EOQ Calculator
Find the order size that keeps your ordering and holding costs as low as possible, how often to order, and when to reorder.
Admin time, delivery charge per order, receiving and checking. Not the price of the stock.
Needed for holding as a % and for total cost with purchases.
Storage, insurance, money tied up, damage and out-of-date stock. 15–30% of unit cost a year is common.
Use 250–260 if stock only moves on working days. Daily demand, lead time and days between orders use this.
The lower price applies to the whole order once you buy at least this many. Each break is tested.
Must be faster than demand. Price breaks don't apply to a production run.
The smallest order your supplier accepts.
See what it costs you compared with the best order size.
Cost curve and other order sizes
| Order size | Orders a year | Ordering | Holding | Cost a year | vs best |
|---|
How your order quantity is worked out
EOQ = √(2 × yearly demand × cost per order ÷ holding cost per unit a year).
- 1
Yearly demand
12,000 a year
- 2
Holding cost a unit
20% × $20= $4 a year
- 3
Best order size
2 × 12,000× $60 ÷ $4√ = 600 units
- 4
Orders and cost
12,000 ÷ 600 = 20$1,200+ $1,200= $2,400 a year
Read more: the formula, a worked example, reorder point, price breaks and production runs
The economic order quantity (EOQ) is the order size that keeps the yearly cost of placing orders plus the cost of holding stock as low as possible. Order small and often and you pay for lots of orders; order big and rarely and you pay to store lots of stock. The EOQ is the balance point.
The formula
yearly demand (D) = demand × periods in a year
holding cost (H) = holding % × unit cost (or money per unit a year)
EOQ = √(2 × D × cost per order ÷ H)
orders a year = D ÷ order size
days between orders = days in year ÷ orders a year
ordering cost = orders a year × cost per order
holding cost = order size ÷ 2 × H
total with purchases = ordering + holding + D × unit price
reorder point = daily demand × lead time + safety stock
safety stock = z × √(lead time × daily variation² + daily demand² × lead-time variation²)
EPQ = √(2 × D × set-up cost ÷ (H × (1 − demand rate ÷ production rate)))
Worked example
A shop sells 12,000 units a year. Each order costs $60 to place, each unit costs $20, and holding stock costs 20% of its value a year, so holding one unit costs 20% × $20 = $4 a year.
EOQ = √(2 × 12,000 × $60 ÷ $4) = √(1,440,000 ÷ 4) = √360,000 = 600 units. That is 12,000 ÷ 600 = 20 orders a year, one every 365 ÷ 20 = 18.25 days. Ordering costs 20 × $60 = $1,200 and holding costs 600 ÷ 2 × $4 = $1,200 (the average stock is half an order), so the total is $2,400 a year. With the stock itself (12,000 × $20 = $240,000) the total is $242,400.
Reorder point and safety stock
Daily demand is 12,000 ÷ 365 = 32.88 units. With a 7-day lead time you use 32.88 × 7 = 230.14 units while you wait, so with no safety stock you reorder when stock falls to 231. If daily demand varies with a standard deviation of 8 units and you want a 95% service level (z = 1.645), safety stock = 1.645 × 8 × √7 = 1.645 × 21.17 = 34.81, about 35 units, costing about 34.81 × $4 = $139 a year to hold. The reorder point becomes 230.14 + 34.81 = 264.95, so reorder at 265.
| Service level | 50% | 75% | 80% | 85% | 90% | 95% | 97.5% | 98% | 99% | 99.5% | 99.9% |
|---|---|---|---|---|---|---|---|---|---|---|---|
| z-score | 0.000 | 0.674 | 0.842 | 1.036 | 1.282 | 1.645 | 1.960 | 2.054 | 2.326 | 2.576 | 3.090 |
The service level here is the chance of not running out during one lead time (cycle service level). Going from 95% to 99% raises z from 1.645 to 2.326, so safety stock grows by about 41%.
Quantity discounts (price breaks)
Say the supplier charges $20 a unit, $19 for orders of 1,000 or more, and $18.50 for 2,500 or more, with holding at 20% of the price paid. Test each price:
- $20: EOQ = 600, which fits. Cost = $240,000 + $1,200 + $1,200 = $242,400.
- $19: EOQ = √(1,440,000 ÷ 3.80) = 615.6, below 1,000, so raise it to 1,000. Cost = $228,000 + 12 orders × $60 ($720) + 500 × $3.80 ($1,900) = $230,620.
- $18.50: EOQ = 623.9, raised to 2,500. Cost = $222,000 + 4.8 orders × $60 ($288) + 1,250 × $3.70 ($4,625) = $226,913.
The cheapest is to order 2,500 at $18.50, saving $15,487 a year, even though holding cost almost quadruples. Check you have the space and that the stock won't go out of date first.
Production runs (EPQ)
If you make the item at 100 a day while selling 32.88 a day, stock only builds up at the difference, so the most you hold is a run × (1 − 32.88 ÷ 100) = 67.1% of it. EPQ = 600 ÷ √0.6712 = 732 units per run, taking 7.3 days to make and peaking at about 491 units in stock.
Pack sizes and minimum orders
If the item comes in cases of 48, 600 rounds up to 13 cases = 624 units. That costs $2,401.85 a year instead of $2,400, only $1.85 more. The cost curve is flat near the bottom: ordering 25% more or less than the EOQ adds only about 2.5% to these costs, so rounding to a sensible pack size is fine.
When EOQ fits, and when it doesn't
- It assumes steady demand, a fixed cost per order and a fixed holding cost. Seasonal items, fashion and short-life food need shorter planning.
- Recheck it when prices, demand or delivery charges change.
- Holding cost is the hardest number. If you're unsure, try 15%, 25% and 35% to see how much the answer moves (it moves with the square root, so less than you'd think).
Standard EOQ (Harris–Wilson), EPQ and normal-distribution safety stock formulas. Results are a guide for planning, not a promise; real lead times and demand can swing more than a normal curve suggests.
Common questions
How do you calculate economic order quantity?
Multiply 2 by your yearly demand and by the cost of placing one order, divide by the cost of holding one unit for a year, then take the square root. With 12,000 units a year, $60 an order and $4 a unit a year to hold: 2 × 12,000 × $60 ÷ $4 = 360,000, and √360,000 = 600 units per order.
What is holding cost in EOQ?
It is what it costs to keep one unit in stock for a year: storage space, insurance, the money tied up in stock, damage, theft and stock that goes out of date. Many businesses use 15% to 30% of the unit cost a year. At 20% of a $20 item, holding one unit costs $4 a year.
Why are ordering cost and holding cost equal at the EOQ?
Bigger orders mean fewer orders, so ordering cost falls, but you keep more stock, so holding cost rises. The total is lowest where the two meet. In the example, 20 orders × $60 = $1,200 of ordering cost and an average of 300 units × $4 = $1,200 of holding cost, $2,400 in all.
How do I work out the reorder point and safety stock?
Reorder point = daily demand × lead time in days + safety stock. Safety stock = z × the standard deviation of daily demand × √lead time. For about 32.9 units a day, a 7-day lead time, a 95% service level (z = 1.645) and a daily standard deviation of 8, safety stock is about 35 and you reorder at 265 units.
Should I take a bulk discount instead of ordering the EOQ?
Test each price break: find the best order size at each price, push it up to the break quantity if it falls short, then compare total yearly cost including what you pay for the stock. In the example, ordering 2,500 at $18.50 costs $226,913 a year against $242,400 for 600 at $20, so the discount wins.
What is EPQ, the production order quantity?
If you make the item yourself, stock builds up slowly while you produce and are also using it, so you never hold the full batch. The EPQ divides the holding cost by (1 − demand rate ÷ production rate). Making 100 a day against 32.9 a day of demand raises the best run from 600 to about 732 units.
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