Economic Order Quantity (EOQ) Calculator
The Economic Order Quantity (EOQ) is the classic Harris–Wilson lot-size model (Harris 1913; Wilson 1934). Enter annual demand, the fixed cost of placing an order and the cost of carrying one unit for a year; the tool returns the order size Q* that minimises total annual inventory cost, plus the matching ordering rhythm and cost breakdown.
Common scenarios (tap to load)
Enter positive values for annual demand, ordering cost and unit holding cost.
Wilson optimum
Optimal order quantity Q*
—
units / order
Orders per year N*
—
orders / year
Cycle length T*
—
days between orders
Annual holding cost
—
Annual ordering cost
—
Annual inventory total
—
—
Assumes steady demand, fixed cost per order, no quantity discounts and no stock-outs. Quantity-discount or stochastic-demand scenarios call for EOQ variants (Quantity-Discount EOQ, Newsvendor).
Formula
Q* = √(2 · D · S / H); N* = D / Q*; T* = 365 / N*; TC(Q*) = √(2 · D · S · H)
- · D = annual demand (units / year); S = fixed cost per order (freight, admin, receiving); H = cost of carrying one unit for a year (warehousing, insurance, capital cost, obsolescence).
- · At Q* the annual holding cost equals the annual ordering cost — that's the defining property of the EOQ (the two cost curves cross). Useful as a sanity check on any reorder calculation.
- · Total cost is flat near the optimum: doubling or halving Q only raises cost by ~25 %. In practice, picking the nearest convenient pack quantity to Q* is fine — no need to hit the decimal.
- · H is typically 15–35 % of unit value — capital opportunity cost (WACC), warehousing, insurance, shrinkage and obsolescence. Worth breaking out for sensitivity analysis.
- · Classical assumptions: steady demand, fixed cost per order, no quantity discounts, no stock-outs. Variants exist for each: Quantity-Discount EOQ for bulk discounts, Newsvendor or (Q, R) models for stochastic demand.
- · EOQ and Just-in-Time (JIT) are not opposites: JIT works by driving S toward zero through process improvement (changeover reduction, supplier integration). As S → 0, the optimal Q* → 1.
Frequently asked
If the cost per order varies with quantity (e.g. volume discounts), does EOQ still apply?
Strictly speaking, basic EOQ assumes S is independent of Q, so it does not directly apply when there are volume discounts. The standard fix is Quantity-Discount EOQ: (1) for each price break i, compute Qᵢ* using Hᵢ (typically unit cost × carrying-rate); (2) if Qᵢ* lies within that price band, evaluate total cost including purchase cost; if outside, use the band's nearest break-point as the candidate; (3) pick the candidate with the lowest total annual cost (including purchases). The same logic applies to freight tiers (e.g. "free shipping above 100 units") using a stepwise S.
Why exactly do annual holding cost and annual ordering cost coincide at Q*?
Because total cost TC(Q) = (Q/2)·H + (D/Q)·S is minimised where d/dQ = 0, giving H/2 − D·S/Q² = 0 — that is, Q² = 2DS/H, so Q* = √(2DS/H). Substituting back, annual holding cost = (Q*/2)·H and annual ordering cost = (D/Q*)·S both equal √(D·S·H/2). So the two curves crossing at the optimum is a mathematical necessity, not a coincidence. In practice you can use the property in reverse as a sanity check: if the two costs differ by more than 10 % at "Q*", something is off — usually an arithmetic mistake or inconsistent units (e.g. S quoted monthly but D quoted yearly).
Q* is usually not a whole number, and often clashes with a supplier MOQ — what then?
Two things to keep in mind. (1) Total cost is flat around the optimum — rounding Q* to the nearest pack / pallet / MOQ usually raises TC by less than 5 %. (2) If MOQ exceeds Q*, treat MOQ as the lower bound (so actual Q = max(Q*, MOQ)) and use that as a trigger to consider consolidating multiple SKUs in one order to dilute S. If the gap is large (say MOQ ≈ 3 × Q*), revisit the H estimate — H is often under-stated, which under-states the optimal Q and hides the real cost of holding stock.
Related tools
Mortgage Monthly Payment Calculator
Enter property price, down payment, term and rate — get monthly payment, total interest and total payable.
Hong Kong Stamp Duty Calculator
Compute Ad Valorem Stamp Duty (AVD) on residential property at the latest rates.
Hong Kong Salaries Tax Calculator
Estimate Hong Kong salaries tax using both the progressive bands and the 15% / 16% two-tier standard rate (Year of Assessment 2024/25).
Hong Kong MPF Contribution Calculator
Hong Kong MPF contributions for employees, employers and self-employed persons using the statutory 5% rate with the $7,100 minimum and $30,000 maximum relevant income thresholds.
Compound Interest Calculator
Project the future value of a principal plus regular monthly or yearly contributions at a given annual rate, with total interest earned.
CAGR (Compound Annual Growth Rate) Calculator
Compute the compound annual growth rate from a start value, end value and number of years — useful for comparing long-term growth.
ROI (Return on Investment) Calculator
Compute total profit, ROI % and annualised return from initial cost, final value and holding period — useful for comparing investments.
Inflation / Purchasing Power Calculator
Project the future purchasing power of an amount given an annual inflation rate and time horizon — and the nominal amount needed to keep up.
Markup & Margin Calculator
Convert between cost, selling price, markup % and gross margin % — handy for retail pricing and SMB profit analysis.
Break-Even Point Calculator
From fixed costs, variable cost per unit and selling price, find the units needed to cover all costs — plus break-even revenue, contribution margin, target-profit volume and margin of safety.
APR ↔ APY Calculator (Nominal vs Effective Annual Rate)
Convert a nominal annual rate (APR) at any compounding frequency to the effective annual yield (APY), or solve the inverse — essential for comparing credit-card, savings-account and mortgage rates.
Rule of 72 Calculator (Doubling Time)
Quickly estimate how many years to double your money at a given compound rate, or what rate is needed to double in a target period — with the exact logarithmic answer alongside.
Loan Payoff Time Calculator
From balance, monthly payment and APR, compute how many months until the loan is paid off, the total interest paid, and the minimum payment that just covers interest.
Savings Goal Calculator
Given goal amount, current savings, monthly deposit and APR, see how many months it takes to hit the target.
Annuity Payment Calculator
Enter principal, annual rate and number of periods to compute the fixed annuity payment (PMT formula) — essential for retirement-income planning.
Net-to-Gross Salary Calculator (Hong Kong)
Enter the after-tax salary you want to take home and the calculator works back to the gross figure you need to offer (HK MPF and salaries-tax aware).
Rental Yield Calculator
Enter property price, monthly rent and yearly expenses (rates, management, insurance, vacancy) to see both gross and net rental yield (%).
Dividend Yield Calculator
Enter annual dividend per share, share price, EPS and amount invested to compute dividend yield (%), payout ratio (%) and projected yearly income.
Sales Tax / VAT Calculator
Enter a price and a tax rate to compute the gross total and tax amount, or work backwards from a tax-inclusive price to the net amount.
Hong Kong Loan-to-Value (LTV) Ratio Calculator
Enter property value and loan amount to get the LTV ratio, the required down-payment, and a live check against HKMA caps and the HKMC mortgage insurance ceilings.
Present Value (PV) Calculator
Discount a future amount back to today using an annual rate, horizon and compounding frequency — get the present value, discount factor and effective annual rate.
Real Interest Rate (Fisher Equation) Calculator
Use the Fisher equation to strip inflation from a nominal rate and find the real return, with the common r ≈ i − π approximation alongside.
Safe Withdrawal Rate (4% Rule) Calculator
Apply the Trinity Study 4% rule: enter your retirement nest egg and a withdrawal rate to see the annual and monthly income it can support.
Debt-to-Income (DTI) Ratio Calculator
Enter monthly debt payments and gross monthly income to compute your DTI ratio against the standard lender bands (36% / 43% / 50%).
Simple Interest Calculator
Enter principal, annual rate and term and apply I = P × r × t to find the interest earned or owed under simple-interest accrual (no compounding).
Net Present Value (NPV) Calculator
Enter the initial outlay, future cash flows and a discount rate to compute the project Net Present Value (NPV) — positive NPV means the project beats your required return.
Internal Rate of Return (IRR) Calculator
Enter the upfront investment, projected yearly cash flows and a hurdle rate to solve for the discount rate that makes NPV = 0 — and see at a glance whether the project beats your required return.
Sharpe Ratio Calculator
Enter your portfolio annual return, the risk-free rate and the annualised standard deviation to compute the Sharpe ratio — excess return earned per unit of risk taken.
Mortgage Refinance Break-Even Calculator
Compare your current mortgage against a new rate, net of refinance closing costs and penalties, to find how many months to break even and whether the whole loan saves or costs more over its lifetime.
Bond Price Calculator
From face value, coupon rate, yield-to-maturity, years to maturity and coupon frequency, compute a fixed-coupon bond's present price, premium/discount and current yield.
Future Value of Annuity Calculator
Compute the future value of a stream of equal payments (e.g. monthly savings or pension contributions) with end- or beginning-of-period timing.
WACC (Weighted Average Cost of Capital) Calculator
Enter the market values of equity and debt, the cost of equity, the cost of debt and the corporate tax rate to compute the weighted-average cost of capital (WACC), capital-structure weights and after-tax cost of debt.
Earnings Per Share (EPS) Calculator
Enter a company's net income, preferred dividends and weighted-average common shares outstanding to compute basic EPS, with an optional dilutive-securities input for diluted EPS.
Dollar-Cost Averaging (DCA) Calculator
Enter a fixed amount per period and the buy price for each period to see total invested, total shares, average cost and current value — with a side-by-side comparison against putting the same money in as a lump sum at the first price.
Position Size Calculator (Stock / Forex Risk)
Enter account size, per-trade risk percent and stop-loss distance to compute the share/lot quantity that caps your loss at the chosen risk.
Debt Snowball Payoff Plan Calculator
Enter several debts (balance, APR, minimum payment) and your monthly extra budget; the tool runs the classic "smallest balance first" snowball method, estimating each debt's payoff month, total interest paid and total months to debt-free.
Payback Period Calculator (Simple & Discounted)
Enter an initial investment, level annual cash inflow, discount rate and horizon to instantly see the simple payback period, the discounted payback period and the terminal Net Present Value (NPV), plus a year-by-year cumulative cash-flow table — built for capital-budgeting, small-business investments, solar installs and equipment purchase decisions.
Pay Raise Calculator (Percentage, Amount, New Salary)
Enter your current salary, raise percentage or dollar amount and instantly see your new salary plus annual, monthly, weekly and hourly differences — handy for comparing offers, negotiating reviews and gauging inflation-adjusted raises.
Sinking Fund Payment Calculator (Save-to-Target)
Enter a target amount (FV), expected annual return and term — the tool back-solves the periodic payment you need to reach that target, the classic "how much to save monthly to hit $X by year Y" question.
Perpetuity Present Value Calculator
Enter the level periodic cash flow C and the discount rate r — the tool returns the perpetuity present value PV = C / r and, optionally, the growing-perpetuity Gordon value PV = C / (r − g) used for consols, preferred shares and dividend-discount models.
Mortgage Discount Points Break-Even Calculator
Enter the loan amount, the number of discount points bought and the rate reduction per point — the tool returns the upfront cost, the monthly payment saving and the break-even month so you can decide whether paying points is worth it.
Debt Service Coverage Ratio (DSCR) Calculator
Enter net operating income (NOI) and total annual debt service (principal + interest); the tool reports the debt service coverage ratio DSCR = NOI / debt service — the headline risk metric banks use when underwriting commercial property loans, business loans and investment-property mortgages.
Price-to-Earnings (P/E) Ratio Calculator
Enter a share price and EPS — the tool returns the price-to-earnings ratio P/E, the earnings yield (EPS ÷ price), and the PEG ratio (if a growth rate is supplied), then puts the result in context with typical industry bands.
Debt-to-Equity (D/E) Ratio Calculator
Enter total liabilities and shareholders' equity to get the D/E ratio, equity multiplier and debt-to-assets ratio, with industry context (utilities, tech, banking) to flag whether the firm's capital structure is conservative or aggressive.
DuPont Analysis Calculator (3-Factor ROE)
Enter net income, revenue, assets and equity; the tool applies the 3-factor DuPont identity to decompose ROE = Net Margin × Asset Turnover × Equity Multiplier, so you can see whether high returns come from profitability, efficiency or leverage.
Current Ratio Calculator
Enter current assets (cash, receivables, inventory) and current liabilities (short-term debt, payables) to get the current ratio = CA ÷ CL, with industry-standard thresholds (< 1 warning, 1–2 healthy, > 3 idle cash) to flag short-term solvency at a glance.
Quick Ratio Calculator (Acid-Test Ratio)
Enter cash, marketable securities, receivables and current liabilities; the tool returns the quick ratio = (CA − inventory − prepaid expenses) ÷ CL, a stricter view of liquidity than the current ratio because it excludes inventory and prepayments that may not convert to cash quickly.
Return on Equity (ROE) Calculator
Enter net income and shareholders' equity (beginning / ending / average); the tool returns ROE = net income ÷ equity with the conventional bands (< 5% weak, 10–15% healthy, > 20% excellent), so you can read management's efficiency at deploying equity capital at a glance.
Price-to-Book (P/B) Ratio Calculator
Enter share price and book value per share (or total equity + shares outstanding); the tool returns P/B = price ÷ book value and benchmarks it against typical banks, insurers, real estate and SaaS bands — a core value-investing screen used since Benjamin Graham.
Operating Margin Calculator
Enter operating income (EBIT) and total revenue; the tool returns the operating margin = EBIT ÷ revenue, then benchmarks the result against software, branded consumer, manufacturing, retail and airline norms — the cleanest single read on core operating efficiency.
CAPM Calculator (Capital Asset Pricing Model)
Enter the risk-free rate Rf, expected market return Rm and the stock's beta β; the CAPM formula r = Rf + β·(Rm − Rf) returns the required rate of return (cost of equity) and breaks out the equity risk premium component (ERP × β).
Inventory Turnover Ratio Calculator
Enter annual cost of goods sold (COGS) and average inventory; the tool returns the inventory turnover ratio (Turnover = COGS ÷ Avg Inventory) and days inventory outstanding (DIO = 365 ÷ Turnover) — the standard lens for retail, manufacturing and e-commerce to gauge stocking efficiency and working-capital tie-up.