Economic Batch Quantity Calculator
Calculate Economic Batch Quantity step by step: √(2DS ÷ (H × (1 − D ÷ P))).
In short
Formula: EBQ = √(2 × D × S ÷ (H × (1 − D ÷ P))), where P = production rate.
What this calculator does
Calculate Economic Batch Quantity step by step: √(2DS ÷ (H × (1 − D ÷ P))). Worked example, questions and limitations included.
Use it to turn Currency (symbol only, never converted), Annual demand, Setup cost per batch, Holding cost per unit per year, and the other shown inputs into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this inventory calculation.
Inputs and what they mean
- Currency (symbol only, never converted)
- — choice value.
- Annual demand
- — number value.
- Setup cost per batch
- — number value.
- Holding cost per unit per year
- — number value.
- Annual production rate
- — number value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Economic production quantity model (Silver, Pyke and Thomas; ASCM dictionary).
Stock builds gradually during the run, so the batch is larger than the EOQ.
D and P must use the same time unit.
EBQ = √(2 × D × S ÷ (H × (1 − D ÷ P))), where P = production rate.
Inputs used: Currency (symbol only, never converted), Annual demand, Setup cost per batch, Holding cost per unit per year, Annual production rate.
Worked example
Machined part
- 1 − 10,000 ÷ 40,000 = 0.75.
- 2 × 10,000 × 200 ÷ (4 × 0.75) = 1,333,333.
- √ = 1,154.70 units.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Steady demand and production rate.
- One product per line.
- No setup time constraint.
- Results are planning estimates built only from the figures you enter. No prices, rates, demand patterns or service levels are built in, and the results are not supplier quotes or carrier rates.
- The result depends on the values you enter for this economic batch quantity calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Common questions
How is this different from EOQ?
EOQ assumes the whole order arrives at once; EBQ assumes it is produced over time while being consumed. Check the formula, example, and limitations on this page before using the result for a real inventory decision.
What if production barely exceeds demand?
The batch size grows very large — the line is effectively running continuously. Check the formula, example, and limitations on this page before using the result for a real inventory decision.
Does it include capacity limits?
No. Check total setup and run time with the capacity planning calculator.
How do I use the Economic Batch Quantity Calculator?
Enter the required values for Currency (symbol only, never converted), Annual demand, Setup cost per batch, Holding cost per unit per year, Annual production rate. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Economic Batch Quantity Calculator use?
EBQ = √(2 × D × S ÷ (H × (1 − D ÷ P))), where P = production rate. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Economic Batch Quantity Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Related tools
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