Calculate EOQ and EPQ to find the optimal order or production batch size, orders per year, cycle length, and annual inventory cost.

EOQ / EPQ Calculator

Enter your numbers below to find the optimal order (or production) quantity.

EOQ · Ordering
EPQ · Producing
Economic Order Quantity
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Epq (Economic Production Quantity) Formula

The following formula is used to calculate the Economic Production Quantity (EPQ). 

EPQ = sqrt((2 * D * S) / (H * (1 - (D / P))))

Variables:

  • EPQ is the Economic Production Quantity (units)
  • D is the demand rate (units per year, or per chosen time period)
  • S is the setup (or ordering) cost per batch/order ($)
  • H is the holding or storage cost per unit per year ($) (or per chosen time period)
  • P is the production rate (units per year, or per chosen time period)

To calculate the Economic Production Quantity, multiply twice the demand rate by the setup cost per batch. Divide this result by the product of the holding cost per unit per period and the difference between 1 and the ratio of the demand rate to the production rate. Finally, take the square root of the entire expression. (For the EPQ model to be valid, the production rate must be greater than the demand rate, i.e., P > D.)

What is a Epq (Economic Production Quantity)?

The Economic Production Quantity (EPQ) model is used in operations management and logistics to determine the optimum production lot size (batch size) that minimizes total inventory costs when inventory is replenished gradually through production (rather than arriving all at once). It considers factors such as demand rate, production rate, setup costs, and holding costs. The EPQ model is useful for businesses that produce their own inventory and need to balance the costs of setup and storage under a finite production rate.

How to Calculate Epq (Economic Production Quantity)?

The following steps outline how to calculate the Economic Production Quantity (EPQ).

  1. First, determine the demand rate (D) in units per year (or per chosen time period).
  2. Next, determine the setup or ordering cost per batch/order (S) in dollars.
  3. Next, determine the holding or storage cost per unit per year (H) in dollars (or per chosen time period).
  4. Next, determine the production rate (P) in units per year (or per chosen time period).
  5. Next, gather the formula from above: EPQ = sqrt((2 * D * S) / (H * (1 – (D / P))))
  6. Finally, calculate the Economic Production Quantity (EPQ).
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Demand rate (D) = 500 units per year

Setup cost per batch (S) = $100

Holding cost per unit per year (H) = $5

Production rate (P) = 1000 units per year

EPQ = sqrt((2 * 500 * 100) / (5 * (1 – (500 / 1000)))) = 200 units