EOQ Calculator
Economic order quantity and cycle cost.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- Economic order quantity
- 1,095
- Orders per year
- 21.9
- Total annual cost
- $3,724.51
- Days between orders
- 16.7
Quick answer
Economic order quantity (EOQ) is the order size that minimizes the combined cost of placing orders and holding stock: EOQ = √(2 × annual demand × cost per order ÷ holding cost per unit per year). With demand of 24,000 units a year, $85 per order and $3.40 to hold one unit for a year, EOQ is 1,095 units — about 22 orders a year, one every 17 days.
What the EOQ calculator does
This calculator finds the order quantity at which the yearly cost of placing orders equals the yearly cost of holding inventory, which is where their total is lowest. It also shows how many orders you will place a year, the days between orders, and the total annual ordering-plus-holding cost.
It suits retailers, wholesalers, manufacturers buying components, and anyone restocking items with fairly steady demand. The model assumes demand is constant through the year, each order arrives in full, the unit price does not change with order size, and you never run out. Real businesses break these assumptions, so treat EOQ as a baseline to adjust for supplier minimums, pack sizes, quantity discounts and storage limits.
EOQ tells you how much to order, not when. Set the reorder point separately from daily demand, supplier lead time and a buffer from the safety stock calculator.
The formula
EOQ = √(2DS ÷ H) Orders per year = D ÷ EOQ Total annual cost = (D ÷ Q) × S + (Q ÷ 2) × H
| Symbol | Meaning | Unit |
|---|---|---|
| D | Annual demand | units/yr |
| S | Fixed cost per order: purchasing admin, receiving, inspection and delivery charges that do not vary with quantity | $/order |
| H | Cost to hold one unit for a year: capital tied up, storage, insurance, shrinkage and obsolescence | $/unit/yr |
| Q | Order quantity (the EOQ at the optimum) | units |
This is the Wilson (Harris) EOQ model, first published by Ford W. Harris in 1913 and a standard topic in operations management texts and the APICS/ASCM body of knowledge. The total cost shown excludes the price of the goods themselves, which is the same whatever the order size unless you get a quantity discount. Average inventory is assumed to be Q ÷ 2.
Worked examples
Wholesaler restocking a fast mover
A packaging wholesaler sells 24,000 cartons of a box a year. Each purchase order costs $85 to place and receive, and holding a carton for a year costs $3.40.
Inputs
- Annual demand24000 units
- Cost per order85 $
- Holding cost per unit/yr3.4 $
Result
- Economic order quantity1,095
- Orders per year21.9
- Total annual cost$3,724.51
- Days between orders16.7
Order about 1,095 cartons, roughly every 17 days. If the supplier sells in pallets of 1,000 or 1,200, either is close enough to the optimum to make little difference to cost.
Small shop with a slow-moving item
A bike shop sells 1,800 inner tubes a year. Ordering costs $40 including shipping, and holding a tube costs $6 a year.
Inputs
- Annual demand1800 units
- Cost per order40 $
- Holding cost per unit/yr6 $
Result
- Economic order quantity155
- Orders per year11.6
- Total annual cost$929.52
- Days between orders31.4
The EOQ is 155 tubes, about one order a month, for a total ordering and holding cost of $929.52 a year. Combining this order with other items from the same supplier would cut the effective order cost and lower the EOQ.
Manufacturer buying a cheap component
A factory uses 150,000 fasteners a year. Each order costs $250 (purchasing, freight and inspection) and holding cost is $0.80 per unit a year.
Inputs
- Annual demand150000 units
- Cost per order250 $
- Holding cost per unit/yr0.8 $
Result
- Economic order quantity9,682
- Orders per year15.5
- Total annual cost$7,745.97
- Days between orders23.6
Order about 9,682 units, roughly 15 to 16 times a year. Cheap, small parts have low holding costs, so the optimum batch is large relative to monthly use.
Why ordering near the EOQ is good enough
The total cost curve is flat around the optimum: ordering somewhat more or less than the EOQ barely raises cost. That gives you room to round to case packs, pallet sizes or supplier minimums. The extra cost depends only on how far you are from the EOQ, as a ratio.
| Order size | Cost increase |
|---|---|
| 0.5 × EOQ | +25% |
| 0.8 × EOQ | +2.5% |
| 1.0 × EOQ | 0% |
| 1.2 × EOQ | +1.7% |
| 1.5 × EOQ | +8.3% |
| 2.0 × EOQ | +25% |
Estimating holding and ordering costs
- Holding cost is usually estimated as a percentage of the item's unit cost per year, covering the cost of capital, warehouse space, insurance, damage, theft and obsolescence. Many businesses use something in the 20–30% range; perishable or fast-dating goods can be far higher. A $15 item at 25% gives H = $3.75.
- Ordering cost includes only costs that occur once per order: buyer time, invoice processing, receiving and inspection, and any fixed delivery charge. Freight charged per unit belongs in the unit price instead.
Because both sit inside a square root, a 20% error in either one changes the EOQ by only about 10%.
Quantity discounts and other real-world limits
When a supplier offers a lower price for larger orders, compare the total annual cost including the goods at each price break: (D × unit price) + ordering cost + holding cost. A discount often justifies ordering more than the EOQ, but holding cost also rises with the unit's value.
Other limits to check: supplier minimum order quantities, storage space, shelf life, and cash flow. Larger, less frequent orders tie up more working capital and lower your inventory turnover. If demand is seasonal, recalculate EOQ for each season with that season's annualized demand.
How to use the EOQ Calculator
- 1Enter annual demand in units — last year's sales or usage, adjusted for expected growth.
- 2Enter the fixed cost of placing one order, including receiving and any flat delivery charge.
- 3Enter the yearly cost of holding one unit; if unsure, multiply the unit cost by your holding cost percentage (for example 25%).
- 4Read the EOQ, orders per year, days between orders and total annual ordering-plus-holding cost, then round to your supplier's pack size.
Frequently asked questions
How do you calculate economic order quantity?
Multiply 2 × annual demand × cost per order, divide by the holding cost per unit per year, and take the square root. For 5,000 units, $50 per order and $2 holding cost: √(2 × 5,000 × 50 ÷ 2) = 500 units.
What is included in holding cost?
The cost of money tied up in stock, storage space, insurance, handling, damage, theft and obsolescence. It is usually expressed per unit per year or as a percentage of unit cost.
Why are ordering and holding costs equal at the EOQ?
Ordering cost falls and holding cost rises as order size grows; their sum is lowest where the two lines cross. At 1,095 units in the default example, both come to about $1,862 a year.
What are the limitations of the EOQ model?
It assumes steady demand, a fixed unit price, instant replenishment and no stockouts. Use it as a starting point, then adjust for lead time, safety stock, quantity discounts and supplier minimums.
How is EOQ different from a reorder point?
EOQ is how much to order; the reorder point is the stock level that triggers the order. Reorder point = average daily demand × lead time in days + safety stock.
References
- ASCM Supply Chain Dictionary — Association for Supply Chain Management (ASCM)
- Operations Management (inventory management chapter) — McGraw Hill (Stevenson)
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
- Report an error