Economic Order Quantity Calculator
Calculate the continuous EOQ batch size, implied orders per year, and relevant annual ordering and holding costs from annual demand and unit cost inputs.
Earlier editorial review
- Reviewed
- 2026-09-18
- Methodology
- 1.0
Sources
How it works
Enter expected annual unit demand, the incremental cost of placing one order, and the annual cost of holding one unit. Demand is measured in units per year. The two costs use the same currency, and holding cost is per unit per year.
The EOQ formula balances annual ordering cost against annual cycle stock holding cost. At the minimum, those two modeled cost components are equal. The calculator also divides demand by EOQ to show the implied long run orders per year.
The result is a continuous mathematical quantity. Orders per year may be fractional because it is a long run average. The total is relevant annual ordering plus holding cost, not total spend or profit.
Compare the continuous quantity with feasible pack sizes or supplier minimums outside this calculator. Recalculate ordering and holding cost for practical quantities if those constraints apply. Use separate methods for reorder timing, lead time, safety stock, or quantity discounts.
Step by step
- Enter annual demand in units per year.
- Enter cost per order and holding cost per unit per year in the same currency.
- Review the continuous EOQ, implied order frequency, and two annual cost components.
Worked example
Enter annual demand of 10,000 units, cost per order of $40, and annual holding cost of $5 per unit. The continuous EOQ is 400 units and the implied frequency is 25 orders per year.
Annual ordering cost is $1,000 and annual holding cost is $1,000, for $2,000 in relevant annual cost. These values are checked by the calculator test using the same three inputs.
When to use this calculator
Use EOQ as a starting estimate for a product with repeat demand when annual demand, order cost, and holding cost can be estimated on consistent units.
Then compare the continuous quantity with practical order constraints. Analyze reorder timing, safety stock, capacity, and supplier discounts separately when they matter.
Common input mistakes
Keep demand and holding cost on the same annual basis. Do not enter monthly demand with annual holding cost. Enter demand in units per year, cost per order, and holding cost per unit per year.
A carrying rate is not the holding cost per unit. Convert the rate to an annual currency amount per unit before entering it. Use the same currency for both cost inputs; no conversion is performed.
Formula and units
Q* = √(2 × D × S ÷ H)
Orders per year = D ÷ Q*
Annual ordering cost = (D ÷ Q*) × S
Annual holding cost = (Q* ÷ 2) × H
Relevant annual cost = annual ordering cost + annual holding cost
D is annual demand in units per year, S is cost per order, and H is holding cost per unit per year. The calculator keeps the continuous quantity and fractional long run order frequency; it does not round to whole orders or package sizes.
Assumptions and limitations
The basic model assumes known constant demand, constant ordering and holding costs, immediate complete replenishment, and no shortages. The total excludes purchase cost when unit price is constant. It does not include lead time, safety stock, discounts, storage capacity, spoilage, or changing costs. The continuous quantity and fractional frequency are model outputs, not a practical order schedule. Use a different model if these assumptions do not fit.
Key terms
- Economic order quantity
- The continuous batch quantity that minimizes annual ordering plus annual holding cost under the basic EOQ assumptions.
- Orders per year
- Annual demand divided by EOQ, interpreted as a long run average rather than a whole order count for a specific year.
- Relevant annual inventory cost
- Annual cost of ordering and holding average cycle stock. Purchase cost is excluded when unit price is constant.
Compare with other planning steps
EOQ estimates a batch quantity under a steady demand model. A reorder point answers when to place an order and may include lead time and safety stock. Those are separate calculations and are not outputs here.
If prices change with order size, compare feasible supplier quantities using purchase cost as well as ordering and holding cost. EOQ alone does not evaluate discounts, stockout risk, or storage limits.
FAQ
What does EOQ calculate?
Economic order quantity is the batch size that minimizes annual ordering cost plus annual holding cost in the basic model. Smaller batches require more orders but keep average cycle stock lower. Larger batches reduce order frequency but raise average stock. EOQ gives the mathematical balance for the inputs supplied; it is not a purchase schedule or profit estimate.
How does the EOQ formula work?
The formula is the square root of twice annual demand multiplied by cost per order, divided by annual holding cost per unit. At the optimum, annual ordering cost equals annual holding cost. Their sum is the relevant annual cost shown here. Purchase cost is excluded when unit price is constant across order quantities.
Why can orders per year be fractional?
Orders per year is annual demand divided by the continuous EOQ. It can be fractional because it represents a long run average frequency, not a count of orders that will occur in one particular calendar year. Actual orders may need whole pack sizes, minimum quantities, or supplier schedules that this calculator does not model.
What units should I use?
Enter demand in units per year, cost per order in the selected currency, and holding cost in that same currency per unit per year. Keep the time basis annual and use consistent units. If the holding input is a carrying rate, convert it to a yearly amount per unit before entering it.
What assumptions does this estimate use?
The model assumes known constant demand and costs, immediate replenishment, and no shortages. It does not model lead time, safety stock, quantity discounts, capacity limits, or changing unit prices. Those conditions can make a practical order quantity differ from the continuous EOQ.
Related tools
A separate reorder point calculation estimates order timing when lead time matters. Cash Conversion Cycle can place inventory in a broader working capital view. Neither calculation changes the EOQ assumptions used here.