Economic Order Quantity (EOQ)

Excel Formulas › Retail & Inventory

All versionsSQRT

EOQ finds the order size that minimizes total ordering and holding cost — the classic inventory optimization. A square-root formula balances big batches (fewer orders) against carrying cost.

Quick formula: EOQ from demand, order cost, holding cost:
=SQRT(2 * annual_demand * order_cost / holding_cost)
Square root of (2 × demand × cost-per-order ÷ cost-to-hold-one-unit) is the cost-minimizing order size.

Functions used (tap for the full reference guide):

SQRT

The example

D=1200, order $50, hold $3.

AB
1ItemValue
2Inputs—
3EOQ~200 units

The formula

The formula:

=SQRT(2 * B2 * B3 / B4) // √(2DS / H)

How it works

How it works:

  1. Annual demand (D), cost per order (S), and holding cost per unit per year (H) are the inputs.
  2. The formula SQRT(2DS/H) balances ordering cost (favors big orders) against holding cost (favors small ones).
  3. The result is the order quantity with the lowest total cost.
  4. Number of orders per year is D / EOQ; time between orders is EOQ / D × 365.

EOQ is a starting point, not gospel. It assumes steady demand and constant costs. Real orders round to case or pallet quantities, and supplier discounts for larger orders can shift the optimum. Use EOQ to anchor the decision, then adjust for minimums and price breaks.

Try it: interactive demo

Live demo

Annual demand, order cost, holding cost.

EOQ · ~ orders/yr

Variations

Orders per year

Frequency:

=annual_demand / EOQ

Total annual cost

At EOQ:

=D/EOQ*S + EOQ/2*H

Cycle time (days)

Between orders:

=EOQ / annual_demand * 365

Pitfalls & errors

Consistent units. Demand and holding cost must be on the same annual basis.

Steady-demand assumption. EOQ assumes stable demand; lumpy demand needs other models.

Round sensibly. Adjust to case/pallet sizes and supplier minimums.

Practice workbook

📊
Download the free Economic Order Quantity (EOQ) practice workbook
An EOQ sheet with the orders-per-year, total-cost, and cycle-time variants, plus 4 challenges with answers. No sign-up required.

Frequently asked questions

How do I calculate EOQ in Excel?
Use =SQRT(2 * annual_demand * order_cost / holding_cost). It gives the order size that minimizes total ordering and holding cost.
How many orders per year does EOQ imply?
Divide annual demand by EOQ: =annual_demand / EOQ gives the optimal number of orders.
What are EOQ's limitations?
It assumes steady demand and constant costs. Adjust for case sizes, supplier minimums, and quantity discounts.

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Related formulas: Reorder point · Powers & roots · Inventory turnover

Function references: SQRT