What is the Economic Order Quantity formula?

EOQ = sqrt(2 * D * S / H), where D is annual demand in units, S is the fixed cost to place one order and H is the annual holding cost per unit. The formula (developed by Ford W. Harris in 1913 and popularised by R. H. Wilson) finds the order size at which the sum of ordering costs and holding costs is minimised.

Why are ordering cost and holding cost equal at the EOQ?

The total inventory cost curve is a U-shape. As order size rises, holding cost rises (more average stock) while ordering cost falls (fewer orders per year). The minimum of the combined curve occurs where both cost lines cross — i.e. where they are exactly equal. The EOQ formula solves for this crossing point analytically.

How do I calculate the reorder point?

ROP = (annual demand / 365) x lead time in days. This is the stock level at which you should place a new order so that the shipment arrives just as you run out. Add a safety stock buffer if your demand or lead time is variable.

What holding rate should I use?

Most operations use 20–30% of unit cost per year as a rule of thumb. This covers the opportunity cost of capital (often 8–15%), warehouse space and handling (5–10%), obsolescence and shrinkage (2–5%) and insurance (1–2%). Industries with perishables or high obsolescence risk (electronics, fashion) use higher rates.

Does EOQ work for all businesses?

The classic EOQ model assumes constant demand, a fixed ordering cost and a fixed linear holding cost with no quantity discounts. It is a useful baseline for stable-demand products. For seasonal demand, supplier quantity discounts or items ordered in lot sizes, extensions like the EOQ with discounts or the lot-sizing model (Wagner-Whitin) are more appropriate — but the basic EOQ is still a valuable starting point.

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Economic Order Quantity (EOQ) Calculator

Every business that holds physical stock faces the same tension: order too infrequently and you spend a lot on each delivery; order too often and warehousing costs mount up. The Economic Order Quantity (EOQ) is the mathematically optimal order size that resolves this tension — the exact batch size at which your combined ordering and holding costs are as low as they can be.

How it works

The EOQ formula was derived independently by Ford W. Harris (1913) and later popularised by R. H. Wilson. It models total annual inventory cost as two competing components:

Total ordering cost = (D / Q) × S — the number of orders placed per year multiplied by the fixed cost of each order.
Total holding cost = (Q / 2) × H — the average stock on hand (half the order quantity, assuming demand is steady) multiplied by the annual cost to hold one unit.

Both terms depend on order quantity Q, but in opposite directions: a larger Q reduces ordering cost but increases holding cost. The total cost function is a convex curve with a single minimum. Setting its derivative to zero and solving for Q gives:

EOQ = sqrt(2 × D × S / H)

At this quantity, total ordering cost and total holding cost are exactly equal — a geometric consequence of the two cost functions being mirror images at their crossing point.

Derived metrics calculated for you:

Orders per year = D / EOQ
Cycle time = 365 / (orders per year) — average days between orders
Average inventory = EOQ / 2 — the expected stock level between deliveries
Reorder Point (ROP) = (D / 365) × lead time — how many units you need on hand when you place the next order

Worked example

A hardware wholesaler sells 1,200 widgets per year. Each purchase order costs £50 (admin, freight, goods-in processing). Widgets cost £20 each and the business applies a 20% annual holding rate, giving a holding cost of £4.00 per unit per year.

Plugging into the formula:

EOQ = sqrt(2 × 1200 × 50 / 4)
    = sqrt(120,000 / 4)
    = sqrt(30,000)
    ≈ 173 units

Annual cost breakdown at EOQ:

Component	Calculation	Cost
Ordering cost	(1200 / 173) × £50 = 6.93 orders × £50	£346.41
Holding cost	(173 / 2) × £4 = 86.6 units × £4	£346.41
Total		£692.82

Note that ordering cost and holding cost are identical at the EOQ — this equality is always the case and serves as a quick sanity-check on your numbers.

With a 7-day lead time the reorder point is (1200 / 365) × 7 ≈ 23 units — place a new order when stock drops to 23 widgets and the delivery will arrive just as stock runs out.

What happens if you order a different quantity?

Order size	Orders/year	Ordering cost	Holding cost	Total cost
100 units	12	£600	£200	£800
173 units (EOQ)	6.9	£346	£346	£693
250 units	4.8	£240	£500	£740
400 units	3	£150	£800	£950

Ordering at either extreme costs significantly more than the EOQ. The U-shaped total cost curve is relatively flat near the minimum, which means small deviations from EOQ have modest cost impact — but the benefit of finding the optimum over ad hoc guesswork compounds across many SKUs and years.