What is EOQ in inventory management?

Economic Order Quantity (EOQ) is the order size that minimizes the sum of annual ordering and holding costs for a single item with constant demand. It tells you how many units to order each time you replenish stock.

What is the EOQ formula?

The basic EOQ formula is Q* = sqrt(2DS / H), where Q* is the optimal order quantity, D is annual demand, S is ordering cost per order, and H is annual holding cost per unit.

When should I not use EOQ?

EOQ is less appropriate when demand is highly variable, lead times are long or uncertain, quantity discounts are significant, or capacity and cash constraints dominate ordering decisions. In those cases, more advanced inventory models or planning systems are preferred.

Does EOQ include purchase cost?

In the basic EOQ model, unit purchase cost is assumed constant and does not affect the optimal order quantity. You can still compute total spend as purchase cost plus ordering and holding costs, but EOQ itself is driven by ordering and holding costs only.

EOQ Calculator – Economic Order Quantity with Holding & Ordering Costs

What is EOQ (Economic Order Quantity)?

Economic Order Quantity (EOQ) is a classic inventory management formula that tells you how many units to order each time you replenish stock in order to minimize the sum of:

Ordering costs – admin, shipping, setup, and processing costs per order.
Holding (carrying) costs – capital cost, storage, insurance, shrinkage, and obsolescence per unit per year.

EOQ is widely taught in operations management, corporate finance, and supply chain courses. In practice, it is most useful as a benchmark or sanity check for order sizes, especially for stable, high-volume items.

EOQ formula

Basic EOQ formula:

\[ Q^* = \sqrt{\frac{2DS}{H}} \]

$Q^*$ = optimal order quantity (units per order)
$D$ = annual demand (units / year)
$S$ = ordering cost per order (currency / order)
$H$ = annual holding cost per unit (currency / unit / year)

At the EOQ point, annual ordering cost equals annual holding cost:

\[ \text{Ordering cost} = \text{Holding cost} \] \[ S \cdot \frac{D}{Q^*} = H \cdot \frac{Q^*}{2} \]

Related formulas our calculator uses

Number of orders per year:

\[ N = \frac{D}{Q^*} \]

Cycle time (time between orders):

\[ T = \frac{\text{working days per year}}{N} \]

Annual ordering cost:

\[ C_{\text{order}} = S \cdot \frac{D}{Q^*} \]

Annual holding cost:

\[ C_{\text{hold}} = H \cdot \frac{Q^*}{2} \]

Total relevant inventory cost:

\[ C_{\text{total}} = C_{\text{order}} + C_{\text{hold}} \]

Reorder point (if lead time is known):

\[ \text{ROP} = d \cdot L = \left(\frac{D}{\text{working days per year}}\right) \cdot L \]

where $d$ is average daily demand and $L$ is lead time in days.

How to use this EOQ calculator

Enter annual demand (D)
Use forecasted demand for the next 12 months for a single SKU or item.
Enter ordering cost per order (S)
Include internal admin time, supplier order fees, transport, and setup costs.
Enter annual holding cost per unit (H)
This is often estimated as a percentage of unit cost (e.g. 20–30% of C per year).
Optionally enter unit purchase cost (C)
This lets the tool show total spend including purchase cost, but it does not change EOQ.
Set working days per year
Default is 250. Adjust if your operation runs more or fewer days.
Optionally enter lead time
If you know supplier lead time in days, the calculator estimates a simple reorder point.
Click “Calculate EOQ”
The tool will display EOQ, number of orders per year, days between orders, and cost breakdown.

Worked EOQ example

Suppose you manage a part with:

Annual demand $D = 10{,}000$ units
Ordering cost $S = \$75$ per order
Annual holding cost $H = \$2.50$ per unit

EOQ is:

\[ Q^* = \sqrt{\frac{2DS}{H}} = \sqrt{\frac{2 \cdot 10{,}000 \cdot 75}{2.5}} = \sqrt{\frac{1{,}500{,}000}{2.5}} = \sqrt{600{,}000} \approx 774.6 \text{ units} \]

So you would order about 775 units per order.

Number of orders per year:

\[ N = \frac{D}{Q^*} \approx \frac{10{,}000}{774.6} \approx 12.9 \text{ orders/year} \]

If you operate 250 days per year, days between orders:

\[ T = \frac{250}{12.9} \approx 19.4 \text{ days} \]

Annual ordering and holding costs at EOQ:

\[ C_{\text{order}} = S \cdot \frac{D}{Q^*} \approx 75 \cdot 12.9 \approx \$968 \] \[ C_{\text{hold}} = H \cdot \frac{Q^*}{2} \approx 2.5 \cdot \frac{774.6}{2} \approx \$968 \]

As expected, ordering and holding costs are roughly equal at EOQ.

Assumptions and limitations of the EOQ model

The classic EOQ model is simple because it relies on strong assumptions:

Demand is known, constant, and spread evenly over time.
Lead time is known and constant.
No stockouts or backorders are allowed.
Unit purchase cost is constant (no quantity discounts).
Ordering cost per order and holding cost per unit are constant.
Each item is managed independently (no capacity or budget constraints).

In real-world supply chains, these assumptions rarely hold perfectly. However, EOQ is still useful as:

A baseline for order quantity decisions.
A way to understand the trade-off between ordering more often vs. holding more stock.
A teaching tool for inventory and operations management.

When EOQ is most useful

High-volume, stable-demand items (A-class SKUs).
Situations where ordering cost and holding cost are reasonably well known.
Single-location, single-echelon inventory systems.
As a cross-check against ERP or MRP system recommendations.

When EOQ may not be appropriate

Highly seasonal or intermittent demand.
Long, uncertain, or variable lead times.
Supplier quantity discounts or price breaks.
Strong capacity, cash, or storage constraints.
Multi-echelon networks where upstream and downstream inventories interact.

Frequently asked questions

Does EOQ change if my supplier offers discounts?

The basic EOQ formula assumes a constant unit price. If you have quantity discounts, you should use an EOQ with quantity discounts approach: compute EOQ for each price tier, adjust to the nearest feasible quantity, and compare total annual cost (including purchase cost) across tiers.

How do I estimate holding cost (H)?

A common shortcut is to estimate holding cost as a percentage of unit cost:

Holding cost rate (e.g. 20–30% per year) × unit cost (C) = H.
For example, if C = $50 and holding rate = 25%, then H = 0.25 × 50 = $12.50 per unit per year.

Do companies actually use EOQ in practice?

Many modern companies rely on ERP/MRP systems and more advanced inventory models. However, EOQ is still widely used as a rule-of-thumb, for policy setting (e.g. minimum order quantities), and as a sanity check on system-generated order quantities.

Can I use EOQ for multiple items ordered together?

The basic EOQ model is single-item. For joint ordering of multiple SKUs with shared ordering costs, more advanced models (like joint replenishment) are needed. You can still apply EOQ per item as an approximation, but it will not fully capture shared ordering cost savings.

EOQ Calculator (Economic Order Quantity)

Economic Order Quantity Calculator

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