Economic Order Quantity Calculator | EOQ, Reorder Point & Safety Stock
Calculate the optimal Economic Order Quantity (EOQ) using the Wilson formula √(2DS/H), together with reorder point (ROP), safety stock, cycle stock, average inventory, annual ordering cost, annual holding cost, and total inventory cost.
What Is the Economic Order Quantity Calculator | EOQ, Reorder Point & Safety Stock?
The Economic Order Quantity (EOQ) model answers a fundamental inventory question: how many units should you order at a time to minimize total inventory cost? Ordering too frequently incurs high ordering costs; ordering too rarely increases holding (storage) costs. The EOQ sits at the sweet spot where both costs are balanced.
- ▸EOQ: the optimal number of units to order each time you place an order.
- ▸Reorder Point: the inventory level at which a new order should be placed to avoid stockouts.
- ▸Safety Stock: extra inventory held as a buffer against demand variability and supply uncertainty.
- ▸Cycle Time: the average number of days between orders at the EOQ.
- ▸Total Annual Cost: sum of holding, ordering, and (optionally) purchase costs at the EOQ.
The EOQ model assumes constant demand rate, fixed ordering and holding costs, and instantaneous replenishment. In practice, these assumptions are approximations, but EOQ gives an excellent starting point for any inventory optimization.
Formula
The Economic Order Quantity model uses five core formulas to minimize total inventory cost.
EOQ = √(2·D·S / H)
Optimal order quantity in units per order.
ROP = d·L + Safety Stock
d = D/365 (daily demand), L = lead time (days).
SS = z·σ·√L
z = service level z-score, σ = daily demand std dev.
TC = H·(EOQ/2+SS) + S·(D/EOQ)
Sum of holding and ordering costs is minimized at EOQ.
How to Use
- 1
Enter annual demand D (units per year), ordering cost S (dollars per order), and holding cost H (dollars per unit per year).
- 2
Enter the lead time in days to calculate the reorder point.
- 3
Enter daily demand standard deviation to compute safety stock, or leave at 0 for deterministic EOQ.
- 4
Select the service level (90%, 95%, or 99%) to set the z-score for safety stock calculation.
- 5
Optionally enter unit cost to include annual purchase cost in the total annual cost figure.
- 6
Click Calculate EOQ and review the results: EOQ, reorder point, safety stock, number of orders per year, cycle time, holding cost, ordering cost, and total annual inventory cost.
- 1
Enter annual demand D
Total units expected to be sold or used per year. Use the retail store preset for a quick example (D = 1,200 units/yr).
- 2
Enter ordering and holding costs
S is the cost per purchase order placed (shipping, admin, setup). H is the cost to hold one unit for one year (storage, insurance, capital cost).
- 3
Enter lead time
The number of days between placing an order and receiving it. Used to calculate the reorder point.
- 4
Enter demand variability (optional)
Enter the daily demand standard deviation σ and choose a service level to compute safety stock. Leave σ at 0 for deterministic demand.
- 5
Review all outputs
Read EOQ, reorder point, safety stock, number of orders per year, cycle time, and the full cost breakdown.
Example Calculation
Example | Retail Store Inventory Optimization
A retail store sells 1,200 units/year of a product. Each purchase order costs $50. Holding cost is $5/unit/year. Lead time is 7 days. Daily demand std dev is 5 units. Service level: 95% (z = 1.645).
Understanding Economic Order Quantity | EOQ, Reorder Point & Safety Stock
What Is EOQ and Why Does It Matter?
Every business that holds inventory faces a trade-off: order in large quantities infrequently (low ordering cost but high storage cost) or order in small quantities frequently (low storage cost but high ordering cost). The Economic Order Quantity model, developed by Ford Harris in 1913 and popularized by R. H. Wilson, finds the mathematically optimal order size that minimizes the sum of these two costs.
The EOQ Cost Curve
Total inventory cost has a characteristic U-shape when plotted against order quantity. The holding cost line slopes upward (larger orders mean more average inventory), the ordering cost curve slopes downward (larger orders mean fewer orders per year), and the total cost curve is minimized exactly where the two component curves intersect — at EOQ.
- ▸Annual ordering cost = S × (D / Q) — decreases as order size Q increases.
- ▸Annual holding cost = H × (Q/2 + Safety Stock) — increases as Q increases.
- ▸Total cost is minimized at Q = EOQ = √(2DS/H).
- ▸At EOQ, annual ordering cost equals annual holding cost (for cycle stock).
Practical Inventory Management Tips
- ▸Set the ROP as a trigger in your inventory management system so orders are placed automatically.
- ▸Review EOQ inputs quarterly — changes in demand, supplier fees, or storage costs can shift the optimal order quantity significantly.
- ▸For ABC analysis, use EOQ for A-items (high value), and simpler rules for B and C items.
- ▸Consider quantity discount breaks: if a supplier offers a 10% discount at twice the EOQ, recalculate total cost including purchase price to see if the discount justifies the extra holding cost.
- ▸Safety stock is not free — every extra unit in safety stock adds H dollars per year in holding cost. Target the service level that matches the cost of a stockout for your business.
Frequently Asked Questions
What is the Economic Order Quantity (EOQ)?
EOQ is the optimal order quantity that minimizes total annual inventory cost — the sum of ordering cost and holding cost. It is computed as EOQ = √(2DS/H) where D is annual demand, S is ordering cost per order, and H is holding cost per unit per year. At EOQ, annual ordering cost exactly equals annual holding cost.
What is safety stock and when do I need it?
Safety stock is extra inventory held as a buffer against demand variability and supply uncertainty. It protects against stockouts when actual demand exceeds the average rate or when a supplier delivers late. Safety stock = z × σ × √L where z is the service-level z-score, σ is daily demand standard deviation, and L is lead time in days. Without demand variability (σ = 0), no safety stock is needed.
What does the reorder point (ROP) mean?
The reorder point is the inventory level at which you should place a new order so that it arrives before you run out. ROP = daily demand × lead time + safety stock. When your inventory drops to the ROP, place an order for EOQ units. The order will arrive, on average, just as your regular cycle stock runs out, with safety stock still available as a buffer.
What are the key assumptions of the EOQ model?
The classic EOQ model assumes constant and known annual demand, fixed and known ordering and holding costs, instantaneous replenishment (no lead time affects cycle stock in the basic model), no quantity discounts, and no backorders allowed. In practice these assumptions are approximations, but EOQ provides an excellent near-optimal baseline even when conditions deviate moderately.
How do service level and z-score relate to safety stock?
The service level is the probability of not stocking out during a replenishment cycle. A 95% service level means a 5% chance of stockout per order cycle. Each service level maps to a z-score from the standard normal distribution: 90% → z = 1.28, 95% → z = 1.645, 99% → z = 2.326. Higher service levels require more safety stock, increasing holding costs. The optimal service level trades off the cost of extra safety stock against the cost of stockouts.
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