Cost Accounting · Material Costs

Economic Order Quantity (EOQ) Formula and Numericals

Updated 10 October 2026 · Fact-checked

Economic Order Quantity is the order size that gives the lowest total of ordering cost and carrying cost for a year. Use EOQ = √(2 × A × O ÷ C). With quantity discounts, compute total annual cost at each discount price and choose the lowest total.

Understand Economic Order Quantity (EOQ)

Every time you buy materials, you face two opposing costs. Ordering cost is the cost of placing and receiving an order. It does not change with the order size. Examples are purchase department expenses, stationery, transport paperwork and inspection. Carrying cost is the cost of holding stock. It rises with the quantity held. Examples are storage, insurance, obsolescence and interest on money locked up in stock.

If you order in small lots, you place many orders. Ordering cost is high and carrying cost is low. If you order in large lots, you place few orders. Ordering cost is low but carrying cost is high. EOQ is the lot size where the total of the two costs is lowest. At this point, annual ordering cost equals annual carrying cost.

Carrying cost is charged on the average stock, which is half of the order quantity (because stock falls steadily from Q to zero). That is why the formula has Q ÷ 2 in it.

EOQ rests on assumptions: demand is known and steady, the price is constant (no discounts), lead time is fixed, no stock-outs are allowed, the whole order arrives at once, and ordering and carrying costs are stable. Real life breaks these often. So treat EOQ as a guide, not an exact answer.

When the supplier offers quantity discounts, the purchase price changes with the order size. Now purchase cost must be included in the comparison, and the simple formula alone is not enough.

Key rules to remember

Economic Order Quantity: EOQ = √(2 × A × O ÷ C); A = annual consumption in units, O = ordering cost per order, C = carrying cost per unit per year. If carrying cost is a percentage, C = percentage × purchase price per unit.
Carrying cost per unit: C = carrying cost % × price per unit; Use this when the question gives carrying cost as a percentage of the stock value.
Number of orders per year: Number of orders = A ÷ EOQ; Gives how many orders you place in a year.
Annual ordering cost: (A ÷ Q) × O; Q is the order quantity used.
Annual carrying cost: (Q ÷ 2) × C; Based on average stock of Q ÷ 2.
Total inventory cost with discounts: Total cost = A × price + (A ÷ Q) × O + (Q ÷ 2) × C; Compute at each price level and pick the lowest total. Include purchase cost, as price differs between options.
EOQ condition: Annual ordering cost = Annual carrying cost at EOQ; A quick check of your answer.

How to solve Economic Order Quantity (EOQ) questions

Use this method for any EOQ question, with or without discounts.

1List the data: annual demand (A), cost per order (O), carrying cost (C) and price. Convert monthly or weekly demand into a yearly figure.
2Find C per unit per year. If it is a percentage, multiply it by the price per unit.
3Compute EOQ = √(2AO ÷ C) and round sensibly, as the question asks.
4If there are no discounts, add the number of orders, ordering cost, carrying cost and total cost as asked.
5If there are discounts, check each price level. Use the EOQ at that price only if it falls inside the quantity range. Otherwise use the minimum quantity of that range.
6For each valid quantity, prepare a table of purchase cost, ordering cost, carrying cost and total cost.
7Choose the quantity with the lowest total cost and state the conclusion in a line.
8State any assumption you made, such as carrying cost on average stock.

Quickest way: Quick EOQ and discount shortcut

When to use it: Use this for MCQs and for time-pressed numericals.

Write A, O and C in one line, then compute 2AO ÷ C before taking the root.
Simplify 2AO ÷ C to a manageable number, then take the square root, approximating if it is not a perfect square.
Verify by checking that (A ÷ Q) × O equals (Q ÷ 2) × C. If not, recheck.
For discounts, go slab by slab. If a slab's EOQ is feasible, use it. If it is infeasible, use the slab's minimum quantity (do not skip the slab). Compare total costs across all valid quantities.
At the EOQ, ordering cost equals carrying cost, so their total is twice the carrying cost: 2 × (Q ÷ 2) × C = Q × C. This shortcut holds only at the EOQ itself. At a discount slab's minimum quantity, ordering and carrying cost are not equal, so calculate each one separately and add them.

Common mistakes in Economic Order Quantity (EOQ)

Using monthly demand directly in the formula while ordering and carrying costs are yearly.
Students copy the first number they see.
Fix: Convert A to a yearly figure first and keep all inputs on a yearly basis.
Treating carrying cost percentage as the rupee value C.
The question says 10%, and students put 10 in the formula.
Fix: Multiply the percentage by the unit price to get C in rupees per unit per year.
Ignoring purchase cost in discount problems.
Students think EOQ only involves ordering and carrying costs.
Fix: Include A × price in the total cost, because price changes with the option.
Accepting an EOQ that lies outside the discount range.
Students compute EOQ at the lowest price and use it without checking the slab.
Fix: If the EOQ at a price is not within that slab, use the minimum quantity of the slab.
Charging carrying cost on the full order quantity.
Forgetting that stock falls gradually.
Fix: Use Q ÷ 2, the average stock.
Mixing up ordering and carrying costs, for example putting storage rent under ordering cost.
Both are inventory-related.
Fix: Ask: does it occur per order, or per unit held? Per order is ordering cost. Per unit held is carrying cost.

Worked examples

Example 1

A company uses 9,000 units of a material a year. Ordering cost is ₹200 per order. Carrying cost is ₹8 per unit per year. Calculate EOQ, number of orders, and total annual ordering and carrying cost.

Show the solution

A = 9,000; O = ₹200; C = ₹8.
EOQ = √(2 × 9,000 × 200 ÷ 8) = √(36,00,000 ÷ 8) = √4,50,000.
Check: 2 × 9,000 × 200 = 36,00,000. Divide by 8 = 4,50,000. √4,50,000 ≈ 670.8, so EOQ ≈ 671 units.
Number of orders = 9,000 ÷ 670.82 ≈ 13.416, so about 13.4 orders a year.
Ordering cost = 13.416 × 200 ≈ ₹2,683 (using EOQ 670.82).
Carrying cost = (670.82 ÷ 2) × 8 ≈ ₹2,683.
Total = ₹5,367 approx. (equals Q × C = 670.82 × 8 = ₹5,366.56).

Answer: EOQ ≈ 671 units; about 13.4 orders a year; ordering cost ≈ ₹2,683 and carrying cost ≈ ₹2,683; total ≈ ₹5,367.

Example 2

Annual demand is 4,000 units. Ordering cost is ₹100 per order. Carrying cost is 20% of the purchase price. The supplier's prices are: ₹50 per unit for orders below 500 units, and ₹48 per unit for orders of 500 units or more. Find the best order quantity.

Show the solution

At ₹50: C = 20% × 50 = ₹10. EOQ = √(2 × 4,000 × 100 ÷ 10) = √80,000 ≈ 282.84 units. This is below 500, so it is valid for the ₹50 price.
Cost at 282.84 units: purchase = 4,000 × 50 = ₹2,00,000. Ordering = (4,000 ÷ 282.84) × 100 = ₹1,414.21. Carrying = (282.84 ÷ 2) × 10 = ₹1,414.21. Total = ₹2,02,828.43.
At ₹48: C = 20% × 48 = ₹9.60. EOQ = √(800,000 ÷ 9.6) = √83,333.33 ≈ 288.68 units. This is below 500, so it is not valid. Use 500 units.
Cost at 500 units: purchase = 4,000 × 48 = ₹1,92,000. Ordering = (4,000 ÷ 500) × 100 = ₹800. Carrying = (500 ÷ 2) × 9.60 = ₹2,400. Total = ₹1,95,200.
Compare: ₹1,95,200 is lower than ₹2,02,828.

Answer: Order 500 units at a time to take the ₹48 price. Total annual cost is ₹1,95,200 against ₹2,02,828 at the EOQ of about 283 units.

Exam tips

Write the formula, then the substitution, then the answer. Step marks follow the working.
In discount questions, always present a comparison table with purchase, ordering, carrying and total cost.
For MCQs, check whether carrying cost is given as rupees or as a percentage before calculating.
Write the assumptions or limitations in two or three bullet points if the question asks for them. Typical points are constant demand, fixed price, fixed lead time and no stock-outs.
Keep the ordering versus carrying cost difference ready for short notes: ordering cost is per order and falls as order size rises; carrying cost is per unit held and rises with order size.

Practice questions from Material Costs

Economic Order Quantity (EOQ) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Economic Order Quantity (EOQ): frequently asked questions

What is the difference between ordering cost and carrying cost?

Ordering cost is incurred each time you place and receive an order, such as paperwork and inspection. Carrying cost is the cost of holding stock, such as storage, insurance and interest. Ordering cost per year falls as order size rises, while carrying cost per year rises.

How do I calculate EOQ with a quantity discount?

Find the EOQ at each price and check whether it lies within that price's quantity range. If not, use the minimum quantity of the range. Then calculate total annual cost, including purchase cost, for each valid quantity and choose the lowest.

What are the main assumptions of EOQ?

Demand is known and uniform, price is constant, lead time is fixed, no stock-outs are permitted and the whole order is delivered at once. Ordering cost per order and carrying cost per unit are also assumed to be constant.

What are the limitations of EOQ?

It depends on assumptions that rarely hold exactly, such as steady demand and fixed costs. It ignores quantity discounts unless adjusted, and cost estimates can be hard to make. It is a guide, not a precise rule.