Some EOQ questions give carrying cost as a flat amount per unit. Others say something like “carrying cost is 15% per annum of purchase price”. This post walks through the EOQ formula with carrying cost percentage in two solved examples in B.Com style, starting with the extra step most mistakes come from. Each answer comes from our EOQ calculator engine.

What EOQ balances

Economic order quantity is the order size that keeps the yearly cost of placing orders plus the yearly cost of holding stock as low as possible. Large orders mean fewer orders but more stock sitting in the warehouse. Small orders mean less stock but more ordering cost. EOQ is the point between the two where the total is lowest.

Carrying cost covers the cost of capital tied up in stock, storage, insurance and the risk of damage or obsolescence. Because most of these scale with the value of the stock, textbooks often express carrying cost as a percentage of the item’s purchase price. Our EOQ guide covers these components in more detail.

EOQ formula with carrying cost percentage

Convert the percentage into an amount per unit per year first. Then use the usual Wilson formula.

Economic order quantity

C = Purchase price per unit × Carrying cost % per year
EOQ = √( 2 × A × O ÷ C )

Here A is annual demand in units and O is the cost of placing one order. Once you have EOQ, the number of orders a year is A ÷ EOQ, annual ordering cost is (A ÷ EOQ) × O, annual carrying cost is (EOQ ÷ 2) × C, and the time between orders is 365 ÷ number of orders.

Where the formula comes from

If each order is for Q units, the firm places A ÷ Q orders a year, so annual ordering cost is (A ÷ Q) × O. Stock falls steadily from Q to zero between deliveries, so average stock is Q ÷ 2 and annual carrying cost is (Q ÷ 2) × C. Total cost is the sum of the two.

Ordering cost falls as Q rises and carrying cost rises with Q. Total cost is lowest where the two are equal: (A ÷ Q) × O = (Q ÷ 2) × C. Rearranging gives Q² = 2AO ÷ C, and taking the square root gives the EOQ formula. That is why the equal-costs check in the examples below works.

The formula assumes demand is known and steady through the year, each order arrives in full, the price does not change with order size and there is no safety stock. If a supplier offers a discount for larger orders, EOQ is only the starting point: compare total cost, including the purchase price, at EOQ and at each discount quantity.

Solved numericals

Example 1: carrying cost at 20% of purchase price

Question: A firm uses 20,000 units of a component a year. Each order costs $250 to place. The purchase price is $50 per unit and carrying cost is 20% per annum of inventory value. Calculate (a) EOQ, (b) number of orders per year and (c) total annual inventory cost at EOQ.

Solution:

  1. Carrying cost per unit per year, C = $50 × 20% = $10.
  2. EOQ = √(2 × 20,000 × $250 ÷ $10) = √1,000,000 = 1,000 units.
  3. Number of orders = 20,000 ÷ 1,000 = 20 a year, about every 18.25 days.
  4. Annual ordering cost = 20 × $250 = $5,000.
  5. Annual carrying cost = (1,000 ÷ 2) × $10 = $5,000.

Answer: (a) EOQ = 1,000 units; (b) 20 orders a year; (c) total inventory cost = $5,000 + $5,000 = $10,000.

Example 2: carrying cost at 15% of a higher unit price

Question: Annual demand for a raw material is 14,400 units. Ordering cost is $150 per order, the purchase price is $80 per unit and carrying cost is 15% per annum of purchase price. Find EOQ, the number of orders, the time between orders and the total cost of ordering and carrying.

Solution:

  1. C = $80 × 15% = $12 per unit per year.
  2. EOQ = √(2 × 14,400 × $150 ÷ $12) = √360,000 = 600 units.
  3. Number of orders = 14,400 ÷ 600 = 24. Time between orders = 365 ÷ 24 = 15.21 days.
  4. Annual ordering cost = 24 × $150 = $3,600.
  5. Annual carrying cost = (600 ÷ 2) × $12 = $3,600.

Answer: EOQ = 600 units, 24 orders a year (about every 15.21 days), total ordering and carrying cost = $7,200.

In both examples, annual ordering cost equals annual carrying cost at EOQ. That is a quick check on your arithmetic: if the two figures differ by more than rounding, recheck C. A common slip is to use the percentage itself (20 or 15) as C, which gives an EOQ that is far too small.

Notice also how price feeds into the answer. In Example 2 the unit is more expensive, so each unit costs more to hold, which pushes EOQ down relative to demand. If the supplier raised the price with no change in the carrying percentage, C would rise and EOQ would fall. That is the mechanism behind the “what happens if price rises” part some questions add at the end.

Common mistakes students make

  • Putting the carrying percentage straight into the formula instead of converting it to an amount per unit first.
  • Using monthly demand with an annual carrying cost, or the other way round. Both must cover the same period.
  • Charging carrying cost on the full EOQ instead of on average stock of EOQ ÷ 2.
  • Adding the purchase cost of the goods to “total inventory cost” when the question asks only for ordering and carrying cost.
  • Forgetting the square root after working out 2AO ÷ C.

Check your answer

Enter annual demand, ordering cost and the carrying cost per unit (price × percentage) in the EOQ calculator. It shows EOQ, orders per year, the cost split and the days between orders, so you can match each line of your working. To see how quickly stock moves at that order size, try the inventory turnover calculator.

Last updated: 23 October 2026