Quick answer
Economic order quantity (EOQ) = √(2DS ÷ H), where D is annual demand, S the cost per order and H the holding cost per unit per year. With 12,000 units, $50 per order and $2 holding cost, EOQ is 774.6 units, about 15.49 orders a year, for a total cost of $1,549.19.
Enter annual demand, cost per order and holding cost per unit. The calculator returns the order size that balances ordering and holding costs.
Related tools: Inventory Reorder Point Calculator: Stock level at which to reorder. Inventory Turnover Calculator: How many times inventory is sold and replaced. Average Order Value Calculator: Revenue per order.
How to use the Economic Order Quantity Calculator
- Enter annual demand (units) (above 0).
- Enter cost per order ($) (above 0).
- Enter holding cost per unit per year ($) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Annual demand | A number, in units | > 0 |
| Cost per order | A number, in $ | > 0 |
| Holding cost per unit per year | A number, in $ | > 0 |
Formula and method
Formula
EOQ = √(2DS ÷ H)
IEEE-754 double precision; shown to the decimals indicated.
Assumes constant demand and no shortages.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Annual demand = 12000; Cost per order = 50; Holding cost per unit per year = 2.
| Result | Value |
|---|---|
| Economic order quantity | 774.6 |
| Orders per year | 15.49 |
| Total annual cost | $1,549.19 |
Example 2
Inputs: Annual demand = 5000; Cost per order = 100; Holding cost per unit per year = 4.
| Result | Value |
|---|---|
| Economic order quantity | 500 |
| Orders per year | 10 |
| Total annual cost | $2,000.00 |
The first line is the headline result (economic order quantity). Below it the economic Order Quantity Calculator lists orders per year and total annual cost, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
The balance
Ordering more often raises order costs; ordering larger lots raises holding costs. At the EOQ the two are equal: ordering cost 15.49 × $50 = $774.60 and holding cost 387.3 average units × $2 = $774.60, so the total is $1,549.19.
Assumptions
EOQ assumes steady demand, fixed costs and no quantity discounts or shortages. Real demand fluctuates, so many firms round to practical lot sizes and add safety stock.
How the result changes with annual demand
Holding every other input at the first worked example, this table changes only annual demand. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Annual demand | Economic order quantity | Orders per year | Total annual cost |
|---|---|---|---|
| 6000 | 547.72 | 10.95 | $1,095.45 |
| 12000 | 774.6 | 15.49 | $1,549.19 |
| 24000 | 1,095.45 | 21.91 | $2,190.89 |
| 48000 | 1,549.19 | 30.98 | $3,098.39 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Annual demand: entering "0" shows "Annual demand must be greater than 0." beside that field and no result.
- Holding cost per unit per year: entering "0" shows "Holding cost per unit per year must be greater than 0." beside that field and no result.
Choosing between the Economic Order Quantity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Inventory Reorder Point Calculator](/business/inventory-reorder-point-calculator/) | average daily demand, lead time and safety stock | Reorder point |
| [Inventory Turnover Calculator](/business/inventory-turnover-calculator/) | cost of goods sold, beginning inventory and ending inventory | Inventory turnover |
| [Average Order Value Calculator](/business/average-order-value-calculator/) | total revenue and number of orders | Average order value |
| [Rebar Quantity Calculator](/construction/rebar-quantity-calculator/) | slab length, slab width and bar spacing | Total rebar length |
| [Margin Calculator](/business/margin-calculator/) | cost and revenue | Gross margin |
Background: business metrics
Business ratios depend on exactly which costs and revenues you include, so read each page's definition. Two common checks: break-even units = fixed costs ÷ (price − variable cost per unit), so $50,000 of fixed costs with a $10 price and $5 variable cost breaks even at 10,000 units; and net profit margin = net profit ÷ revenue, so $20,000 profit on $100,000 revenue is 20%.
Return on investment ignores time: 20% over five years is far less impressive than 20% in one, so compare returns over the same period.
Assumptions and limitations
- Real demand fluctuates
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for annual demand and holding cost per unit per year to confirm this.
Frequently asked questions
What if demand doubles?
EOQ rises by the square root of 2, about 41%.
Does it include the purchase price?
No, only ordering and holding costs.
What is the holding cost?
Storage, insurance, capital and obsolescence per unit per year.
What does the Economic Order Quantity Calculator calculate?
Order size that minimizes ordering and holding costs. It returns Economic order quantity, Orders per year and Total annual cost.
What formula does the Economic Order Quantity Calculator use?
EOQ = √(2DS ÷ H). Assumes constant demand and no shortages.
What do I need to enter in the economic Order Quantity Calculator?
You enter Annual demand (units), Cost per order ($) and Holding cost per unit per year ($).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Real demand fluctuates.
What is an example of a economic Order Quantity result?
With annual demand 12000, cost per order 50 and holding cost per unit per year 2, the economic order quantity is 774.6.
Where does the method come from?
The method follows: Harris (1913); standard inventory management texts.
Related calculators
- Inventory Reorder Point Calculator — Stock level at which to reorder.
- Inventory Turnover Calculator — How many times inventory is sold and replaced.
- Average Order Value Calculator — Revenue per order.
- Margin Calculator — Profit, gross margin and markup from cost and revenue.
- ROI Calculator — Return on investment, with optional annualized return.
Sources
- Harris (1913); standard inventory management texts
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.