Economic Order Quantity (EOQ) Calculator
Find the order size that costs you the least overall. The EOQ balances the cost of placing orders against the cost of holding stock, giving the quantity that minimizes total inventory cost, plus how often to order.
Calculate EOQ →What is Economic Order Quantity?
The Economic Order Quantity (EOQ) is the order size that minimizes the total cost of inventory, balancing two opposing costs. Ordering cost (the fixed cost of placing an order) falls as you order larger quantities less often, while holding cost (the cost of storing inventory) rises as you order larger quantities. EOQ finds the quantity where their sum is lowest.
The classic EOQ formula assumes steady, known demand, a fixed ordering cost, a constant holding cost per unit, and instantaneous replenishment with no shortages. Under these assumptions, the total-cost curve is minimized at a single order quantity, the square root of twice the demand times the ordering cost, divided by the holding cost.
Although its assumptions are idealized, EOQ remains a foundational and surprisingly robust tool. The total-cost curve is fairly flat near the optimum, so moderate deviations from the exact EOQ raise costs only slightly, which makes the result useful even when real conditions depart somewhat from the assumptions.
In plain terms: Order too much at once and you pay to store it. Order too little too often and you rack up ordering costs. EOQ finds the Goldilocks quantity where the total of those two costs is lowest. Handily, being a bit off the exact number barely matters, the cost curve is flat near the bottom.
The Cost Trade-off
Ordering Cost
The fixed cost per order. Ordering larger amounts less often reduces total ordering cost.
Holding Cost
The cost of storing a unit over time. Ordering larger amounts raises average inventory and holding cost.
The Balance
EOQ is the order size where ordering and holding costs are balanced and their sum is minimized.
Key Formulas
Using the Result
EOQ gives the order quantity, from which you get the number of orders per year and the total annual inventory cost. At the EOQ, annual ordering cost and annual holding cost are equal, which is the signature of the optimum.
Because the total-cost curve is flat near the minimum, you can round the EOQ to a convenient order size, a case, pallet or supplier minimum, with little cost penalty. This robustness is one reason EOQ remains practical despite its simplifying assumptions.
Assumptions & Validation
Steady Known Demand
Demand is constant and known.
If violated: For uncertain demand, add safety stock and use a reorder point; for single perishable orders, use the newsvendor model.
Fixed Ordering Cost
Each order costs the same fixed amount.
If violated: Adjust if ordering cost varies with quantity.
Constant Holding Cost
Holding cost per unit is constant.
If violated: Model tiered or capacity-limited holding separately.
No Shortages
Replenishment is instantaneous and shortages are not allowed.
If violated: Use models with lead time and backorders where relevant.
⚠️ Check assumptions first
EOQ assumes steady, known demand, fixed ordering cost, constant holding cost, and instant replenishment with no shortages. Real demand is rarely constant, so EOQ is best used together with a reorder point and safety stock to handle variability, EOQ sets how much to order, while those tools handle when and how much buffer. For quantity discounts or single perishable orders, extended or different models apply.
When NOT to Use EOQ Calculator
Highly Variable Demand
When demand is uncertain, pair EOQ with safety stock and a reorder point, or use stochastic models.
Single Perishable Order
For a one-time order of a perishable item under uncertainty, use the newsvendor model.
Quantity Discounts
When price depends on order size, use the quantity-discount extension of EOQ.
Industry Applications
Purchasing Decisions
Set economical order sizes for regularly consumed materials or products.
Inventory Cost Reduction
Lower total inventory cost by balancing ordering and holding costs.
Replenishment Planning
Determine how often to reorder each item across a catalog.
Supply Chain Baselines
Provide a baseline order policy that other models refine for variability.
Frequently Asked Questions
What is Economic Order Quantity (EOQ)?
Economic Order Quantity is the order size that minimizes the total cost of inventory by balancing ordering cost against holding cost. Ordering cost falls when you order larger amounts less often, while holding cost rises with larger orders. EOQ is the quantity where their sum is lowest, calculated as the square root of twice the annual demand times the ordering cost, divided by the holding cost per unit.
What are the assumptions of the EOQ model?
The classic EOQ model assumes demand is steady and known, ordering cost is a fixed amount per order, holding cost per unit is constant, and replenishment is instantaneous with no shortages allowed. These assumptions are idealized, but the model remains useful because the total-cost curve is flat near the optimum, so real-world departures from the assumptions raise costs only modestly.
What happens if I don't order exactly the EOQ?
Because the total-cost curve is relatively flat near its minimum, ordering a quantity somewhat above or below the exact EOQ increases total cost only slightly. This robustness means you can round the EOQ to a convenient order size, such as a full case, pallet, or supplier minimum, without a meaningful cost penalty, which is one reason EOQ is so practical despite its simplifying assumptions.
How does EOQ relate to the reorder point?
EOQ and the reorder point answer different questions. EOQ determines how much to order to minimize total cost, while the reorder point determines when to place that order, based on demand during the replenishment lead time plus safety stock. They are used together: EOQ sets the order size, and the reorder point triggers each order at the right inventory level.
Can EOQ handle uncertain demand?
The basic EOQ model assumes demand is constant and known, so it does not directly handle uncertainty. In practice, EOQ is combined with safety stock and a reorder point to cope with demand and lead-time variability: EOQ sets the order quantity, while safety stock and the reorder point provide a buffer and trigger orders. For single perishable orders under uncertainty, the newsvendor model is used instead.
What is the total cost at the EOQ?
At the Economic Order Quantity, the annual ordering cost and the annual holding cost are equal, and their sum, the total variable inventory cost, is at its minimum. This equality of the two cost components is the defining characteristic of the EOQ optimum. The calculator reports this total cost along with the order quantity and the number of orders per year.
Find Your Lowest-Cost Order Size
Balance ordering and holding costs to minimize total inventory cost. Free during Beta.
Calculate EOQ →