Finance Formulas with Calculators

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Finance Formulas with Calculators and Worked Solutions

This section collects the formulas used in corporate finance, investing, accounting and personal finance courses, each on its own page with the formula written out, a plain-English definition of every variable and a calculator that solves it with your numbers. Every calculator prints its working step by step, so you can check a homework answer, follow how a spreadsheet function reaches its result, or copy the method into a report.

The formulas are grouped the way textbooks teach them: the time value of money (present and future value, annuities, NPV and IRR), loans and amortization, returns and investment analysis (ROI, CAGR, CAPM, WACC, bond pricing and yield), financial statement ratios, depreciation methods, and break-even and leverage analysis for business decisions. Type in the search box to jump straight to a formula.

Each page opens with a worked default example so you can see a complete solution before entering your own figures. The calculations were checked against numpy-financial, SciPy and the published examples for the equivalent spreadsheet functions (PV, FV, PMT, NPV, IRR, MIRR, DB, DDB, SYD and others). Everything runs in your browser; nothing you type is sent anywhere.

Jump to: Time value of money · Loans · Returns and investing · Financial ratios · Depreciation · Break-even, margins and leverage

Time value of money (26)

Present and future value, annuities, perpetuities, NPV, IRR, payback, interest-rate conversions and doubling time.

Present Value Formula and CalculatorWhat a future lump sum is worth today: PV = FV ÷ (1 + r)ⁿ.Future Value Formula and CalculatorWhat a sum invested today grows to: FV = PV × (1 + r)ⁿ.Present Value of Annuity FormulaToday's value of equal payments at the end of each period.Future Value of Annuity FormulaWhat equal end-of-period deposits grow to by the last payment.Present Value of Annuity Due FormulaToday's value of equal payments made at the start of each period.Future Value of Annuity Due FormulaWhat equal start-of-period deposits grow to.Perpetuity Formula and CalculatorValue of a constant payment forever: PV = P ÷ r.Growing Perpetuity FormulaPayment growing at rate g forever: PV = P₁ ÷ (r − g).Present Value of Growing Annuity FormulaToday's value of n payments that grow by g each period.Future Value of Growing Annuity FormulaWhat deposits that rise by g each period grow to.Net Present Value (NPV) FormulaSum of discounted cash flows minus the investment; accept if NPV > 0.IRR Formula and CalculatorThe discount rate at which a project's NPV is exactly zero.MIRR Formula and CalculatorIRR with realistic reinvestment: one answer even for odd cash flows.Payback Period Formula and CalculatorHow long until the cash flows repay the initial investment.Discounted Payback Period FormulaPayback period using present values of the cash flows.Profitability Index Formula and CalculatorPresent value created per unit invested; accept if PI > 1.Effective Annual Rate (EAR) FormulaThe true yearly rate after compounding: (1 + i/m)ᵐ − 1.APR to APY Formula and CalculatorTurn a quoted APR into the annual percentage yield.APY to APR Formula and CalculatorFind the nominal rate behind an advertised APY.Continuous Compounding Formula (Pe^rt)Growth when interest compounds every instant: A = Pe^(rt).Rule of 72 Calculator and FormulaQuick doubling-time estimate: 72 ÷ rate, versus the exact answer.Doubling Time Formula and CalculatorExact years to double for any rate and compounding frequency.Compound Interest Formula A = P(1 + r/n)^ntBalance with interest on interest: A = P(1 + r/n)ⁿᵗ.Simple Interest Formula I = PrtInterest on the principal only: I = P × r × t.Sinking Fund Formula and CalculatorRegular deposit needed to reach a target amount.Number of Periods Formula (Solve for n)How many periods to grow PV into FV at rate r.

Loans (6)

Loan payments, balloon and interest-only loans, remaining balance, payoff time and a full amortization schedule.

Loan Payment Formula and CalculatorLevel payment for an amortizing loan: P = Lr ÷ [1 − (1 + r)⁻ⁿ].Balloon Payment Formula and CalculatorRegular payment plus a lump sum at the end; solve for either.Remaining Loan Balance FormulaWhat you still owe on a loan after k payments.Amortization Schedule Formula and TablePayment-by-payment split of interest, principal and balance.Interest-Only Loan Payment FormulaPayment while only interest is paid, and the jump afterwards.Loan Payoff Time (Number of Payments)How long a given payment takes to clear a loan balance.

Returns and investing (25)

ROI, CAGR, average returns, dividends and valuation, CAPM, WACC, beta, risk-adjusted ratios and bonds.

ROI Formula and CalculatorGain relative to cost, with an annualized version.CAGR Formula and CalculatorSteady yearly growth rate between a start and end value.Holding Period Return FormulaTotal return over the time you held an asset, income included.Geometric Mean Return FormulaThe compound average return actually earned over several periods.Arithmetic Mean Return FormulaSimple average of periodic returns, with volatility and drag.Dividend Yield Formula and CalculatorAnnual dividend income as a percentage of the share price.Dividend Payout Ratio FormulaShare of earnings paid out as dividends, and the share retained.Gordon Growth Model Formula (DDM)Share value from a dividend growing at a constant rate forever.Two-Stage Dividend Discount ModelHigh growth for N years, then stable growth forever.CAPM Formula and CalculatorRequired return from beta: Rf + β(Rm − Rf).WACC Formula and CalculatorBlended after-tax cost of a company's debt and equity.Beta Formula and Calculator (Stock Beta)Stock's sensitivity to the market from paired returns.Sharpe Ratio Formula and CalculatorExcess return per unit of total risk (volatility).Treynor Ratio Formula and CalculatorExcess return per unit of market risk (beta).Jensen's Alpha Formula and CalculatorReturn above what CAPM predicts for the portfolio's beta.P/E Ratio Formula and CalculatorShare price per unit of earnings, plus earnings yield and PEG.Earnings Per Share (EPS) FormulaProfit attributable to each common share.Price-to-Book (P/B) Ratio FormulaShare price relative to accounting equity per share.Bond Price Formula and CalculatorPrice of a coupon bond from its yield to maturity.Yield to Maturity (YTM) FormulaThe discount rate that equates a bond's cash flows to its price.Current Yield Formula for BondsA bond's annual coupon income as a percentage of its price.Bond Duration Formula (Macaulay, Modified)Weighted-average time to cash flows and price sensitivity to yield.Zero-Coupon Bond Price FormulaPrice of a bond that pays only its face value at maturity.Real Rate of Return Formula (Fisher)Return after inflation, exact Fisher version and shortcut.Portfolio Expected Return FormulaWeighted average of the returns of the assets held.

Financial ratios (21)

Liquidity, leverage, profitability and efficiency ratios from the balance sheet and income statement, plus DuPont analysis.

Current Ratio Formula and CalculatorCurrent assets per unit of short-term liabilities.Quick Ratio (Acid-Test) FormulaLiquid assets, excluding inventory, per unit of current liabilities.Cash Ratio Formula and CalculatorCash and securities per unit of current liabilities.Debt-to-Equity Ratio FormulaLiabilities (or debt) per unit of shareholders' equity.Debt Ratio Formula and CalculatorShare of total assets financed with liabilities.Interest Coverage Ratio FormulaHow many times operating profit covers interest expense.Return on Assets (ROA) FormulaNet income per unit of average total assets.Return on Equity (ROE) FormulaNet income per unit of average shareholders' equity.Gross Profit Margin FormulaShare of revenue left after the direct cost of sales.Operating Profit Margin FormulaShare of revenue left after all operating costs (EBIT margin).Net Profit Margin Formula and CalculatorShare of revenue kept as profit after every expense.Asset Turnover Ratio FormulaRevenue generated per unit of average total assets.Inventory Turnover Ratio FormulaHow many times inventory is sold and replaced in a period.Receivables Turnover Ratio FormulaHow many times receivables are collected in a period.Days Sales Outstanding (DSO) FormulaAverage days to collect cash after a credit sale.Days Inventory Outstanding (DIO) FormulaAverage days inventory is held before being sold.Cash Conversion Cycle Formula (CCC)Days between paying suppliers and collecting from customers.DuPont Analysis Formula (ROE Breakdown)ROE split into margin, turnover and leverage (3 and 5 steps).Equity Multiplier Formula and CalculatorTotal assets per unit of shareholders' equity.Net Working Capital FormulaCurrent assets minus current liabilities, in money terms.Debt Service Coverage Ratio (DSCR)Operating income per unit of principal and interest due.

Depreciation (5)

Straight-line, declining balance, double declining balance, sum-of-the-years'-digits and units of production, each with a schedule.

Straight-Line Depreciation FormulaEqual depreciation every year: (cost − salvage) ÷ life.Declining Balance Depreciation FormulaFixed percentage of book value each year (Excel DB method).Double Declining Balance Formula (DDB)Accelerated depreciation at twice the straight-line rate.Sum-of-the-Years'-Digits DepreciationAccelerated depreciation that falls by the same amount each year.Units of Production Depreciation FormulaDepreciation tied to actual usage (units, hours or miles).

Break-even, margins and leverage (7)

Break-even point, contribution margin, markup versus margin, and operating, financial and combined leverage.

Break-Even Point Formula and CalculatorUnits and sales needed to cover all costs, or reach a target profit.Contribution Margin Formula and RatioWhat each sale contributes to fixed costs and profit.Markup vs Margin Formula and CalculatorMarkup on cost and margin on price for the same sale.Margin to Markup Conversion FormulaConvert a margin to a markup or back, and price from cost.Degree of Operating Leverage (DOL) FormulaHow strongly operating profit reacts to a change in sales.Degree of Financial Leverage (DFL) FormulaHow strongly EPS reacts to a change in operating profit.Degree of Combined Leverage (DCL) FormulaOperating × financial leverage: EPS sensitivity to sales.

Frequently asked questions

Are these finance calculators free?

Yes. Every formula page and calculator is free to use, with no sign-up.

Do the calculators show the working?

Yes. Each result comes with the formula, your numbers substituted in and every intermediate value, in the order a textbook solution would use.

How accurate are the results?

The calculations were validated against numpy-financial, SciPy and spreadsheet reference examples on more than 600 test cases.

Which formula do I need to value an investment project?

Start with net present value (NPV). Use IRR or MIRR to express the return as a rate, the profitability index to rank projects when capital is limited, and the payback period for a quick liquidity check.

What is the difference between APR, APY and the effective annual rate?

APR is a nominal annual rate; APY and the effective annual rate are the same thing, the rate actually earned or paid over a year once compounding is included.

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Last reviewed: September 26, 2026. 90 formulas, each validated against numpy-financial, SciPy or published spreadsheet examples.