Reorder Point Calculator

What this generator does

Multiplies daily demand by the lead time to get expected demand during replenishment, then adds safety stock: the service-level z-score times the daily standard deviation times the square root of the lead time. It reports each part separately so the buffer can be seen for what it is.

How to use this tool

1. Type the daily demand, how much it varies, the lead time in days and the service level you want, then press Calculate.
2. Read the reorder point and note how it splits into expected demand plus safety stock.
3. Change the service level from 95 to 99 and calculate again — the extra four points cost considerably more buffer.
4. Multiply the lead time by four and calculate again: the safety stock only doubles.
5. Or press Generate a scenario for a made-up case to practise on; its figures fill the same boxes.

Understanding the controls

Daily demand (units)

The average number of units used or sold in a day, from 0.1 to 1,000,000. Decimals are fine for a slow mover — 0.5 is one every other day.

Daily variation (standard deviation)

How far a single day typically strays from that average, in units. Enter 0 for demand that never varies, and the safety stock comes out as nothing.

Lead time (days)

Whole days between placing the order and having the stock, from 1 to 730. It multiplies expected demand directly and the safety stock only by its square root.

Service level (%)

The chance of getting through a lead time without running out, from 50 to 99.9. At 50 there is no buffer at all; 100 is not offered because it would need an infinite one.

Calculate

Works the four figures in the boxes. A figure outside its range is pulled back into range when you leave the box.

Generate a scenario

Draws a daily demand of 10 to 200, a variation of 2 to 40, a lead time of 1 to 30 days and one of four common service levels (90, 95, 97.5 or 99), works them, and fills the boxes with them.

Seed

Any word reproduces the same generated scenario unless this tool has changed since, so a worked example can be set and marked later. Calculate ignores it.

Common use cases

• Setting reorder levels for a stocked item with variable demand
• Teaching the square-root relationship between lead time and safety stock
• Showing what a higher service level actually costs in stock
• Worked examples for an inventory management course
• Producing practice problems with known answers

How this generator works

The reorder point shown is the lead-time demand and the safety stock added as they appear in the table, each to one decimal place, so the rows sum to the answer. Demand over a lead time of several days is the sum of several days' demand, and the variance of a sum of independent draws adds — so the standard deviation grows with the square root, not in proportion. The z-score comes from inverting the normal distribution with a rational approximation accurate to several decimal places, checked in the tests against the familiar values of 1.645 at 95% and 2.326 at 99%.

Randomness and fairness

Calculating with your own figures involves no randomness. Generate a scenario draws its figures — daily demand, its variation, lead time and service level — so the relationships can be explored, and the reorder point is then a deterministic calculation. A seed reproduces the same scenario exactly and is therefore explicitly not cryptographically secure; without one the browser's cryptographically secure generator supplies the figures.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• Assumes demand is normally distributed and independent between days; correlated demand needs a larger buffer.
• Lead time is treated as fixed. Variable lead time adds a second term to the safety stock formula.
• Service level here is the probability of not running out during a cycle, not the fraction of demand met.
• No stockout cost is modelled, so the service level is your choice rather than an optimised value.
• The page keeps no history, so note the figures of a case you want to compare against later, or the seed of a generated one.

Privacy and your data

Every figure here is worked out on your own device. The figures you type, a generated scenario and your seed never leave the browser and are not stored anywhere. What is measured is that the tool was used.