Economic Order Quantity (EOQ) Calculator

What Economic Order Quantity (EOQ) means

Economic Order Quantity (EOQ) is a classic inventory-management equation that helps companies determine the optimal order size for replenishing inventory. It answers the fundamental question: how much should we order in a single batch to minimize the total combined costs of placing orders and holding physical stock?

In any inventory system, you face a trade-off between two opposing cost drivers:

• Ordering (Setup) Costs: Every time you place an order with a supplier, you incur fixed overheads—including freight, receiving labor, purchase-order processing, and quality inspections. To reduce these annual costs, you want to place fewer, larger orders.
• Holding (Carrying) Costs: Holding inventory ties up valuable capital, requires warehouse space, and risks shrinkage, damage, or obsolescence. To reduce these annual costs, you want to carry smaller inventory quantities, meaning more frequent, smaller orders.

The Economic Order Quantity is the model point where the sum of these two conflicting costs is minimized under the classic assumptions.

The EOQ formula and variable definitions

The classic Economic Order Quantity model uses this EOQ formula:

EOQ = √((2 × D × S) / H)

Where the variables are defined as:

• D (Annual Demand): The total volume of units sold or consumed per year. This must be stable and predictable.
• S (Ordering Cost): The fixed administrative and transactional cost incurred per order, completely independent of the quantity ordered.
• H (Annual Holding Cost per Unit): The cost to store and finance one unit of stock for one full year. This can be entered directly (Mode A) or derived (Mode B) as:
  H = Unit Purchase Cost × Annual Carrying-Cost Rate (%)

How to use the calculator

1. Select your preferred Calculation Mode using the switch at the top. Use Direct holding cost if you have a pre-calculated cost per unit per year. Use Derive holding cost to compute H based on unit pricing and your overall carrying rate percentage.
2. Enter your Annual demand in units and the fixed Ordering cost per order in your preferred currency.
3. Specify either the annual unit holding cost or your unit cost and carrying-cost rate depending on your active mode.
4. Optionally, enter your Current order quantity to compare your current inventory procurement policy with the EOQ estimate.
5. Enter Operating days per year if your business operates on a non-standard calendar (for example, 250 working days instead of 365) to get an order-interval estimate.

How to interpret ordering cost vs holding cost

A key mathematical property of the classic EOQ model is that the optimal point occurs where annual ordering cost is equal to annual holding cost.

If your calculated ordering cost is much higher than your holding cost, your batch sizes are too small, causing you to spend too much on purchasing overhead. Conversely, if holding cost dominates your annual bill, you are ordering too much at once and holding excess stock. The EOQ coordinates your order intervals to bring these forces into balance.

EOQ vs Reorder Point vs Safety Stock

Effective inventory planning requires answering three distinct questions, each addressed by a separate tool:

• EOQ Calculator (This tool): Answers how much to order in a replenishment cycle to minimize cost under stable conditions.
• Reorder Point Calculator: Answers when to order, specifying the exact inventory trigger level needed to cover transit times before the next batch arrives.
• Safety Stock Calculator: Determines the extra buffer stock needed to protect against random demand spikes or supplier delays.

Worked example

Let's examine a common retail scenario:

• Annual demand (D) = 12,000 units
• Ordering cost (S) = $75 per order
• Annual holding cost (H) = $4 per unit per year (derived from a $20 unit cost and 20% carrying rate)

Using the formula:

EOQ = √((2 × 12,000 × 75) / 4) = √(1,800,000 / 4) = √(450,000) ≈ 670.82 units.

For practical fulfillment, this rounds to a recommended order quantity of 671 units. At this optimum:

• The company places about 17.89 orders per year.
• Orders occur roughly every 20.4 operating days (on a 365-day year).
• Annual ordering cost = (12,000 ÷ 670.82) × $75 = $1,341.64.
• Annual holding cost = (670.82 ÷ 2) × $4 = $1,341.64.
• Total relevant annual cost = $2,683.28.

If the business was previously ordering 200 units at a time, its total cost was $4,900 annually. Moving to the EOQ size reduces the modeled ordering and holding costs by $2,216.72 per year, a 45.2% reduction.

Assumptions and limitations

The classic EOQ model is useful, but it is based on several simplifying assumptions:

• Predictable Demand: Demand is constant and stable throughout the year (no seasonal surges).
• Instant replenishment: Ordered stock arrives in one complete batch immediately when the stock level drops to its target.
• No Quantity Discounts: The unit purchase price is constant, regardless of order volume.
• No Stockouts: Lead times are reliable and no inventory stockouts occur.
• Safety Stock is Separate: Any extra buffers are handled as a standalone safety stock and are not factored into the basic EOQ calculation.

How EOQ fits with safety stock and reorder point

EOQ answers how much to order; the Safety Stock Calculator and Reorder Point Calculator answer when to order. See the Inventory Planning Formulas guide for one worked scenario that carries all four inventory formulas through together.