TAHA Engineering Toolsby TAHA Knowledge Lab

Industrial & Manufacturing

Economic Order Quantity (EOQ) Calculator

The order size that minimises total ordering and holding cost.

Inputs

Cost of placing and receiving one order (paperwork, transport, inspection). Any currency.

Cost of keeping one unit in stock for a year (storage, capital, insurance, losses). Same currency as above.

Used only for the time between orders.

Result

Economic order quantity
200units
Orders per year
5orders
Time between orders
60working days
Total annual ordering + holding cost
100(currency)

Ordering about 200 units at a time keeps the combined ordering and holding cost lowest, at 100 per year in your currency. That means about 5 orders a year, one every 60 working days.

Educational estimate — check the assumptions below.

About this calculator

Ordering in large batches means fewer orders but more stock sitting on the shelf. Ordering in small batches means less stock but many more orders. The economic order quantity (EOQ) is the order size where these two costs balance and the total is lowest. It is a starting point for purchasing and inventory decisions.

Formula

Q* = √(2DS ÷ H)

Total cost = (D ÷ Q) × S + (Q ÷ 2) × H

D = annual demand (units), S = cost per order, H = holding cost per unit per year. At Q*, ordering cost equals holding cost.

Worked example

Annual demand 1000 units, cost per order 10, holding cost 0.50 per unit per year:

  • Q* = √(2 × 1000 × 10 ÷ 0.5) = √40 000 = 200 units
  • Orders per year = 1000 ÷ 200 = 5
  • Total cost = 5 × 10 + 100 × 0.5 = 50 + 50 = 100 per year
  • With 300 working days: one order every 60 days

Assumptions and limitations

  • Demand is steady and known, each order arrives complete and on time, and there are no stock-outs.
  • Cost per order and holding cost per unit are constant; quantity discounts are not considered.
  • Round the EOQ to a practical pack or pallet size. Total cost changes very little near the optimum.
  • EOQ does not include safety stock. Use a reorder point with safety stock for uncertain demand or lead time.

References

  • Harris (1913) / Wilson economic order quantity model, as presented in operations-management texts.