CAGR Calculator — Compound Annual Growth Rate

What CAGR actually answers

Compound Annual Growth Rate (CAGR) is the rate that, if compounded annually, would turn a starting value into an ending value over a given period. It restates a total change as an annual rate, which total return on its own does not do, because total return carries no information about how long the change took. A 50% total return over 2 years is a 22.5% CAGR; the same 50% total return over 10 years is a 4.1% CAGR. Those are different annual rates behind an identical headline figure. CAGR is a standard measure for comparing values recorded over different time periods.

The formula in plain terms

CAGR = (Ending Value / Starting Value)^(1/years) − 1. Where 10,000 grows to 17,500 over 5 years: CAGR = (17500/10000)^(1/5) − 1 = 1.75^0.2 − 1 = 11.84% per year. The year-root is where compounding is expressed: it is the rate that, applied five times in succession, moves the starting value to the ending value. The calculator above performs this arithmetic; the sections below describe what the measure captures and what it leaves out.

Where CAGR is informative

Three common applications show the range. The first is comparing holdings measured over different periods. Fund A returned 85% over 6 years; Fund B returned 55% over 4 years. The total returns are not directly comparable. Converted to CAGR, Fund A is 10.8% and Fund B is 11.6%, so Fund B produced the higher annualised rate despite the lower total return.

The second is restating total-return figures in annual terms. A figure of 100% over 10 years corresponds to a 7.2% CAGR. The conversion expresses the same performance on an annual basis.

The third is setting a reference rate for modelling. Where an asset has historically produced an 8% CAGR, that rate is one reference point for forward scenarios, though past rates do not determine future ones.

The volatility CAGR smooths over

CAGR is a smoothed figure. It describes the constant rate that reproduces the two endpoints, not the path between them. Real holdings rarely grow at a constant rate. A sequence of −15%, +40%, +5%, −8%, +33% and +16% across six years compounds to a growth factor of 1.7735, which is a CAGR of 10.02%, one rate standing in for six very different years. The CAGR describes the endpoints; the dispersion of the annual figures describes the variation along the way. Two holdings can share a CAGR and differ substantially in year-to-year variation.

CAGR compared with the arithmetic mean of annual returns

These are distinct quantities and are often conflated. Take annual returns of 20%, −10%, 20% and −10%. Their arithmetic mean is 5% per year. The CAGR is (1.2 × 0.9 × 1.2 × 0.9)^0.25 − 1 = 3.92% per year. CAGR is always lower than or equal to the arithmetic mean, and the gap widens as the annual figures become more dispersed. An advertised average of 10% a year over a variable period can correspond to a CAGR of 5–6%, which compounds to a materially smaller ending value. The two measures answer different questions: the arithmetic mean describes a typical year, CAGR describes the endpoints.

The calculator's Simple Annual Return (Total ÷ Years) row is a third quantity again: total return divided by the number of years. It is not the arithmetic mean of annual returns, which cannot be derived here because the tool takes two endpoint values rather than a year-by-year series.

Identical CAGR, different paths

Consider two funds that both produce close to 8% CAGR over four years. Fund X grows at a steady 8% each year. Fund Y returns +25%, −15%, +35% and −5%, which compounds to a growth factor of 1.3627, or 8.04% annualised. The CAGR is effectively the same; the year-by-year path is not. Risk-adjusted measures such as the Sharpe ratio (the return in excess of a risk-free rate, divided by the standard deviation of that excess return) describe the variability that CAGR on its own leaves out.

Where CAGR can mislead

Two situations account for most of the distortion. The first is endpoint sensitivity. A CAGR measured from a post-crash low to a later peak differs sharply from one measured from a prior peak to a later trough, because only the two endpoints enter the calculation. Windows of 20 years or more dampen this effect; shorter windows can amplify it considerably.

The second is a single dominant year. A holding that returned +100% in year one and +2% per year for years two through ten compounds to a CAGR of 9.10%. That first year on its own, spread across the same ten years, comes to 7.18%, roughly four-fifths of the total in log terms. What produced a CAGR is separate information from its value.

How long-run CAGR ranges differ by asset class

Long-run annualised rates differ across asset classes for structural reasons. Broad equity indices have historically shown the widest range of outcomes, reflecting both higher year-to-year variation and the residual claim equity carries on company earnings. Government and investment-grade bond returns have historically clustered in a narrower band, since those cash flows are contractual. Cash-equivalent instruments have historically shown the narrowest range, and over most long windows the lowest rates, though over some periods cash has outrun bonds. Where inflation is positive, adjusting any of these for it lowers the figure, and the adjustment is proportionally largest for the lowest-returning assets. Published long-run figures vary by index, country, currency, start date, and whether income is treated as reinvested, so no single global figure applies.

Portfolio CAGR versus component CAGR

A portfolio's CAGR is not the weighted average of its components' CAGRs, because growth factors combine multiplicatively while rates do not. The relationship depends on rebalancing. A portfolio held at 60% in an asset compounding at 8% and 40% in an asset compounding at 4%, rebalanced back to those weights every year, returns 0.6 × 8% + 0.4 × 4% = 6.4% in each year, so its CAGR is exactly 6.4%. Left unrebalanced for ten years, the same pair produces a growth factor of 0.6 × 1.08^10 + 0.4 × 1.04^10 = 1.8875, a CAGR of 6.56%. Where each holding compounds at a steady rate, the unrebalanced figure is the higher of the two, because the faster-growing holding takes up more of the portfolio as the period runs on. With variable annual returns that ordering is not fixed: two holdings whose returns move in opposite directions can leave the rebalanced portfolio ahead. Contributions and withdrawals shift the figure again, and a CAGR read off two endpoint values does not register them.

CAGR compared with IRR

CAGR and internal rate of return answer related questions from different inputs. CAGR takes two endpoint values and a duration. IRR takes a dated series of cash flows and finds the rate that sets their net present value to zero. Where money enters or leaves partway through a period, the two diverge, because CAGR has no way to register the timing or size of those flows. Where a holding is bought once and sold once with nothing in between, the two agree.

Negative rates and part-year periods

A negative CAGR uses identical arithmetic. Where an ending value falls below the starting value, the ratio is less than 1, the root of that ratio is also less than 1, and the resulting rate is negative. A value of 10,000 falling to 7,000 over three years annualises to −11.21%. An ending value of zero is a total loss, and the ratio of zero gives exactly −100%, which is the floor of the measure.

Periods that are not whole years are valid inputs. The exponent 1/n is defined for fractional n, so 18 months entered as 1.5 years annualises correctly. Short periods extrapolate a brief window across a full year, so a rate drawn from three months carries far less information than one drawn from ten years. Two cases have no defined rate and return a message rather than a result: a starting value of zero or below, since the ratio requires division by that value, and a negative ending value, since a fractional root of a negative number is undefined.

What the calculator shows

The tool computes CAGR from a starting value, an ending value and a time period, alongside total return, absolute gain, the total-divided-by-years figure, and the time a value would take to double at the computed rate. That doubling row uses the exact expression rather than the Rule of 72 shortcut: at a rate near 9.8% the shortcut gives 7.33 years against an exact 7.40, and the two separate further as rates climb. The Rule of 72 Calculator works that shortcut directly. The tool does not model year-to-year variation, sequence effects, contributions or withdrawals during the period, fees, tax, or inflation. For a completed holding, the CAGR figure is exact arithmetic on the two endpoints. For forward scenarios, a historical CAGR is a reference point, though past rates do not determine future ones.