Economic Order Quantity (EOQ): Formula, Example, and Reorder Point

Economic Order Quantity (EOQ) is the order size that minimizes the total cost of managing inventory — balancing the cost of placing orders against the cost of holding stock. Order too much and holding costs soar; order too little and you pay to reorder constantly. EOQ finds the sweet spot. This guide works through the formula and a full example.

Compute EOQ, order frequency, and reorder point instantly with the free EOQ Calculator.

The EOQ Formula

📐 Formula

EOQ = √( 2·D·S / H ) D = annual demand (units) S = ordering cost per order H = holding cost per unit per year

The formula comes from setting annual ordering cost equal to annual holding cost — the point where total cost is minimized.

Step-by-Step Example

A retailer sells 1,000 units per year. Each order costs $50 to place, and holding one unit for a year costs $2.

Step 1: Apply the formula

📐 Formula

EOQ = √( 2 × 1000 × 50 / 2 ) = √50,000 ≈ 223.6 → 224 units

Step 2: Order frequency and cycle time

📐 Formula

Orders per year = D / EOQ = 1000 / 224 ≈ 4.46 orders Days between orders ≈ 365 / 4.46 ≈ 82 days

Step 3: Total annual cost

📐 Formula

Annual ordering cost = (D/EOQ)·S ≈ 4.46 × 50 ≈ 223 Annual holding cost = (EOQ/2)·H = 112 × 2 = 224 Total ≈ 447 (excluding purchase cost)

Notice that ordering and holding costs are nearly equal at the EOQ — that is the hallmark of the optimal order size.

The Reorder Point

The reorder point (ROP) is the inventory level at which you place a new order so stock arrives just as you run out:

📐 Formula

ROP = daily demand × lead time = (1000 / 365) × lead time

If the lead time is 10 days, ROP ≈ 2.74 × 10 ≈ 28 units. Add safety stock if demand or lead time is uncertain.

Assumptions and Limits

EOQ assumes steady demand, a fixed ordering cost, a constant holding cost, and instant replenishment. When production is gradual rather than instant, use the Economic Production Quantity (EPQ) model instead. When demand varies, layer in safety stock.

Common Mistakes

Mismatched time units — demand, ordering, and holding costs must all be on the same annual basis.
Ignoring the reorder point — the right order size still needs the right order timing.
Forgetting safety stock — real demand fluctuates.

Try It Yourself

Enter your demand, ordering cost, and holding cost into the EOQ Calculator to get the optimal order quantity, order frequency, total cost, and reorder point with a full step-by-step breakdown. For multi-item analysis (ABC classification, safety stock), use the Inventory Control Solver.

Key Takeaways

EOQ = √(2DS/H) minimizes total inventory cost.
For D = 1000, S = $50, H = $2, EOQ ≈ 224 units.
At the EOQ, annual ordering and holding costs are roughly equal.
The reorder point ensures stock arrives before you run out.