The Square Root Behind the EOQ Formula
The economic order quantity formula is EOQ = √(2DS/H), where D is annual demand in units, S is the fixed cost of placing one order, and H is what one unit costs to hold for a year. The tool derives H for you as unit cost × holding rate, so an $8 item at 25% carries a $2.00 per-unit annual holding charge. No pre-multiplying, no unit-conversion traps.
The square root shapes every result that follows. Doubling demand to 24,000 units lifts the optimal batch only 41%, from 775 to 1,095 units, because batch size grows with the square root of scale. Fast-moving SKUs justify surprisingly frequent ordering, while slow movers cluster into a few large buys per year — the formula produces both behaviors from the same equation.
At the EOQ, annual ordering cost and annual holding cost land exactly on top of each other — $774.60 each in the worked example below. Total relevant cost equals D×S/Q + Q/2×H, and that curve bottoms out precisely where the two terms cross. That balance, first published by Ford Harris in 1913, is the entire point of the model.
Ordering Cost vs Holding Cost
Every purchase order drags a batch of fixed work behind it: requisition approval, PO entry, supplier communication, receiving, inspection, and invoice matching. That stack typically runs $25 to $150 per order for small businesses. Order 12 times a year at $50 each and you spend $600 on paperwork alone. Treat it like any average fixed cost calculator input and measure it from actual AP data, not guesses.
Holding cost runs the other direction. Capital tied up in stock earns its next-best return elsewhere, and on top of that sit storage space, insurance, shrinkage, and obsolescence. Most operations land between 20% and 30% of unit value per year. The $8 item at the default 25% rate costs $2.00 per unit per year to keep on the shelf.
Bigger batches spread ordering cost thinner but raise average stock to Q/2. The trade-off is forgiving near the optimum: ordering 20% above EOQ adds only 1.67% to total cost ($25.82 here), while halving or doubling the batch each adds a flat 25% ($387.30). Precision matters far less than escaping the 2,000-unit habit that costs $750.81 extra per year.
Reading the Results: A Worked Example
With the defaults — 12,000 units of annual demand, $50 per order, $8 unit cost, 25% holding rate — the tool returns an EOQ of 775 units. That means 15.5 orders per year, a fresh PO every 24 days, and $1,549.19 in combined ordering and holding cost. Purchase spend of $96,000 stays constant no matter how you slice the deliveries.
The current order size of 2,000 units costs $2,300 per year: just $300 of ordering spread over six POs, but $2,000 of holding on an average stock of 1,000 units. Moving to 775-unit batches cuts average stock to 387 units and frees $4,901.61 of cash currently parked on shelves, on this one SKU alone.
Notice what the formula ignores: the $96,000 of purchases. Batch size changes when cash leaves and how much return you forfeit on stored value, not the annual COGS calculator total. That exclusion is deliberate — including purchase cost at a flat price would push every answer toward the largest possible order and hide the real trade-off.
The Reorder Point: When to Place the Order
EOQ answers how much to buy; the reorder point answers when to trigger the buy. Multiply daily demand by supplier lead time: 32.9 units per day × 14 days = 461 units on hand when the next PO should go out. The tool computes this automatically from your lead time entry, right alongside the batch size itself.
That 461-unit trigger assumes demand runs perfectly flat. Real demand wiggles, so most buyers add safety stock on top of the lead-time demand figure — classic EOQ deliberately leaves that buffer out. Getting the lead time itself right matters just as much; the lead time calculator breaks it into processing, production, transit, and queue components you can measure separately.
Compare lead time to your 24-day order cycle. When the supplier takes longer than the cycle, multiple POs will be open at once and the reorder point still holds. When lead time is short, stock swings between the reorder point and the reorder point plus one batch — 461 to 1,236 units in this example — without ever touching zero.
What the Classic EOQ Model Ignores
The 1913 model assumes demand is known and constant, which no real product enjoys. Seasonal items distort it twice: off-season orders sit longer, and peak-season demand burns through batches faster. The practical fix is running the formula on annualized peak-quarter demand, or computing separate summer and winter order quantities for strongly seasonal lines.
Quantity discounts, minimum order quantities, and pallet multiples all sit outside the basic formula too. A supplier forcing 3,000-unit batches can still be the cheaper option once price breaks enter the math, covered in the next section. The model also says nothing about shelf-life caps or warehouse slot limits that hard-cap batch size regardless of cost.
Obsolescence-heavy stock deserves an inflated holding rate. Electronics and fashion can realistically carry 35% or more once markdown risk counts, and at that rate this example's EOQ falls from 775 to 655 units. Measure where you actually stand with the ending inventory calculator and the days inventory outstanding calculator before committing to new batch sizes.
Quantity Discounts: Ordering More Than EOQ on Purpose
Suppose the supplier offers 2% off for orders of 3,000 units or more. Purchase spend drops from $96,000 to $94,080, saving $1,920 a year. Relevant cost rises from $1,549.19 to $3,140.00 at the bigger batch — an extra $1,590.81 — so the discount nets out to $329.19 ahead. The bigger order wins on total cost.
The method generalizes: price total cost, purchases included, at the EOQ and at each price-break minimum, then pick the cheapest. A useful screen is that the discount percentage must beat the added carrying cost it triggers. Checking the unit price calculator math on volume tiers keeps that comparison honest.
Minimum order quantities follow the same logic in reverse. If an MOQ sits far above your EOQ, either absorb the carrying cost and confirm the sales volume justifies it, or negotiate. Suppliers move on MOQ more often than on unit price, and a markup calculator view of their side sometimes reveals room you didn't expect.
Where EOQ Fits in the Cash Conversion Cycle
Inventory occupies the middle leg of the cash conversion cycle: inventory days plus receivable days minus payable days. Ordering 775 instead of 2,000 units cuts average stock from 1,000 to 387 units, which trims inventory days and pulls cash back toward the business. Run the full picture with the cash conversion cycle calculator.
The $4,901.61 released on this single SKU compounds across a catalog. Two hundred similar items free roughly $980,000 — enough to retire a credit line or fund a product launch without borrowing. That cash shows up where it counts in the cash flow calculator view of the business.
Purchasing budgets gain from the same discipline. Once batch sizes and order counts per SKU are set, projected purchase timing maps cleanly into a business budget calculator by month, and supplier payment terms slot into the payable-day leg of the cycle analysis.
Running EOQ Across a Whole Catalog
Apply the formula per SKU, then let ABC classification set the effort level. A-items — the 20% of products driving 80% of value — deserve fresh EOQ runs and explicit safety stock. C-items can be ordered in coarse bulk rounds; their carrying cost barely registers next to the admin time of tuning them.
Inputs drift, so refresh them. Cutting order cost from $50 to $25 drops the optimum from 775 to 548 units, and a holding rate moving from 25% to 35% pulls it to 655. Any supplier renegotiation, storage change, or rate move past roughly 10% deserves a re-run — the square root softens the swing but does not erase it.
Treat every EOQ output as a negotiation starting point rather than a fixed rule. Batch-size talks with suppliers open doors to price breaks, consignment terms, and smaller MOQs that pure math cannot see. Combine the batch sizes with reorder triggers and a periodic stock-days review, and purchasing runs itself between reviews.