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HoldingCost

Economic order quantity calculator

The order size that minimises the total annual cost of ordering plus holding inventory.

Calculator logistics

Logic updated April 2026

This calculator computes the Economic Order Quantity — the order size that minimises total inventory cost (ordering plus holding) for a constant demand stream. It uses the classical Wilson formula and surfaces alternative order sizes so you can see how sensitive total cost is to deviations from the optimum.

How this is calculated

Formula 

EOQ = √(2 × D × S / H)   where D = annual demand, S = cost per order, H = annual holding cost per unit

Step-by-step

  1. Multiply annual demand (D) by the fixed cost per order (S), then double the result
  2. Divide by the annual holding cost per unit (H)
  3. Take the square root — that's the Economic Order Quantity
  4. Total ordering cost at EOQ = (D ÷ EOQ) × S = number of orders per year × order cost
  5. Total holding cost at EOQ = (EOQ ÷ 2) × H = average inventory × per-unit holding cost
  6. At EOQ, total ordering cost equals total holding cost — that's where total cost is minimised
Rounding mode
ROUND_HALF_UP
Precision
20-digit internal precision (Decimal.js), rounded to 2 decimal places for display
Logic last reviewed

Assumptions & limitations

What this calculator assumes

  • Demand is constant and known over the planning horizon (365 days)
  • Lead time is constant — orders arrive in a single batch
  • No quantity discounts — unit price is independent of order size
  • No stockouts permitted — orders are timed to avoid them
  • Holding cost per unit is a linear function of average inventory

What this calculator doesn’t account for

  • Real demand is rarely constant — seasonal swings invalidate the model
  • Doesn't model volume discounts that reward larger order sizes
  • Doesn't include capacity constraints (storage limits, supplier order minimums)
  • Doesn't factor in safety stock needs
  • Doesn't model demand uncertainty (a stochastic EOQ variant exists for that)

Worked example

A retailer sells 12,000 units a year, pays $50 to place each order, and incurs $4 per unit per year in holding cost.

Input Value
Annual demand 12,000 units
Cost per order $50
Annual holding cost per unit $4

EOQ: ~548 units — Orders per year: ~22 — Total annual cost: ~$2,191

EOQ = √(2 × 12,000 × 50 ÷ 4) = √300,000 ≈ 548 units per order. Number of orders per year: 12,000 ÷ 548 ≈ 22. Total ordering cost: 22 × $50 = $1,100. Total holding cost: (548 ÷ 2) × $4 = $1,096. Total: $2,196 (rounding noise). The two costs are roughly equal — that's the EOQ property. Ordering 1,000 units at a time would push total cost to ~$2,600; ordering 200 at a time pushes it to ~$3,400.

Frequently asked questions

What is economic order quantity?

The order quantity that minimises total inventory cost. Below EOQ, ordering cost dominates (you're ordering too often). Above EOQ, holding cost dominates (orders are too large, sitting in the warehouse). At EOQ, the two costs are equal and total cost is at its minimum. The model originated in 1913 (Harris) and remains a foundational supply-chain heuristic.

What are the assumptions of the EOQ model?

Constant demand, instantaneous replenishment (or short fixed lead time), no quantity discounts, no stockouts, and linear holding cost. None of these is perfectly true in practice, but the model is robust to small violations — EOQ is approximately right across a range of typical inventory situations. Use it as a starting point, then adjust for your specific constraints.

How does ordering cost affect EOQ?

EOQ scales with the square root of ordering cost. Doubling ordering cost increases EOQ by about 41%; halving it decreases EOQ by about 29%. The square-root structure means EOQ is relatively insensitive to small parameter changes — a rough estimate of ordering cost is usually good enough for the headline answer.

When does the EOQ model break down?

When demand is highly seasonal or variable (use a stochastic inventory model), when significant quantity discounts exist (model the discount tiers), or when storage capacity is constrained (the optimum may be capacity-limited rather than cost-minimising). For modern e-commerce with daily-changing demand, EOQ is often used as a baseline that's then overridden by demand-forecast-driven systems.

What is the relationship between EOQ and inventory turns?

Inventory turns = annual demand ÷ average inventory = D ÷ (EOQ ÷ 2) = 2D ÷ EOQ. Smaller EOQ means more turns — your inventory cycles through faster. Higher turns is generally good (less capital tied up, less obsolescence risk) but higher ordering frequency adds cost. EOQ is the balance point where the two costs trade off.

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