EOQ Calculator
Free Eoqcalculator Calculator for operations & inventory. Enter your numbers to see returns, costs, and optimized scenarios instantly.
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The Economic Order Quantity formula calculates the optimal order size by taking the square root of (2 times annual demand D times ordering cost per order S, divided by annual holding cost per unit H). This minimizes total inventory costs by balancing ordering and holding costs.
Last reviewed: December 2025
Worked Examples
Example 1: Manufacturing Parts Ordering
Example 2: Retail Store Inventory
Background & Theory
The EOQ Calculator applies the following established principles and formulas. Break-even analysis identifies the sales volume at which total revenue equals total costs, producing neither profit nor loss. The formula divides total fixed costs by the contribution margin per unit, where contribution margin equals selling price minus variable cost per unit. If a software product has $50,000 in monthly fixed costs and each licence generates $20 above its variable cost, break-even requires 2,500 unit sales per month. Above that threshold, each additional unit contributes directly to profit. Gross margin expresses the percentage of revenue remaining after direct cost of goods sold: gross margin equals revenue minus COGS, divided by revenue. A SaaS company with 80 percent gross margins retains $0.80 of every revenue dollar to cover operating expenses, while a manufacturer with 30 percent gross margins faces much tighter operating leverage. Customer acquisition cost (CAC) divides total sales and marketing expenditure in a period by the number of new customers acquired in that same period. Customer lifetime value (LTV) estimates the total profit attributable to a customer relationship. The standard formula multiplies average revenue per user (ARPU) by gross margin and divides by the monthly churn rate. A business with $50 ARPU, 75 percent gross margin, and 2 percent monthly churn has an LTV of $1,875. The LTV:CAC ratio benchmarks unit economics health; a ratio above 3:1 is generally considered sustainable, while ratios below 1:1 indicate the business is acquiring customers at a loss. Burn rate measures monthly cash expenditure net of revenue. Cash runway equals current cash reserves divided by net monthly burn. A company with $1.2 million in the bank burning $100,000 per month has twelve months of runway. The Rule of 40 is a benchmark for SaaS health: the sum of annual revenue growth rate (as a percentage) and profit margin (as a percentage) should equal or exceed 40. High-growth companies burning cash can still pass this rule if their growth rate compensates.
History
The history behind the EOQ Calculator traces back through the following developments. Early economic thought centred on mercantilism, the 16th and 17th century doctrine that national wealth derived from accumulating precious metals through export surpluses and colonial extraction. Adam Smith's "Wealth of Nations" in 1776 dismantled this framework, arguing that genuine prosperity arose from specialisation, division of labour, and freely operating markets. David Ricardo extended Smith's work with the theory of comparative advantage in 1817, demonstrating mathematically that mutually beneficial trade was possible even when one country was less productive in every industry. Alfred Marshall's "Principles of Economics" published in 1890 provided the modern framework of supply and demand curves, consumer surplus, price elasticity, and marginal analysis, establishing neoclassical economics as the dominant academic paradigm for decades. The Great Depression exposed the limits of laissez-faire assumptions, and John Maynard Keynes's "General Theory of Employment, Interest and Money" in 1936 argued that private-sector aggregate demand failures required countercyclical government fiscal intervention to restore full employment, shifting the policy consensus toward active macroeconomic management. The post-World War II decades constructed mixed-economy models combining market allocation with expanded welfare states and Keynesian demand management. Milton Friedman and the Chicago School challenged this consensus from the 1960s onward, championing monetarism and arguing that stable money supply growth was superior to discretionary fiscal policy. Their influence shaped the deregulatory and privatisation policies of the Reagan and Thatcher eras in the 1980s. Behavioural economics emerged through the work of Daniel Kahneman and Amos Tversky in the 1970s and Richard Thaler in the 1980s, using psychology to demonstrate that real human decision-making deviates systematically from rational-actor models through heuristics and biases. The rise of the internet and mobile platforms in the 2000s and 2010s created a new category of platform economics, where network effects, near-zero marginal cost of digital goods, and two-sided market dynamics generated winner-take-most competitive outcomes requiring new analytical frameworks for business valuation.
Frequently Asked Questions
Formula
EOQ = √(2DS / H)
The Economic Order Quantity formula calculates the optimal order size by taking the square root of (2 times annual demand D times ordering cost per order S, divided by annual holding cost per unit H). This minimizes total inventory costs by balancing ordering and holding costs.
Worked Examples
Example 1: Manufacturing Parts Ordering
Problem: A factory uses 10,000 widgets per year. Each order costs $150 to place, and annual holding cost is $2 per widget. Lead time is 7 working days with 250 working days per year.
Solution: D = 10,000 units/year, S = $150/order, H = $2/unit/year\nEOQ = sqrt(2 × 10,000 × 150 / 2) = sqrt(1,500,000) = 1,225 units\nOrders per year = 10,000 / 1,225 = 8.16 orders\nAnnual ordering cost = 8.16 × $150 = $1,224\nAnnual holding cost = (1,225/2) × $2 = $1,225\nReorder point = (10,000/250) × 7 = 280 units
Result: EOQ = 1,225 units | 8.16 orders/year | Total cost = $2,449 | ROP = 280 units
Example 2: Retail Store Inventory
Problem: A store sells 5,200 units annually. Ordering cost is $75 per order, and holding cost is $4.50 per unit per year. Lead time is 3 days.
Solution: D = 5,200 units/year, S = $75/order, H = $4.50/unit/year\nEOQ = sqrt(2 × 5,200 × 75 / 4.50) = sqrt(173,333) = 416 units\nOrders per year = 5,200 / 416 = 12.5 orders\nOrder cycle = 250/12.5 = 20 working days\nReorder point = (5,200/250) × 3 = 62 units
Result: EOQ = 416 units | 12.5 orders/year | Total cost = $1,873 | ROP = 62 units
Frequently Asked Questions
What is the Economic Order Quantity (EOQ) model?
The Economic Order Quantity (EOQ) model is a fundamental inventory management formula that determines the optimal order quantity to minimize total inventory costs. Developed by Ford W. Harris in 1913 and later refined by R.H. Wilson, the EOQ model balances two opposing costs: ordering costs (which decrease as order size increases because fewer orders are needed) and holding costs (which increase as order size increases because more inventory is stored). The classic EOQ formula is Q* = sqrt(2DS/H), where D is annual demand, S is the ordering cost per order, and H is the annual holding cost per unit. The model assumes constant demand, fixed ordering costs, constant holding costs, instantaneous replenishment, and no quantity discounts, making it a starting point that many businesses adapt to their specific circumstances.
What are the limitations of the EOQ model?
The classic EOQ model has several important limitations that practitioners should understand. It assumes constant and known demand, which rarely occurs in practice as demand fluctuates seasonally and unpredictably. It assumes instantaneous replenishment, ignoring lead times and production schedules. It does not account for quantity discounts, which are common in real purchasing situations. The model assumes a single product in isolation, ignoring interactions between multiple products sharing warehouse space or transportation. It does not consider stockout costs or service level targets. Holding and ordering costs are assumed constant, when in reality they may vary with volume. Despite these limitations, EOQ remains valuable as a baseline calculation. Many extensions have been developed, including EOQ with quantity discounts, EOQ with backorders, the production EOQ model, and stochastic demand models.
How does lead time affect the EOQ reorder point?
Lead time does not affect the EOQ quantity itself but critically determines when to place an order, known as the reorder point (ROP). The basic reorder point formula is ROP = daily demand multiplied by lead time in days. For example, if daily demand is 20 units and lead time is 5 days, you should reorder when inventory drops to 100 units. In practice, companies add safety stock to account for variability in both demand and lead time: ROP = (average daily demand multiplied by average lead time) plus safety stock. Safety stock is typically calculated using the standard deviation of demand during lead time multiplied by a service level factor (z-score). Longer lead times require higher reorder points and often more safety stock, increasing average inventory levels and costs. Reducing lead times through supplier management, better logistics, or local sourcing can significantly reduce inventory investment.
How do I calculate EOQ with quantity discounts?
When suppliers offer quantity discounts, the standard EOQ formula must be extended because the unit purchase cost changes at different order quantities. The procedure involves several steps: first, calculate the EOQ at each price level using the standard formula. Then, check if each calculated EOQ falls within its valid price range. If an EOQ falls below its price break quantity, adjust it up to the minimum quantity for that price level. Next, calculate the total annual cost (ordering plus holding plus purchase cost) at each viable order quantity. Finally, select the quantity with the lowest total cost. The total cost formula is TC = (D/Q) multiplied by S plus (Q/2) multiplied by H plus D multiplied by the unit price. Sometimes ordering more than the EOQ is justified because the price discount savings exceed the additional holding cost. This analysis is essential for procurement professionals making bulk purchasing decisions.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
Can I use EOQ Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
References
Reviewed by Sahil, Senior Finance & Tax Editor · Editorial policy