sdLead | Standard deviation over the lead time | Standard deviation of demand per period × √lead time. |
| leadDemand | Average demand over the lead time | Average demand per period × lead time. |
| reorder | Reorder point | Average demand over the lead time + safety stock: order again when stock falls to this level. |

## 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.

## Assumptions

- 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).

## Worked examples

1. level = 90%, sd = 4, lead = 1, demand = 20 gives z = 1.281552, safety = 5.126206, whole = 6, reorder = 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. level = 95%, sd = 10, lead = 9 gives z = 1.644854, sdLead = 30, safety = 49.345609, whole = 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. level = 99%, sd = 25, lead = 4, demand = 120 gives z = 2.326348, safety = 116.317394, whole = 117, leadDemand = 480, reorder = 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. level = 50%, sd = 10, lead = 9, demand = 50 gives z = 0, safety = 0, whole = 0, reorder = 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/.

## FAQ

### 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.

## Sources

- Azim Abbas and Seyed Goosheh, Operations Management (eCampusOntario, 2024), section 13.7, Inventory Models for Uncertain Demand: σL = σt × √L, safety stock SS = Z × σL for the chosen cycle service level, reorder point ROP = d × L + SS; kiosk example with Z = 1.28 for 90%. https://ecampusontario.pressbooks.pub/opsmgmt/chapter/13-7-inventory-models-for-uncertain-demand/ (retrieved 2026-10-18)
- NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.6.7.1, Cumulative Distribution Function of the Standard Normal Distribution (critical values 1.282, 1.645, 1.960 and 2.326 for 0.90, 0.95, 0.975 and 0.99). https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm (retrieved 2026-10-18)