EOQ Calculator
Work out the economic order quantity from yearly demand, order cost and holding cost, with orders per year, the reorder point, safety stock and total cost. Holding cost can be money per unit or a percentage of the unit cost, and every result shows the working.
Your numbers
Units sold or used. Pick the period it covers.
Fixed cost per order, whatever its size: purchasing time, receiving, freight charged per order.
Storage, capital tied up, insurance, shrinkage and obsolescence for one unit kept a year.
Needed for a % holding cost; also gives the yearly purchase cost.
Days from placing an order to having it on the shelf. Adds the reorder point.
365 for calendar days. Use working days (say 250) if the lead time is in working days.
How much daily demand varies, in units. With a lead time it adds safety stock.
Chance of not running out before a delivery arrives.
To see what it costs a year compared with the EOQ.
Economic order quantity (EOQ)
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- Orders a year
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- Days between orders
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- Ordering cost a year
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- Holding cost a year (cycle stock)
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- Ordering + holding cost a year
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- Average cycle stock
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The calculation runs in your browser and ParrotNotes does not store your numbers. They sit in the page address so you can bookmark or share the result.
How the EOQ is worked out
Every order has a fixed cost (raising the purchase order, receiving it, freight charged per delivery), and every unit on the shelf costs money to keep. Ordering big means few orders but a lot of stock; ordering small means little stock but many orders. The economic order quantity is the size where the two yearly costs add up to the least: EOQ = √(2 × D × S ÷ H), with D the yearly demand, S the cost of one order and H the cost of holding one unit for a year. At the EOQ the yearly ordering cost and the yearly holding cost come out equal.
Worked example from MIT's logistics course: 2,000 units a year, $500 an order, a $50 unit with a 25% holding rate ($12.50 a unit a year). EOQ = √(2 × 2,000 × 500 ÷ 12.50) = √160,000 = 400 units. That is 2,000 ÷ 400 = 5 orders a year, one every 73 days; ordering costs 5 × $500 = $2,500 and holding costs 400 ÷ 2 × $12.50 = $2,500, $5,000 a year in all.
Holding cost: money or a percentage
Holding (carrying) cost is entered either as money per unit per year or as a yearly rate times the unit cost. The rate is the more common way to state it, because it scales with the price of the item: the same 25% means $12.50 a year on a $50 part and $125 on a $500 one. Demand can be typed per year, month or week; the calculator turns it into a yearly figure (× 12 or × 52).
The model behind the formula assumes steady, known demand, a fixed cost per order, a constant holding cost, no quantity discounts and no stockouts. Real demand moves, which is why the page adds safety stock and the reorder point, and why a price break for bigger orders needs its own comparison.
Reorder point and safety stock
The EOQ says how much to order; the reorder point says when. In an order-point, order-quantity system you order the EOQ whenever stock (on hand plus on order) falls to the reorder point: the demand expected over the lead time plus safety stock. Daily demand is the yearly demand divided by the days in the year; use working days for both if your lead time is in working days.
Safety stock covers demand that runs above average while you wait. If each day's demand varies independently, the variation over the lead time grows with its square root, so safety stock = z × σ daily × √(lead time). z is set by the cycle service level, the chance of not running out in a replenishment cycle: 1.282 for 90%, 1.645 for 95%, 2.326 for 99%. The table below gives more.
Service level and z
z is the inverse of the standard normal distribution at the cycle service level, the figure the calculator multiplies by σ × √(lead time). Computed on the page and checked against the NIST table.
| Cycle service level | z |
|---|---|
| 80% | 0.842 |
| 85% | 1.036 |
| 90% | 1.282 |
| 95% | 1.645 |
| 97.5% | 1.96 |
| 98% | 2.054 |
| 99% | 2.326 |
| 99.5% | 2.576 |
| 99.9% | 3.09 |
Close to the EOQ is good enough
Total cost changes slowly around the EOQ: the cost of ordering Q instead of the EOQ is ½ × (EOQ ÷ Q + Q ÷ EOQ) times the best cost. Ordering 25% more costs 2.5% more; ordering half as much costs 25% more. So round the EOQ to a case, a layer or a pallet, and spend the effort on the inputs that move it: a lower cost per order or a lower holding cost.
How this differs from the lead time and DSI calculators
The lead time calculator counts business days from order to delivery and the order-by date for a needed date; its answer is the lead time this page takes as an input. The days sales in inventory calculator looks back at the books and says how many days of sales the inventory covered. This page looks forward: how much to order each time, how often, and at what stock level to reorder.
For distributor and manufacturing sales reps
When a buyer asks for a better price on a bigger order, or wants to cut stock, the EOQ puts both sides in the same numbers: what an order costs them, what holding costs them, and what a different order size or a shorter lead time is worth a year. Write down the buyer's figures in the meeting, run them through the calculator, and send the working with your follow-up.
Sources, each read on 2026-11-01. Results are arithmetic on your own numbers under the EOQ model's assumptions:
- MIT OpenCourseWare ESD.260 Logistics Systems (Chris Caplice, 2006), Inventory Management: Fundamental Concepts & EOQ: formula, total cost, worked example, sensitivity
- MIT OpenCourseWare ESD.260, Inventory Management: Probabilistic Demand: reorder point s = x_L + kσ_L, cycle service level, σ over longer periods = √n × σ
- NIST/SEMATECH e-Handbook of Statistical Methods 1.3.6.7.1: cumulative distribution of the standard normal (to check z)
Related: the lead time calculator for the lead time in business days, the days sales in inventory calculator for how long stock lasts, and the pallet calculator to round an order to full pallets.
More for distributor and manufacturing sales: Distributor sales, Industrial distributor, Manufacturing sales process.
The buyer's numbers come up in the meeting
Order cost, holding cost, lead time and how much the buyer can store all come up when you sit down with purchasing. Record the meeting in ParrotNotes and you get a transcript, a summary and the action items, so the figures you run through the EOQ are the buyer's own.
Get Started FreeRelated tools
- Lead Time CalculatorCount business days from order to delivery, find the order-by date for a needed date, and add up supplier, production and shipping lead times.Open the tool
- Days Sales in Inventory CalculatorWork out days sales in inventory (DSI) from average inventory and cost of goods sold, with inventory turnover for the same period.Open the tool
- Pallet CalculatorWork out how many boxes fit on a pallet, per layer and in total, with the stack height, load weight and pallets for an order.Open the tool