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Cost and Management Accounting · Unit & Batch Costing

Economic Batch Quantity (EBQ): Formula and Calculation

Updated 4 October 2026 · Fact-checked

Economic Batch Quantity is the batch size that gives the lowest total of set-up cost and carrying cost per year. Use EBQ = √(2DS ÷ C), where D is annual demand, S is set-up cost per batch and C is carrying cost per unit per year. Then find batches and total cost.

Understand Economic Batch Quantity (EBQ)

In batch costing, you make products in lots. Each time you start a new batch, you incur a set-up cost: machine setting, tooling, first-piece inspection, paperwork. This cost is the same whether the batch is small or large.

If batches are small, you set up many times a year. Total set-up cost is high. If batches are large, you set up rarely, but you hold more stock for longer. Total carrying cost (interest on funds, storage, insurance) is high.

The Economic Batch Quantity (EBQ) is the batch size where these two costs balance and their total is minimum. At EBQ, annual set-up cost equals annual carrying cost.

EBQ vs EOQ: The logic and formula are the same. EOQ applies to purchased material, where you pay an ordering cost per order. EBQ applies to goods you manufacture, where you pay a set-up cost per batch. Treat set-up cost in EBQ like ordering cost in EOQ.

The basic formula assumes constant demand and a batch that arrives all at once. If the question gives a production rate and demand rate, so stock builds up gradually, read the question carefully and follow the method it implies.

Key rules to remember

Economic Batch Quantity
EBQ = √(2 × D × S ÷ C)
D = annual demand (units), S = set-up cost per batch (₹), C = carrying cost per unit per year (₹).
Carrying cost per unit when given as a percentage
C = Cost per unit × carrying cost % per year
Use this when the question says carrying cost is, say, 10% of unit cost.
Number of batches per year
Number of batches = D ÷ EBQ
Round only if the question asks you to.
Total set-up cost
(D ÷ Q) × S
Q is the batch size.
Total carrying cost
(Q ÷ 2) × C
Average stock is half the batch size.
Total relevant cost
Set-up cost + Carrying cost
At EBQ the two parts are equal.

How to solve Economic Batch Quantity (EBQ) questions

Use this order for any EBQ question. It keeps units consistent and shows each step for marks.

  1. 1Write down D, S and C from the question. Check D is annual and C is per unit per year.
  2. 2If carrying cost is a percentage, convert it to rupees per unit per year.
  3. 3If set-up cost is given as a total for several items, or per hour or per shift, convert it to cost per batch.
  4. 4Substitute in EBQ = √(2DS ÷ C) and compute the value.
  5. 5Find the number of batches per year as D ÷ EBQ.
  6. 6If asked, compute total set-up cost, total carrying cost and their sum. At EBQ the two should match.
  7. 7State the answer with units, and add a one-line conclusion or comparison if the question asks for it.

Quickest way: Fast EBQ under time pressure

When to use it: Use for MCQs and for the first part of written answers where only EBQ and number of batches are asked.

  1. Compute 2 × D × S first, then divide by C, then take the square root.
  2. For MCQs, test the option: square it and check that Q² × C equals 2DS.
  3. Check that the answer is sensible: higher set-up cost raises EBQ, higher carrying cost lowers it.
  4. In written answers, write the formula, the substitution and the result on separate lines. Then add batches per year and total cost only if asked.
  5. If a comparison with the current batch size is asked, compute total cost for both sizes using (D ÷ Q) × S + (Q ÷ 2) × C.

Common mistakes in Economic Batch Quantity (EBQ)

  • Using monthly demand with an annual carrying cost.

    The question gives data in mixed periods and students plug in numbers as printed.

    Fix: Convert everything to one period, usually a year, before using the formula.

  • Forgetting to convert carrying cost from a percentage into rupees per unit.

    Students put 10 or 0.10 directly into C.

    Fix: Multiply the unit cost by the percentage first. For example, 10% of ₹50 gives C = ₹5.

  • Using total set-up cost instead of set-up cost per batch.

    The question may give total set-up cost for a past period.

    Fix: Divide total set-up cost by the number of batches to get S per batch.

  • Calculating total carrying cost as Q × C.

    Students forget that stock falls from Q to zero, so average stock is Q ÷ 2.

    Fix: Always use (Q ÷ 2) × C.

  • Rounding EBQ too early and then finding that set-up and carrying costs do not match.

    Square roots rarely come out whole.

    Fix: Keep the exact value for later steps unless the question states otherwise, and round only the final answer.

  • Mixing up EBQ and EOQ terms.

    The formulas look identical.

    Fix: Use set-up cost per batch for manufactured items and ordering cost per order for purchased items.

Worked examples

Example 1

A company makes 24,000 units of a component a year. Set-up cost is ₹800 per batch. Carrying cost is ₹3 per unit per year. Find the EBQ, the number of batches and the total relevant cost at EBQ.

Show the solution
  1. D = 24,000 units, S = ₹800, C = ₹3.
  2. EBQ = √(2 × 24,000 × 800 ÷ 3).
  3. 2 × 24,000 × 800 = 3,84,00,000. Divide by 3 to get 1,28,00,000.
  4. √1,28,00,000 = 3,578 units approximately (3,577.7).
  5. Number of batches = 24,000 ÷ 3,577.7 = 6.71 batches approximately.
  6. Set-up cost = 6.71 × 800 = ₹5,367 approximately. Carrying cost = (3,577.7 ÷ 2) × 3 = ₹5,367 approximately.
  7. Total relevant cost = ₹10,733 approximately.

Answer: EBQ is about 3,578 units. Batches per year are about 6.7. Total relevant cost at EBQ is about ₹10,733.

Example 2

Annual demand for a product is 10,000 units. Set-up cost per batch is ₹500. Unit cost is ₹40 and carrying cost is 25% of unit cost per year. Find the EBQ. Then compare the total relevant cost at EBQ with that at a batch size of 2,000 units.

Show the solution
  1. C = 25% × ₹40 = ₹10 per unit per year.
  2. EBQ = √(2 × 10,000 × 500 ÷ 10).
  3. 2 × 10,000 × 500 = 1,00,00,000. Divide by 10 to get 10,00,000. √10,00,000 = 1,000 units.
  4. At EBQ: batches = 10,000 ÷ 1,000 = 10. Set-up cost = 10 × 500 = ₹5,000.
  5. Carrying cost at EBQ = (1,000 ÷ 2) × 10 = ₹5,000. Total = ₹10,000.
  6. At Q = 2,000: batches = 10,000 ÷ 2,000 = 5. Set-up cost = 5 × 500 = ₹2,500.
  7. Carrying cost at Q = 2,000 = (2,000 ÷ 2) × 10 = ₹10,000. Total = ₹12,500.
  8. Extra cost of the 2,000 batch size = ₹12,500 − ₹10,000 = ₹2,500.

Answer: EBQ is 1,000 units with 10 batches a year, and total relevant cost is ₹10,000. A batch size of 2,000 units costs ₹12,500, so it costs ₹2,500 more per year than EBQ.

Exam tips

  • Read what the question calls cost: only set-up and carrying costs are relevant. Ignore the purchase or production cost per unit except to compute a percentage carrying cost.
  • In descriptive answers, show the formula, substitution and result line by line. Step marks are awarded even if the arithmetic slips.
  • Questions often combine EBQ with a batch cost sheet. Compute EBQ first, then spread set-up cost over the batch to find cost per unit.
  • For MCQs, square your option and check it against 2DS ÷ C. It is faster than redoing the full calculation.
  • Check units at the end: EBQ is in units, total cost in rupees.

Practice questions from Unit & Batch Costing

Economic Batch Quantity (EBQ) in other exams

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

Economic Batch Quantity (EBQ): frequently asked questions

What is the EBQ formula in CA Intermediate?

EBQ = √(2DS ÷ C). D is annual demand, S is set-up cost per batch and C is carrying cost per unit per year. It gives the batch size with the lowest total of set-up and carrying costs.

What is the difference between EBQ and EOQ?

EOQ is for purchased materials and uses ordering cost per order. EBQ is for items you produce and uses set-up cost per batch. The formula and logic are the same.

Why is carrying cost multiplied by half the batch size?

Stock starts at the full batch size and falls to zero before the next batch, if demand is steady. The average stock held is therefore half the batch size.

Should I round off the EBQ?

Keep the exact value while calculating and round only the final answer, unless the question asks for whole units. Early rounding can make set-up and carrying costs appear unequal.