Safety Stock Calculator
Safety stock is the cover you hold for the demand and the delays you did not plan for, and this page works it out the way the textbook does: z x sqrt(L x sd(D)² + D² x sd(L)²), with that line printed under the answer with your own figures inside it. Enter 120 units a day with a standard deviation of 25, a lead time of 7 days with a standard deviation of 1.5, and a service factor of 1.65, and the answer is 317 units, with a reorder point of 1,157. The service factor z is yours to set rather than a default nobody can check, the figure is rounded up to a whole unit with the unrounded one printed beside it, and the assumptions the formula rests on are listed with the result instead of left implied. The simpler maximum minus average method is here too, in its own mode with its own label: on the same demand and lead time, with a worst case of 180 a day over 9 days, it returns 780 units, and the two methods do not agree. It runs in your browser, with no account, and nothing you type leaves the page.
Enter the average demand and its standard deviation, the lead time and its standard deviation, and a service factor z. The formula and the working appear here.
- Safety stock
- Reorder point
- z
- Method
Demand and the lead time have to be read over the same period: days here, so the demand boxes are units per day and the lead time is in days. A figure typed with commas, 1,200, is read as one thousand two hundred.
Worked examples
Common questions
- What is the safety stock formula?
- The one this page uses is z x sqrt(L x sd(D)² + D² x sd(L)²), where L is the average lead time, sd(D) is the standard deviation of demand in one period, D is the average demand in that period and sd(L) is the standard deviation of the lead time. Both sources of variation are in it: demand wobbling over the lead time, and the lead time itself wobbling. With 120 units a day, sd 25, a lead time of 7 days, sd 1.5 and z 1.65, it gives 316.4173, which the page shows as 317 units after rounding up to a whole unit.
- How do I calculate safety stock when the lead time is constant?
- Enter 0 in the lead time standard deviation box. The second term drops out and the formula becomes z x sd(D) x sqrt(L), which is the version most courses teach first. A lead time of 4 days, a daily standard deviation of 10 and z 1.65 gives exactly 33 units, and the page says so rather than rounding a figure that needed no rounding.
- What is the reorder point, and how is it different from safety stock?
- Safety stock is the buffer; the reorder point is the level at which you place the order. It is the demand you expect during the lead time plus the safety stock, so 120 a day for 7 days is 840, plus 317 of safety stock, is a reorder point of 1,157. The page shows both, and the line that adds them is printed on the working.
- Which z value goes with which service level?
- Under the normal assumption, z 1.28 covers about 90%, z 1.65 about 95.1%, z 1.96 about 97.5% and z 2.33 about 99%. The page computes that percentage from the normal curve rather than a lookup table, marks it as an approximation, and prints it beside the z you entered. It is a property of the curve, not a measured service level: real demand is rarely normal, so the fill rate you observe is usually lower.
- What is the maximum minus average method, and why is it separate?
- It is the simpler heuristic: the most you could use over the longest lead time, minus what you use on average. With a maximum of 180 a day over 9 days against an average of 120 a day over 7 days, it gives 780 units, against 317 from the variability formula on the same demand and lead time. Because the two disagree, this page keeps the heuristic in its own mode with its own label and its own boxes rather than blending the answers.
- What does this calculation assume?
- Everything it assumes is listed under the answer, in a section of its own. Demand and the lead time vary independently of each other; both are near enough to a normal distribution; demand, its standard deviation and the lead time are all read over the same period, days with days or weeks with weeks; the standard deviations are the ones you entered, since the page has no access to your sales history; and the safety stock is rounded up to a whole unit. A standard deviation taken from too short a history understates the variation, and the result is only as good as that figure.
- Can I work in weeks, or in cases rather than pieces?
- Yes. The period switch reads the demand boxes as a rate per day, per week or per month, and the lead time in the same units, which is the mistake this arithmetic is most often caught by. The unit box is a word, so the answer comes back as 317 cases or 317 pallets instead of a bare number, and it changes the labels rather than the arithmetic.
- Is anything stored or sent anywhere?
- No. The arithmetic runs in the page itself, there is no sign-up, and nothing you type leaves your browser. The boxes, the method and the period are remembered in your own browser so the page opens where you left it, and clearing your browser data forgets them.
Exact arithmetic on the figures you enter, with the formula printed beside the answer. The service factor z is yours to set, and the simpler maximum-minus-average method is shown as its own mode rather than blended in, because the two do not agree.