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Cost Accounting · Batch Costing

Economic Batch Quantity (EBQ) Formula and Numericals

Updated 10 October 2026 · Fact-checked

Economic Batch Quantity is the batch size that gives the lowest total of set-up cost and carrying cost for a product made in batches. 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. If the production rate matters, use the adjusted formula.

Understand Economic Batch Quantity (EBQ)

In batch costing, a factory makes products in lots. Each time it starts a new lot, it must set up machines, adjust tools and often test the first pieces. This is the set-up cost. It is incurred once per batch, whatever the batch size.

So large batches look attractive: fewer set-ups, lower total set-up cost. But large batches create large stocks of finished goods. Holding stock costs money through interest on funds blocked, storage, insurance and obsolescence. This is the carrying cost (or holding cost), and it rises with batch size.

The two costs pull in opposite directions. Set-up cost per year falls as batch size rises. Carrying cost per year rises as batch size rises. The Economic Batch Quantity (EBQ) is the batch size where the total of both is lowest. At that point, annual set-up cost equals annual carrying cost.

EBQ is the production-side twin of EOQ. EOQ applies when you buy materials from outside and the whole order arrives at once. EBQ applies when you make the item yourself, and the set-up cost replaces the ordering cost. If the item is produced and used or sold at the same time, stock builds up gradually, and a modified formula using the production rate gives a larger EBQ.

The per-unit carrying cost can be given directly in rupees, or as a percentage of the unit cost. In the second case, work out the rupee amount first.

Key rules to remember

Basic EBQ formula
EBQ = √(2 × D × S ÷ C)
D = annual demand (units), S = set-up cost per batch, C = carrying cost per unit per year. Assumes the whole batch is added to stock at once.
Carrying cost from a percentage
C = carrying cost % × cost per unit
Use when the question gives carrying cost as a percentage of unit cost.
EBQ with production rate
EBQ = √[(2DS ÷ C) × (p ÷ (p − d))]
p = production rate, d = demand or usage rate, with p > d. p and d must be in the same time unit (both daily, or both annual). Use when stock builds up gradually during production.
Number of batches per year
Number of batches = D ÷ EBQ
Round only if the question asks; the exact value is used for cost comparison.
Total annual cost of set-up and carrying
Total cost = (D ÷ Q) × S + (Q ÷ 2) × C
Q = batch size. Valid for the basic model with average stock of Q ÷ 2. At EBQ, both parts are equal.
Minimum total annual cost at EBQ
Minimum total annual cost = √(2 × D × S × C)
This is the total of annual set-up cost and annual carrying cost at the EBQ. Applies to the basic model only.

How to solve Economic Batch Quantity (EBQ) questions

Follow the same sequence for any EBQ question. It keeps units consistent and earns step marks.

  1. 1List the data: annual demand D, set-up cost per batch S, carrying cost per unit per year C. Note if production rate or usage rate is given.
  2. 2Convert everything to a yearly basis. If demand is monthly, multiply by 12. If carrying cost is a percentage, convert it to rupees per unit.
  3. 3Choose the formula. Use the basic formula if the batch arrives at once. Use the production-rate version if production and demand run together.
  4. 4Substitute the values and show the working inside the square root before taking the root.
  5. 5Compute EBQ and state the unit (units per batch).
  6. 6Find the number of batches per year (D ÷ EBQ) and, if asked, total set-up cost and total carrying cost.
  7. 7Check that annual set-up cost equals annual carrying cost in the basic model. State the conclusion in one line.

Quickest way: Square-root shortcut with a check

When to use it: For MCQs and short numericals using the basic model.

  1. Compute 2 × D × S first, then divide by C.
  2. Find the square root. Use perfect squares: break numbers into factors like 100, 400, 10,000.
  3. Cross-check: (D ÷ EBQ) × S should equal (EBQ ÷ 2) × C.
  4. For options-based MCQs, square each option and compare with 2DS ÷ C instead of calculating the root.

Common mistakes in Economic Batch Quantity (EBQ)

  • Using monthly demand with an annual carrying cost.

    Students copy the first number they see without checking the time basis.

    Fix: Convert D and C to the same period, normally a year, before substituting.

  • Forgetting to convert a carrying cost percentage into rupees.

    The formula needs C in rupees per unit, but the question gives a percentage.

    Fix: Multiply the percentage by cost per unit first, then use that amount as C.

  • Applying the basic formula when the production rate is given.

    Students memorise only √(2DS ÷ C) and ignore the stem's data on production and usage.

    Fix: If production rate and demand rate are both given, use the modified formula with p ÷ (p − d), keeping p and d in the same time unit.

  • Treating total cost as only set-up cost or only carrying cost.

    Students stop after finding EBQ and answer a cost comparison wrongly.

    Fix: Calculate both parts: (D ÷ Q) × S and (Q ÷ 2) × C, then add them.

  • Confusing EBQ with EOQ in the explanation.

    The formulas look identical.

    Fix: Write that S is a production set-up cost per batch for EBQ, whereas EOQ uses ordering cost per purchase order.

Worked examples

Example 1

A factory makes a component in batches. Annual demand is 12,000 units. Set-up cost is ₹300 per batch. Carrying cost is ₹6 per unit per year. Find the EBQ, the number of batches per year, and the total annual set-up and carrying cost.

Show the solution
  1. D = 12,000 units; S = ₹300; C = ₹6.
  2. EBQ = √(2 × 12,000 × 300 ÷ 6).
  3. 2 × 12,000 × 300 = 72,00,000. Divided by 6 = 12,00,000.
  4. EBQ = √12,00,000 = 1,095 units approximately (1,095.4).
  5. Number of batches = 12,000 ÷ 1,095.4 = 10.95, about 11 batches per year.
  6. Annual set-up cost = 10.95 × ₹300 = ₹3,286 approximately.
  7. Annual carrying cost = (1,095.4 ÷ 2) × ₹6 = ₹3,286 approximately.
  8. Total cost = ₹6,573 approximately, which equals √(2 × 12,000 × 300 × 6) = √4,32,00,000 = ₹6,572.7.

Answer: EBQ ≈ 1,095 units; about 11 batches a year; set-up cost ≈ ₹3,286 and carrying cost ≈ ₹3,286; total ≈ ₹6,573.

Example 2

A company needs 7,200 units of a part a year. Each unit costs ₹50 to make. Set-up cost is ₹400 per batch. Carrying cost is 16% of unit cost per year. Compare the total annual cost of set-up and carrying for a batch size of 600 units with that of the EBQ.

Show the solution
  1. D = 7,200; S = ₹400; unit cost = ₹50.
  2. C = 16% × ₹50 = ₹8 per unit per year.
  3. EBQ = √(2 × 7,200 × 400 ÷ 8).
  4. 2 × 7,200 × 400 = 57,60,000; ÷ 8 = 7,20,000.
  5. EBQ = √7,20,000 = 848.5 units approximately.
  6. Total cost at EBQ = √(2 × 7,200 × 400 × 8) = √4,60,80,000 = ₹6,788 approximately (6,788.2).
  7. At Q = 600: set-up cost = (7,200 ÷ 600) × 400 = 12 × 400 = ₹4,800.
  8. Carrying cost = (600 ÷ 2) × 8 = 300 × 8 = ₹2,400.
  9. Total at 600 = ₹7,200.
  10. Extra cost of using 600 = 7,200 − 6,788 = ₹412 approximately.

Answer: EBQ ≈ 849 units with total cost ≈ ₹6,788. A batch of 600 costs ₹7,200, which is about ₹412 more per year.

Exam tips

  • Write the formula, then substitute. Even if the arithmetic slips, you keep method marks.
  • Read carefully whether carrying cost is in rupees or a percentage of cost. This is the most common trap in MCQs.
  • If the question gives batch cost data such as direct materials and labour per batch, EBQ may only need set-up and carrying costs. Do not include production costs that stay the same for all batch sizes.
  • Show the proof that annual set-up cost equals annual carrying cost at EBQ. It supports your answer and takes one line.
  • In theory questions, state the assumptions: constant demand, fixed set-up cost per batch and constant carrying cost per unit.

Practice questions from 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 CMA Intermediate?

The basic formula is EBQ = √(2DS ÷ C). D is annual demand, S is set-up cost per batch and C is carrying cost per unit per year. If production and demand happen together, use the version with the production rate.

What is the difference between EBQ and EOQ?

EOQ is used for purchased materials ordered from suppliers and balances ordering cost against carrying cost. EBQ is used for items produced in batches and balances set-up cost against carrying cost. The basic formula has the same form, but the cost meaning of S differs.

How do I calculate EBQ when carrying cost is given as a percentage?

Convert the percentage to a rupee amount by multiplying it by the cost per unit. Use that figure as C in the formula. Also check that demand is on an annual basis.

Why are set-up cost and carrying cost equal at EBQ?

Total cost is lowest where the falling set-up cost per year meets the rising carrying cost per year. In the basic model, this meeting point is the EBQ. It is a useful check on your answer.