ROI & CAGR Calculator

Last updated: 2026-05-09

ROI and CAGR: two ways to measure an investment's return

Return on investment (ROI) is the total percentage change in the value of an investment over its holding period: the gain or loss expressed as a fraction of the amount initially put in. The compound annual growth rate (CAGR) restates that same total change as a constant per-year rate, so that returns earned over different lengths of time can be compared on a common annual basis. A 50 % total return earned over two years and a 50 % return earned over twenty years are identical on an ROI basis but very different per year — CAGR is the measure that separates them.

Total return and annualized return

The two figures answer distinct questions about the same trade, and they are not interchangeable: which one is useful depends on whether the period matters.

Total return — how much it grew

Given an initial value $V_0$ and a final value $V_f$, the simple ROI is

This is the headline figure: a single percentage that summarises the whole horizon. It is easy to quote and easy to compare against zero (gain versus loss), but it carries no information about how long the holding period was, so it cannot rank positions held for different lengths of time.

Annualized return — how fast it grew

The compound annual growth rate is the constant per-year rate that takes $V_0$ to $V_f$ over $t$ years:

This is the comparator. A 30 % gain over 5 years (CAGR ≈ 5.4 %) and a 50 % gain over 10 years (CAGR ≈ 4.1 %) are close on a total-return basis, and the longer hold has the larger headline number, yet on a per-year basis the shorter hold has the higher rate. CAGR places every horizon on the same footing.

Worked example: two properties

Property A returned 30 % over five years and Property B returned 50 % over ten years. On total return, B leads by twenty percentage points. On an annualized basis:

Property A's annualized rate is about a hundred and twenty-five basis points higher. The larger total return on B is the reward for holding twice as long; the underlying compounding rate was slower. This is the difference CAGR makes visible and that a total-return figure alone does not show.

The chart: linear path versus compound curve

Both paths in the chart start at $V_0$ at $t = 0$ and end at $V_f$ at $t = t$. They differ in how they get there:

• The linear path $V_s(\tau) = V_0 + (V_f - V_0) \cdot \tau / t$ is simple ROI applied evenly across the horizon — a straight-line interpolation between the two endpoints.
• The compound curve $V_c(\tau) = V_0 \cdot (1 + g)^{\tau}$ is the trajectory under a constant CAGR — rising and accelerating in a gain scenario, declining and decelerating in a loss scenario (the second derivative is positive in both cases).

In the gain regime the linear line sits above the compound curve through the middle of the horizon: simple ROI overstates how much value has accumulated at any interim point. In the loss regime the compound curve still lies below the linear path, meaning losses compound faster early on before decelerating. The two paths agree only at the endpoints — and at $t = 1$ year, where the two formulas coincide.

Scope and limits

A two-input calculator answers the two-input question. Three quantities fall outside that scope:

1. Mid-horizon cash flows. Money added or withdrawn during the holding period — periodic contributions, partial sales, rental income taken as cash rather than reinvested — is not captured by beginning-and-end-value ROI. The appropriate measure is the internal rate of return (IRR), which weights each cash flow by its timing.
2. Inflation, taxes, and fees. The result is a nominal, pre-tax, pre-fee return. For real purchasing-power growth, run the final value through the Inflation Calculator calculator. For an after-tax return, apply the relevant effective rate to the gain.
3. Risk. A 15 % CAGR earned on a single volatile stock is not equivalent to 15 % from a diversified portfolio, though the calculator reports the same number for both. Risk-adjusted comparison requires a volatility measure (such as the Sharpe ratio) and a separate calculation.

Related calculators

The three calculators answer adjacent questions:

• ROI / CAGR characterizes the return of an investment with a known starting and ending value.
• The Compound Interest Calculator projects a future value from a candidate return rate, optionally with monthly contributions.
• The Inflation Calculator translates a nominal return into real purchasing-power terms.

A common workflow chains the three: compute CAGR here for a past investment, use that rate in the compound-interest calculator to project forward, then deflate the projection through inflation to express it in real terms.