The Formula, Term by Term
Safety Stock (units) = Z x σd (units/day) x √L (days)
| Term | What it is | Unit |
|---|---|---|
| Z | Score for your service level | none |
| σd | Standard deviation of daily demand | units per day |
| L | Average lead time, order placed to stock you can sell | days |
The days cancel out, so the answer is in units. That is the number of extra units to keep on hand.
The square root matters. Demand swings do not all stack up in one direction. Some days run high and some run low, so they partly cancel. Four times the lead time needs twice the buffer, not four times.
Pick Your Z Score
Z sets how often you are willing to run out. These are the standard values from a normal table:
| Service level | Z | In plain words |
|---|---|---|
| 90% | 1.28 | Out of stock in about 1 of 10 order cycles |
| 95% | 1.65 | Out of stock in about 1 of 20 order cycles |
| 97.5% | 1.96 | Out of stock in about 1 of 40 order cycles |
| 99% | 2.33 | Out of stock in about 1 of 100 order cycles |
I start most SKUs at 95%. Safety stock moves in step with Z, so the 99% buffer is 2.33 / 1.65 times the 95% buffer. I spend that extra on best sellers, not on everything. Example 2 below runs it on one SKU.
The Max-Minus-Average Formula
No standard deviation? This form needs four numbers you already know:
Safety Stock = (Max Daily Sales x Max Lead Time) - (Avg Daily Sales x Avg Lead Time)
It asks one question. What if your best sales day and your slowest supplier hit at the same time? The answer is the gap between that worst case and a normal cycle.
It is simple, and it runs high. Both worst cases rarely land together. The table under Which Formula to Use, further down, shows when it is still the right pick.
Worked Examples
These are illustrative numbers for one SKU, used in Examples 1 to 3 so you can compare them.
The SKU sells 20 units a day on average. Its best day was 30 units. Daily sales have a standard deviation of 6 units. Lead time averages 16 days, and the slowest order took 21 days.
Example 1: Z-score at 95%
Safety Stock = 1.65 x 6 x √16
= 1.65 x 6 x 4
= 39.6, round up to 40 units
Hold 40 extra units. At 20 sales a day, that is 2 days of cover.
Example 2: The same SKU at 99%
Safety Stock = 2.33 x 6 x √16
= 2.33 x 6 x 4
= 55.9, round up to 56 units
16 more units buy you the drop from 1 miss in 20 cycles to 1 in 100. On a hero SKU that may be worth it. On a slow seller it is cash on a shelf.
Example 3: Max-minus-average
Safety Stock = (30 x 21) - (20 x 16)
= 630 - 320
= 310 units
Same SKU, 310 units. That is almost eight times the Z-score answer at 95%. The gap is the price of planning for the worst day and the worst shipment at once. If you can pull a standard deviation from your sales report, the Z-score form will free up most of that cash.
Example 4: Weekly numbers for an Amazon FBA SKU
This one is a different SKU, also with illustrative numbers. The seller tracks it by the week. It averages 70 units a week, with a standard deviation of 21 units a week. From order to available at Amazon takes about 6 weeks. The target is 97.5%.
Keep everything in weeks:
Safety Stock = 1.96 x 21 x √6
= 1.96 x 21 x 2.449
= 100.8, round up to 101 units
A common slip pairs the weekly standard deviation with a lead time of 42 days:
Safety Stock = 1.96 x 21 x √42
= 1.96 x 21 x 6.481
= 266.8 units
That is about 2.6 times too much, because a weekly swing was paired with a lead time in days. Same SKU, wrong units. If your demand numbers are per week, your lead time is in weeks. If they are per day, it is in days.
How the Calculator Gets σd
The calculator above asks for max and average daily sales, not a standard deviation. It estimates one from them:
σd ≈ (Max Daily Sales - Avg Daily Sales) / 3.29
That treats your max day as a rare high point, about 3.29 standard deviations above the mean. It is a fair shortcut when you have no other data. If your report gives you a real standard deviation, run the formula by hand with that number instead.
With the calculator's starting numbers (average 20, max 35, lead time 14 days, 95%), σd comes out at 4.56. The Z-score result is 28.1 units. The max-minus-average result, using a 21-day max lead time, is 455 units.
When Lead Time Varies Too
The formula above assumes your lead time is steady. If your supplier is sometimes on time and sometimes a week late, there is a longer form that adds lead time spread to demand spread. Our safety stock calculation guide walks through it with a worked example.
Which Formula to Use
| Your situation | Use |
|---|---|
| Less than about 90 days of sales history | Max-minus-average |
| Steady supplier, enough daily history to get σd | Z-score |
| Lead time that varies from order to order | Combined form (see the safety stock calculation guide) |
| A stockout costs far more than the extra stock | Max-minus-average, or Z-score at 99% |
| Slow, cheap items where cash matters more | Z-score at 90% |
Start with the Z-score form whenever you have the data, and treat max-minus-average as an upper bound. If the two land close together, either one is safe to use. If they land far apart, find out which worst case makes the gap: the best sales day or the slowest shipment.
Safety Stock and Buffer Stock
They are the same thing. Some planners say buffer stock for spare units held against sales spikes. In day-to-day use the two words mean one number. Every formula on this page works for either.
Where the Number Goes Next
Safety stock is not a trigger on its own. It is one input to your reorder point:
Reorder Point = (Avg Daily Sales x Lead Time) + Safety Stock
For the SKU in Example 1, that is (20 x 16) + 40 = 360 units. When stock falls to 360, place the order. Run it on your own numbers in the reorder point calculator.
To see your buffer in days, divide it by daily sales. 40 units at 20 a day is 2 days. The days of supply calculator does the same for your whole stock on hand.
When the Formula Breaks
The Z-score form assumes daily sales follow a bell curve. That holds for steady sellers. It fails in three common cases:
Seasonal SKUs. A standard deviation taken across peak and off-peak months is too wide for the quiet months and too narrow for the busy ones. Work out σd for the season you are buying for.
New products. With a few weeks of sales, the standard deviation is a guess. Use max-minus-average until you have about 90 days.
Lumpy sellers. A SKU that sells 0 most days and 40 on a few is not a bell curve. Lean on max-minus-average and check it by hand.
Recalculate when sales or lead time move. A buffer we set last spring is sized for last spring.