EOQ Calculator
Calculate EOQ as √((2 × annual demand × ordering cost) / holding cost), then convert that order size into order cadence, lead-time demand, and annual inventory-cost tradeoffs for purchasing and replenishment planning.
EOQ Inputs
Enter annual demand, order cost, and holding cost to size each purchase order and review the working-day order cycle.
Quick Scenarios
EOQ Summary
Recommended order quantity
707 units
Exact EOQ before unit rounding: 707.11 units
Orders per year
14.14
Working days between orders
17.68
Lead-time demand
280 units
Annual relevant inventory cost
$1,414.21
At EOQ, ordering cost is about $707.11 per year and holding cost is about $707.11 per year, so the model is balancing the two cost pools instead of minimizing only one side.
One order covers roughly 17.68 working days of demand. Lead-time demand is 280 units, so the order cycle is about 2.53x the current lead-time window.
Detailed Breakdown
| Metric | Value |
|---|---|
| Annual demand | 10,000 units |
| Ordering cost per PO | $50 |
| Holding cost per unit/year | $2 |
| Lead time | 7 days |
| Working days per year | 250 |
| Daily demand | 40 units |
| Average cycle stock | 353.55 units |
| Annual ordering cost | $707.11 |
| Annual holding cost | $707.11 |
| Cost difference at EOQ | $0 |
Assumption notes
- Demand, ordering cost, and holding cost are treated as stable over the planning period.
- Relevant cost includes ordering plus holding cost, not total purchase spend.
- Lead-time demand is a base trigger without safety stock layered on top.
Current scenario highlights
- Recommended order size: 707 units
- Order cycle: about 17.68 working days
- Base trigger before safety stock: 280 units
Editorial & Review Information
Reviewed on: 2026-03-12
Published on: 2025-09-11
Author: LumoCalculator Editorial Team
What we checked: Formula math, example arithmetic, result interpretation, boundary guidance, and source accessibility.
Purpose and scope: This page supports order-sizing and replenishment planning. It is not a substitute for a full ERP lot-sizing policy, supplier contract review, or service-level model.
How to use this review: Confirm that demand, ordering cost, and holding cost all describe the same period, then use the EOQ result as a baseline before adding safety stock, supplier minimums, or cash constraints.
Use Scenarios
Purchasing cadence reset
Use EOQ when buyers are ordering by habit, such as monthly or quarterly, and need a cleaner economic baseline for how large each PO should be.
Cost-pressure review
Recalculate when freight, receiving labor, or carrying cost assumptions change. EOQ helps show whether higher logistics costs justify fewer, larger orders or a leaner cycle stock position.
Order-size versus stock-health check
EOQ sizes the order, but it does not show whether the SKU family is already moving too slowly or too quickly. Compare the output with the Inventory Turnover Calculator before applying one rule across the whole assortment.
Formula Explanation
1) EOQ formula
EOQ = sqrt((2 × annual demand × ordering cost) / holding cost)
The formula increases order size when annual demand or order cost rises and decreases order size when holding cost rises. It is solving for the quantity that balances the cost of ordering too often against the cost of carrying too much stock.
2) Ordering cost (S)
Annual ordering cost = (annual demand / EOQ) × ordering cost per PO
Ordering cost should capture the effort or expense triggered by each order, such as PO processing, vendor communication, receiving, and inspection. The lower this cost is, the more often you can afford to place smaller orders.
3) Holding cost (H)
Annual holding cost = (EOQ / 2) × holding cost per unit per year
Holding cost is the annual carrying cost of one unit in stock. It usually combines storage, insurance, capital tied up in inventory, obsolescence, and handling. Higher holding cost pushes EOQ down because each extra unit on the shelf becomes more expensive to keep.
4) Order size versus order timing
Lead-time demand = (annual demand / working days per year) × lead time days
EOQ answers how much to order, not when to release the next PO. Lead-time demand gives the base trigger for when stock is likely to be consumed while the next order is in transit. If you need a reorder trigger that includes demand variability or service-level buffering, continue with the Reorder Point Calculator.
How to Read the Result
EOQ is a planning baseline
Treat the quantity as the economic starting point, then adjust for supplier minimums, pack sizes, shelf-life rules, and cash constraints instead of assuming the exact rounded unit count must always be used.
Annual cost excludes purchase spend
The result shows relevant inventory cost, meaning ordering plus holding cost only. Purchase spend is usually the same regardless of order count unless discounts or price breaks change the economics.
Cost balance matters more than any one number
At EOQ, annual ordering cost and annual holding cost should be close to each other. If one side is much larger than the other in your model, the input assumptions probably need another review.
Lead time still drives service risk
A clean EOQ does not protect against stockouts by itself. Long or unstable lead times still require reorder-point logic and, when appropriate, safety stock on top of the economic order size.
Example Cases
Case 1: Regional accessories retailer
Inputs
- Annual demand: 12,000 units
- Ordering cost: $75
- Holding cost: $3 per unit/year
- Lead time: 8 days
Computed Results
- Recommended order size: 775 units
- Orders per year: 15.49
- Lead-time demand: 384 units
- Relevant annual cost: $2,323.79
Interpretation
The business does not need monthly bulk orders. The economics support a mid-sized, repeatable replenishment cycle that keeps cash tied up in stock lower without creating a daily ordering burden.
Decision Hint
Keep the EOQ-sized cycle, then layer supplier fill-rate and safety-stock rules onto the reorder trigger before changing order size.
Case 2: Industrial distributor with longer lead times
Inputs
- Annual demand: 48,000 units
- Ordering cost: $180
- Holding cost: $4.5 per unit/year
- Lead time: 21 days
Computed Results
- Recommended order size: 1,960 units
- Orders per year: 24.49
- Lead-time demand: 3,876.92 units
- Relevant annual cost: $8,818.16
Interpretation
EOQ still supports a relatively frequent order cadence because the item moves quickly. The real operational pressure comes from the long lead-time window, not from a need to carry an unusually large cycle stock.
Decision Hint
Use the EOQ for order size, but stress-test supplier reliability because late inbound shipments would hit the base trigger quickly.
Case 3: Slower-moving service parts
Inputs
- Annual demand: 6,000 units
- Ordering cost: $40
- Holding cost: $6 per unit/year
- Lead time: 30 days
Computed Results
- Recommended order size: 283 units
- Orders per year: 21.21
- Lead-time demand: 720 units
- Relevant annual cost: $1,697.06
Interpretation
Higher annual carrying cost pushes the recommended order size down even though lead time is long. This is a common pattern for service parts where holding too much inventory is expensive relative to the number of orders placed.
Decision Hint
Check whether supplier minimums or service-level targets force a larger order than EOQ suggests, then quantify the cost trade-off rather than guessing.
Boundary Conditions
Sources & References
- Good Calculators - EOQ (Economic Order Quantity) Calculator - Formula framing, EOQ assumptions, and worked-example structure for order-size decisions.
- Zoho Inventory - EOQ Calculator & Formula - Definitions for demand, ordering cost, holding cost, and practical EOQ planning context.
- Omni Calculator - EOQ Calculator - Example-led explanation of EOQ meaning, total-cost balance, and adjacent inventory decisions.