Economic Order Quantity Calculator
Calculate the optimal order size using the EOQ formula.
About this calculator
This calculator applies the classic Economic Order Quantity (EOQ) formula -- the square root of (2 x Annual Demand x Ordering Cost Per Order) divided by Annual Holding Cost Per Unit -- to find the order size that minimizes total inventory cost. The formula balances two opposing costs: ordering too often racks up fixed Ordering Cost Per Order charges, while ordering too much ties up capital in Annual Holding Cost Per Unit (storage, insurance, spoilage risk, and the opportunity cost of cash). Because both costs sit inside a square root, doubling Annual Demand or Ordering Cost Per Order only grows EOQ by about 41%, not 100% -- and doubling Annual Holding Cost Per Unit shrinks EOQ by a factor of the square root of 2 instead, about 29%, not the same 41% (halving a denominator inside a square root is not the mathematical inverse of doubling a numerator inside one).
Orders Per Year and Order Cycle Time translate that quantity into a practical ordering rhythm. Unit Cost does not affect EOQ, Orders Per Year, or Order Cycle Time at all -- it only feeds into Average Inventory Value, which multiplies half the order quantity by the per-unit purchase price to estimate capital tied up in stock at any given moment. What this calculator does NOT do: it assumes constant, known demand with no seasonality or lead-time variability, ignores quantity discounts and storage capacity limits, and does not compute a reorder point or safety stock -- those require separate calculators.
Inputs
Results
Economic Order Quantity
447 units
How to Use This Calculator
- Enter annual demand in units.
- Input the fixed order cost (cost to place each purchase order).
- Enter the annual holding cost per unit, in dollars.
- Enter the unit cost.
- Review the EOQ (units per order), orders per year, order cycle time, and total annual inventory cost.
How the result changes with Annual Demand
| Annual Demand | Economic Order Quantity |
|---|---|
| 5,000 | 316 units |
| 7,500 | 387 units |
| 15,000 | 548 units |
| 25,000 | 707 units |
What each input means
- Annual Demand
- Annual demand in units.
- Ordering Cost Per Order
- Fixed cost to place one order.
- Annual Holding Cost Per Unit
- Annual cost to hold one unit in inventory.
- Unit Cost
- Purchase cost per unit for inventory valuation.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersAnnual Demand = 10000, Ordering Cost Per Order = 50, Annual Holding Cost Per Unit = 5, Unit Cost = 25 = 4 input(s) provided
- Calculate Economic Order QuantityEconomic Order Quantity447 = 447
- Calculate Orders Per YearOrders Per Year22.4 = 22.4
- Calculate Order Cycle TimeOrder Cycle Time16.3 = 16.3
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why doesn't a higher unit cost change the Economic Order Quantity?
The EOQ formula only balances Ordering Cost Per Order against Annual Holding Cost Per Unit -- Unit Cost never enters the square root at all, so changing it leaves EOQ, Orders Per Year, and Order Cycle Time completely unchanged. Unit Cost only matters for Average Inventory Value, which needs a purchase price to convert units on hand into a dollar figure.
If I double my annual demand, does the order quantity also double?
No -- because EOQ is a square root of a formula containing Annual Demand, doubling demand only grows EOQ by roughly 41%, not 100%. That's the mathematical reason larger operations don't need to scale order sizes in direct proportion to their sales volume; ordering and holding costs balance out at a smaller multiple.
What's the relationship between the total ordering cost and total holding cost at the EOQ?
They come out equal at the order quantity this calculator returns -- that's a defining property of the EOQ formula, not a coincidence. The formula is derived specifically by finding the order size where marginal ordering cost and marginal holding cost cross, which is why Total Ordering Cost and Total Holding Cost land on the same number in the results.
Does this calculator account for bulk purchase discounts?
No -- the classic EOQ formula assumes a constant Unit Cost regardless of order size, so it won't tell you whether a supplier's quantity discount makes a larger order worthwhile. If your suppliers offer price breaks at certain volumes, you'll need to compare the EOQ result against each discount tier's total cost separately.
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