EOQ Calculator

The economic order quantity is the order size that makes the yearly cost of ordering plus the cost of holding stock as small as possible: EOQ = √(2DS ÷ H). With 12,000 units a year, $50 per order and $2.40 to hold a unit for a year, the EOQ is about 707 units.

How to use the EOQ calculator

1. Enter how many units you sell or use in a year.
2. Enter the cost of placing one order.
3. Enter the cost of holding one unit for a year, in dollars or as a percent of the unit cost.
4. Add the supplier lead time to get a reorder point.
5. Press Calculate.

EOQ formula

EOQ = √(2 × D × S ÷ H), where D is annual demand, S is the cost per order and H is the holding cost per unit per year.

• Orders per year = D ÷ EOQ
• Yearly ordering cost = (D ÷ Q) × S
• Yearly holding cost = (Q ÷ 2) × H, since average stock is half an order
• Reorder point = daily demand × lead time

Why the square root?

Bigger orders mean fewer orders (lower ordering cost) but more stock on the shelf (higher holding cost). The total, D × S ÷ Q + Q × H ÷ 2, is smallest where the two parts are equal: D × S ÷ Q = Q × H ÷ 2. Solving for Q gives Q² = 2DS ÷ H, so Q = √(2DS ÷ H).

Worked example

Assumptions and limits

• Demand is steady through the year.
• The cost per order and the holding cost do not change with order size, so there are no quantity discounts.
• Orders arrive all at once after a known lead time, with no stockouts.

Real businesses round the EOQ to case or pallet sizes and add safety stock to the reorder point.

EOQ practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is the EOQ formula?

EOQ = √(2DS ÷ H), where D is yearly demand in units, S is the cost per order and H is the yearly cost of holding one unit.

What does the economic order quantity tell you?

The order size that makes the combined yearly cost of placing orders and holding stock as low as possible.

How do you calculate the reorder point?

Multiply daily demand by the lead time in days, and add safety stock if you keep any. With 33 units a day and a 7-day lead time, reorder at about 230 units.

What is the holding cost?

The yearly cost of keeping one unit in stock: storage, insurance, spoilage and the cost of the money tied up. It is often 15% to 30% of the unit cost per year.

When does the EOQ model not fit?

When demand is seasonal or uncertain, when suppliers give quantity discounts, or when order sizes are fixed by pack or truck sizes. Adjust the EOQ for these.

Sources

• U.S. Small Business Administration: Manage your finances
• Ford W. Harris, "How Many Parts to Make at Once" (1913), reprinted in Operations Research

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