Economic Lot Size Calculator

The Economic Lot Size Calculator calculates the optimal order quantity that minimises total inventory costs using demand, ordering, holding, and lead time inputs.

About the Economic Lot Size Calculator

Economic lot size, often called Economic Order Quantity (EOQ), is the number of units you order each time to minimize your total annual inventory cost. That cost typically includes what you spend placing orders and what you spend carrying inventory. The calculator pinpoints the quantity where those two forces balance.

Use it when you face steady demand and consistent cost behavior. It fits retail, wholesale, manufacturing, and e-commerce operations. It is also a solid baseline for planning when you do not have quantity discounts or tight capacity constraints. Even if your situation is more complex, this gives you a defensible starting point for negotiations and budgeting.

The tool accepts a few core inputs and returns the recommended lot size, cycle time, number of orders per year, and a basic cost breakdown. You can also estimate a reorder point using your lead time and daily demand. If your environment involves in-house production, you can model a production lot size variant as well.

Equations Used by the Economic Lot Size Calculator

The calculator applies standard inventory formulas. These focus on finding the order quantity that minimizes the sum of ordering and holding costs under steady demand. Below are the key relationships.

• Economic Order Quantity (EOQ): Q* = sqrt((2 × D × S) / H)
• Total relevant annual cost: TRC(Q) = (D/Q) × S + (Q/2) × H
• Number of orders per year: N = D / Q
• Cycle time between orders (years): T = Q / D
• Reorder point: ROP = d × L, where d is demand per day and L is lead time (days)
• Economic Production Quantity (EPQ) variant: Qp* = sqrt((2 × D × S × p) / (H × (p − d))) when production rate p > demand rate d

These formulas assume steady demand, known costs, and no stockouts by design. At the optimal quantity, annual ordering cost equals annual holding cost. The EPQ formula adjusts the optimal lot size when inventory builds gradually during production.

The Mechanics Behind Economic Lot Size

Economic lot sizing balances two opposing cost curves. Ordering more often raises ordering cost but lowers average inventory and holding cost. Ordering less often does the opposite. The optimal point is where these forces meet at the lowest total cost.

• Ordering cost covers every batch you buy or make, including administrative time and setup.
• Holding cost reflects storage, insurance, capital cost, obsolescence, and shrinkage per unit per year.
• Demand is assumed constant, so inventory forms a predictable sawtooth over time.
• Lead time does not change the optimal lot size, but it affects when you place the order.
• In production settings, inventory rises during runs, so the EPQ adjusts for the partial build-up rate.

Once you identify the economic lot size, you schedule orders to arrive just as inventory dips to your reorder point. If demand or costs shift, reevaluate the inputs and recalculate to keep costs in line.

Inputs and Assumptions for Economic Lot Size

Provide a few operational and cost inputs. The calculator uses them to compute the optimal quantity and a cost breakdown. Enter realistic values based on recent data, and align units across all fields.

• Annual demand (D): total units needed per year.
• Order/setup cost (S): cost per order or setup event, regardless of order size.
• Holding cost per unit per year (H): carrying cost for one unit for one year.
• Working days per year: used to compute daily demand for the reorder point.
• Lead time (days): time from placing an order to receiving it, for the reorder point.
• Optional: Production rate (units/year) for EPQ; Unit purchase cost (for spend reporting only).

Watch for edge cases. If H is very small, EOQ can get very large. If S is near zero, EOQ can get very small. Avoid zeros or negative values. If demand is seasonal, use a representative average or run separate scenarios for each season.

How to Use the Economic Lot Size Calculator (Steps)

Here’s a concise overview before we dive into the key points:

1. Enter your annual demand in units for the product or SKU.
2. Enter your per-order or per-setup cost, including labor and overhead.
3. Enter holding cost per unit per year, covering capital, space, and risk.
4. Enter working days per year and lead time in days to enable the reorder point.
5. Optional: Enter a production rate if you make the item, not only buy it.
6. Run the calculation and review the recommended lot size, cycle time, and cost breakdown.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

A regional retailer sells 24,000 units per year of a fast-moving item. The order cost is $75 per order. Holding cost is $2 per unit per year. EOQ = sqrt((2 × 24,000 × 75) / 2) = sqrt(1,800,000) ≈ 1,342 units. They place about 24,000 / 1,342 ≈ 18 orders per year. If they operate 365 days and lead time is 7 days, daily demand is 24,000 / 365 ≈ 65.8 units, so ROP ≈ 461 units. What this means: Order about 1,342 units each cycle and reorder when stock hits roughly 461 units.

A manufacturer consumes 120,000 units yearly. Setup cost is $1,000. Holding cost is $6 per unit per year. EOQ = sqrt((2 × 120,000 × 1,000) / 6) = sqrt(40,000,000) ≈ 6,325 units. If they produce in-house at 600,000 units per year, EPQ = sqrt((2 × 120,000 × 1,000 × 600,000) / (6 × (600,000 − 120,000))) = sqrt(50,000,000) ≈ 7,071 units. The EPQ is higher because stock accumulates gradually during production. What this means: Target about 6,325 if buying, or around 7,071 per run if producing.

Assumptions, Caveats & Edge Cases

EOQ is a simplified model that works well when core assumptions hold. Understand the limits before you adopt it as policy. Use the calculator to explore deviations and build scenarios that reflect your operation.

• Steady demand, constant lead time, and no stockouts by design.
• Instant replenishment for EOQ; gradual build-up for EPQ only when p > d.
• Fixed ordering and holding costs; no quantity discounts included in the base model.
• No resource or capacity constraints; check warehouse limits and cash availability.
• Perishability and obsolescence are captured only through H; short shelf life may dominate.

If the output is unrealistic, revisit assumptions. Large EOQ may signal low H or high setup cost. Very small EOQ may signal the opposite. Where discounts exist, run a price-break analysis alongside the EOQ to compare total costs at break points.

Disclaimer: This tool is for educational estimates. Consider professional advice for decisions.

Units Reference

Consistent units keep your results meaningful. Use the same time basis for demand, holding cost, and production rates. If you mix annual and monthly figures, convert them before running the calculation.

To read the table, match your data to the symbols used by the formulas. If your figures are monthly, multiply by 12 to annualize demand or adjust holding cost accordingly before running the calculation.

Troubleshooting

If your EOQ seems too large or too small, start by reviewing the holding cost and setup cost. These two inputs drive most of the result. Confirm that demand is annual and that your currency units are consistent across all fields.

• Unusually large EOQ: H may be underestimated; include capital cost and risk.
• Unusually small EOQ: S may be too low; include all ordering or setup effort.
• ROP looks odd: Check working days and lead time units; use daily demand.
• EPQ error: Ensure production rate exceeds demand rate.

After correcting inputs, rerun the calculator. Then test a few scenarios by varying H and S by 10–20% to see sensitivity and set a practical order policy.

FAQ about Economic Lot Size Calculator

Does EOQ change if my lead time changes?

EOQ does not change with lead time, but your reorder point does. Longer lead time increases ROP because you must cover more days of demand.

Should I include purchase price in the EOQ calculation?

Purchase price does not affect the EOQ unless you have quantity discounts. It is useful for total spend reporting, not for the optimal quantity in the base model.

What if my demand is seasonal?

Use EOQ for each season with its own demand and costs, or use an annual average and add safety stock. Scenario testing can show the cost impact.

How precise should I be when rounding the EOQ?

Round to a practical order size that matches case packs, pallet quantities, or run sizes. Cost near the optimum is usually flat, so small rounding is fine.

Key Terms in Economic Lot Size

Economic Lot Size

The order quantity that minimizes the sum of annual ordering and holding costs under steady demand and fixed cost assumptions.

Holding Cost

The annual cost to carry one unit in inventory, including capital costs, storage, insurance, shrinkage, and obsolescence.

Order or Setup Cost

The fixed cost incurred each time you place an order or set up production, independent of the number of units in the batch.

Demand Rate

The pace at which units are required over time, often shown as units per year or units per day for reorder point calculations.

Reorder Point

The inventory level that triggers a new order so stock arrives before depletion, typically daily demand times lead time.

Cycle Time

The time between the start of one order and the next, computed as lot size divided by annual demand.

Economic Production Quantity

An extension of EOQ used when items are produced internally and inventory builds during production at a rate below the production rate.

Safety Stock

Extra inventory held to buffer against variability in demand or lead time, not included in the basic EOQ but often added to the ROP.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• Wikipedia: Economic Order Quantity (EOQ)
• MIT OpenCourseWare: Inventory Models and EOQ
• Investopedia: Economic Order Quantity Explained
• APICS Magazine: Economic Order Quantity Revisited
• ScienceDirect Topic Overview: Economic Order Quantity

These points provide quick orientation—use them alongside the full explanations in this page.