ROI Calculator

Formula

ROI = (Gain / Cost) × 100

Simple ROI shows total return. Annualized ROI (CAGR) accounts for time, enabling comparison across investments with different holding periods.

Worked Examples

Example 1: Basic ROI Calculation

Problem: You invest $10,000 and sell 3 years later for $15,000. Calculate ROI and annualized ROI.

Solution: Total gain: $15,000 - $10,000 = $5,000\n\nSimple ROI:\nROI = ($5,000 / $10,000) × 100 = 50%\n\nAnnualized ROI:\nFormula: ((Final/Initial)^(1/years) - 1) × 100\n= ((15,000/10,000)^(1/3) - 1) × 100\n= (1.5^0.333 - 1) × 100\n= (1.1447 - 1) × 100\n= 14.47% per year\n\nComparison: The 50% total looks great, but 14.47% annually is the true performance measure.

Result: 50% total | 14.47% annualized

Example 2: Comparing Two Investments

Problem: Investment A: $5,000 → $7,500 over 2 years. Investment B: $5,000 → $9,000 over 5 years. Which is better?

Solution: Investment A:\nTotal ROI: ($7,500-$5,000)/$5,000 = 50%\nAnnualized: (1.5)^(1/2) - 1 = 22.5%/year\n\nInvestment B:\nTotal ROI: ($9,000-$5,000)/$5,000 = 80%\nAnnualized: (1.8)^(1/5) - 1 = 12.5%/year\n\nConclusion:\nB has higher total return (80% vs 50%)\nA has higher annualized return (22.5% vs 12.5%)\n\nA was the better investment - money compounded faster. The extra time in B didn't justify the extra return.

Result: A wins: 22.5% vs 12.5% annualized

Example 3: Real ROI After Fees and Taxes

Problem: $20,000 investment. 15% gross return over 2 years. 1% annual fee. 15% capital gains tax. What's real ROI?

Solution: Gross return: $20,000 × 15% = $3,000 gain\n\nFees:\nYear 1: $20,000 × 1% = $200\nYear 2: $21,500 × 1% = $215 (approx)\nTotal fees: $415\n\nGain after fees: $3,000 - $415 = $2,585\n\nTaxes:\nCapital gains tax: $2,585 × 15% = $388\n\nNet gain: $2,585 - $388 = $2,197\n\nNet ROI: $2,197 / $20,000 = 11.0%\nAnnualized net: (1.11)^(1/2) - 1 = 5.4%/year\n\nFees and taxes reduced 15% to 11% total, 5.4% annualized.

Result: 15% gross → 11% net (5.4% annualized)

Frequently Asked Questions

What is ROI (Return on Investment)?

ROI = (Gain - Cost) ÷ Cost × 100. It measures profitability as a percentage of your investment. Example: invest $10,000, sell for $15,000, gain is $5,000, ROI is 50%. Simple but doesn't account for time - a 50% return over 1 year is very different from 50% over 10 years.

What is annualized ROI?

Annualized ROI accounts for time, allowing comparison of investments with different holding periods. Formula: ((Final/Initial)^(1/years) - 1) × 100. Example: 50% total return over 3 years = 14.5% annualized. Always compare annualized returns when evaluating investments.

What's a good ROI?

Depends on risk and investment type. Stock market average: 10% annually. Savings account: 4-5%. Real estate: 8-12%. Startup investment: 25%+ expected (high risk). Bonds: 4-6%. Compare to alternatives with similar risk levels.

How does ROI differ from IRR?

ROI is simple: total gain divided by cost. IRR (Internal Rate of Return) accounts for timing of cash flows. For investments with regular deposits/withdrawals, IRR is more accurate. For simple 'invest once, sell once' situations, ROI works fine.

Does ROI account for inflation?

Basic ROI does not. Real ROI = Nominal ROI - Inflation. If you earned 8% but inflation was 3%, real return is ~5%. For long-term planning, always consider real (inflation-adjusted) returns. The S&P 500's 10% nominal return is about 7% real.

Should I include fees in ROI calculation?

Yes! Net ROI should include all costs: transaction fees, management fees, taxes, commissions. A 10% gross return with 2% in fees is really 8%. Many investments look worse after accounting for all fees. Always calculate net ROI.

Background & Theory

The ROI Calculator applies the following established principles and formulas. Finance and investing rest on the foundational concept of the time value of money: a dollar received today is worth more than a dollar received in the future, because present funds can be deployed to earn a return. This principle underlies virtually every valuation technique in modern finance. The future value of a present sum P growing at rate r over n periods is expressed as FV = P(1 + r)^n, while the present value of a future cash flow FV is PV = FV / (1 + r)^n. Compound growth amplifies returns significantly over long horizons, a dynamic often described as the eighth wonder of the world. Net Present Value (NPV) extends these mechanics to evaluate investment projects by summing the present values of all expected cash flows minus the initial outlay: NPV = sum[CF_t / (1 + r)^t] - C_0. A positive NPV indicates the project creates value above the required return. The Internal Rate of Return (IRR) is the discount rate that sets NPV to zero, providing a single percentage benchmark for project comparison. The risk-return tradeoff is the central tension of investment theory. Higher expected returns generally require accepting greater uncertainty. Harry Markowitz formalized this in Modern Portfolio Theory by demonstrating that portfolio variance can be reduced through diversification when assets are imperfectly correlated. The efficient frontier represents the set of portfolios offering the maximum return for a given level of risk. The Capital Asset Pricing Model (CAPM) extends this by introducing the market portfolio as a reference, defining expected return as E(r) = r_f + beta * (E(r_m) - r_f), where beta measures an asset's sensitivity to systematic market risk. Asset classes — equities, fixed income, real assets, and alternatives — differ in their return profiles, liquidity, and correlations. Strategic asset allocation determines long-run target weights based on investor objectives and risk tolerance, while tactical allocation permits short-run deviations to exploit perceived mispricings. Discount rates used in valuation models must reflect the cost of capital appropriate to the risk of the cash flows being discounted, a point stressed in corporate finance texts from Brealey, Myers, and Allen through to Damodaran.

History

The history behind the ROI Calculator traces back through the following developments. The formal practice of lending at interest dates to ancient Mesopotamia, where the Code of Hammurabi around 1750 BCE regulated interest rates on grain and silver loans. Banking as an institutional activity took root in medieval Italy, with merchant bankers in Florence and Venice financing trade across Europe through instruments such as bills of exchange. The Medici family operated one of the most sophisticated banking networks of the fifteenth century, pioneering double-entry bookkeeping and correspondent banking relationships. Organized equity markets emerged in the early seventeenth century. The Dutch East India Company (VOC), chartered in 1602, issued shares to the public and created the Amsterdam Stock Exchange — widely regarded as the world's first formal stock exchange. The VOC allowed investors to buy and sell shares freely, establishing the template for the joint-stock company. The period also produced the Dutch tulip mania of 1636 to 1637, one of history's first recorded speculative bubbles, in which tulip bulb futures contracts reached extraordinary prices before collapsing. England's financial revolution followed in the late seventeenth century with the founding of the Bank of England in 1694 and the development of government bond markets. The South Sea Bubble of 1720 illustrated the dangers of speculative excess and contributed to early securities regulation. Throughout the eighteenth and nineteenth centuries, industrialization created enormous demand for capital, fueling the expansion of stock exchanges in London, Paris, New York, and beyond. The New York Stock Exchange, formalized in 1817, became the world's dominant equities market by the twentieth century. The Great Crash of 1929 and subsequent Great Depression prompted the US Securities Act of 1933 and Securities Exchange Act of 1934, establishing the SEC and mandatory disclosure requirements. Harry Markowitz published his landmark portfolio selection paper in 1952, launching quantitative finance. The CAPM emerged in the 1960s through work by Sharpe, Lintner, and Mossin. John Bogle launched the first retail index fund in 1976, democratizing diversified investing and challenging active management orthodoxy.