CAGR Calculator

This page is about what the CAGR engine itself computes and where it stops. For the wider picture — how a total return and a yearly rate are two readings of the same growth, and why annualizing a return is the same arithmetic as a CAGR — the companion guide ROI and CAGR explained works through both from first principles. The full guides index and the methodology page sit behind every figure below.

The geometry behind the rate

CAGR% = ((end ÷ start)^{1 ÷ years} − 1) × 100 — the geometric mean growth per year. In the example, 10,000 → 16,000 is 60% of total growth, and the fifth root of that growth ratio gives 9.86% per year (both numbers computed at build time by the tested engine behind the form). Naively dividing 60% by five would claim 12% a year — wrong, because each year's growth compounds on the last.

CAGR vs. "average return": the volatility tax

The arithmetic average of yearly returns and the CAGR agree only when every year is identical. Take a value that gains 50% one year and loses 30% the next: the average says +10% a year, but 100 becomes 150 and then 105 — a CAGR of just 2.47%. Whenever a track record is quoted as an average of good and bad years, the compound rate is the one your money actually experienced, and it is always the smaller of the two for a volatile series.

Same CAGR, very different rides

Because CAGR sees only the endpoints, it cannot tell a smooth climb from a crash and a scramble back. Two portfolios both start at 10,000 and both end at 16,000 five years later, so both report exactly 9.86% a year. The first compounds quietly at that rate the whole way. The second falls to 6,000 in year one — a -40% drawdown — and must then climb from 6,000 to 16,000 in the four years that remain, which the same formula prices at 27.79% a year, sustained for four straight years. Identical CAGR, but the second investor spent a year staring at a large loss and then needed a run of exceptional returns. Anyone who would have sold at the bottom never earns the smoothed rate — worth remembering whenever a track record arrives as one tidy percentage.

Why the choice of endpoints decides the answer

The engine reads exactly two values and the time between them; nothing else enters the calculation. That is what makes CAGR comparable across investments, and also what makes it easy to steer by choosing where to start and stop the clock. Take the bumpy portfolio from above, which fell to 6,000 in its first year before recovering to 16,000. Measured across the whole five years, it compounds at 9.86% — an ordinary-looking rate. But start the measurement at the 6,000 trough instead, and the remaining four-year climb to 16,000 reports 27.79% a year: the same investment, nearly three times the headline rate, with no arithmetic error anywhere. Neither number is wrong; they answer different questions, because they span different windows. A rate quoted without its start and end dates is unreadable, and a rate measured from a conspicuous low is a sales document as much as a measurement. Whenever a CAGR arrives, the first question is not "how high" but "between which two dates" — and whether those dates were chosen or merely observed.

When the measurement window is too short

The formula will annualize any period, including ones far too short to support an annual claim. Take a user base that grows from 1,000 to 1,500 in one quarter — real growth of 50%. Entered with 0.25 years, the arithmetic reports 406.25% per year, because it assumes the quarter's pace repeats, with compounding, for four quarters running. Nothing grows on that schedule for long. The figure is not a mistake; it is an extrapolation dressed up as a measurement. A practical rule: growth measured over less than a year is a projection to challenge, not a rate to report — and even one- or two-year CAGRs deserve suspicion, since a single unusual year dominates a window that short.

Comparing investments that ran for different lengths

Total growth cannot compare a three-year investment with a six-year one; CAGR can, because it puts both on a per-year footing. Turning 10,000 into 15,000 over three years is 50% in total; turning 10,000 into 19,000 over six years is 90%. The longer investment wins on total growth, yet the shorter one compounded faster — 14.47% a year against 11.29%. Which number should decide depends on what happens next: if the capital can be redeployed at a similar pace, the faster compounder does more work per year; if the realistic alternative is idle cash, six years at 11.29% may still be the better outcome. For the money-in, money-out framing of a single deal, the ROI calculator shows total and annualized return side by side.

What the engine accepts, and what it refuses

The calculation is a pure function with three guarded inputs. The start value and the end value must each be greater than zero, because a compound rate is the geometric mean of their ratio and that ratio has no meaning at or below zero; the number of years must be greater than zero as well, and it may be fractional — 2.5 years, or 0.5 for six months, are read literally. Those are the only restrictions. A decline is not one of them: feeding a drop from 200 to 150 over three years is perfectly valid and returns a negative rate of -9.14% a year — the steady pace that would compound 200 down to 150. What the engine will not do is guess at an undefined case. Ask it for a rate out of a zero or negative value and it returns a plain message naming the offending field instead of an infinity, a NaN, or a stand-in zero. The same design runs throughout Sumvia: an operation with no conventional answer is reported as such rather than papered over, so a number on screen is always a number the arithmetic actually supports.

Reading the rate the page prints

The figure you see is a cleanly rounded presentation of a more precise internal value. The engine carries full double-precision arithmetic through the calculation and does no rounding of its own; the formatting layer then normalizes the result to twelve significant digits — which is what strips the binary artefacts that would otherwise turn a clean third into a trail of stray digits — and shows at most six decimal places. Doubling a value in three years makes the point: the rate is an endless decimal, which the calculator displays as 25.992105% and the shorter examples on this page round further to 25.99%. Both describe the same 100% of total growth; they differ only in how many digits are shown. The six-place limit has a companion rule for the opposite extreme: a rate too small to register at six decimals is shown with six significant figures instead, so a tiny result is never flattened to a misleading "0" — a value creeping from 1,000 to just over it across two years annualizes to 0.0000001% rather than vanishing. Inputs are held to a documented range of ±10¹⁵, where double-precision arithmetic stays dependable for everyday use. One practical consequence follows from all of this: the number on screen is the rounded figure, so for chained work — feeding a CAGR into a further hand calculation — prefer doing the whole calculation in one pass rather than retyping a displayed, rounded rate. The methodology page states the rounding policy in full.

Which tool: CAGR or ROI?

They meet in the middle. Start from money invested and money received, and the ROI calculator is the natural framing — its annualized option is precisely a CAGR. Start from a value observed at two dates, as with a chart or a revenue series, and CAGR is the direct route. For a single change between two values with no time dimension — last month's price against this month's — the price change calculator reports the move in both directions. The guide ROI and CAGR explained lays the two framings side by side and shows exactly where they coincide.

Frequently asked questions

Values are computed on your device and never transmitted. CAGR is a descriptive statistic of two endpoints — it is not a forecast, and this page offers no investment advice. Formula details: methodology.