CAGR Calculator
Fill any three of start value, end value, years, and rate — the blank one is solved. Leave the rate empty for the classic question: what did this actually compound at?
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| Tab / Shift+Tab | Next / previous field |
| ↑ / ↓ | Step a value by 1 (Shift: 10, Alt: 0.1) |
| Enter | Copy the primary result |
| [ / ] | Fewer / more decimal places (percent) |
| Esc | Clear the field |
The CAGR formula, in all four directions
One relationship, end = start × (1 + r)years, rearranged for
whichever piece is missing:
- Rate (the classic):
r = (end ÷ start)1/years − 1. $10,000 → $20,000 in 10 years is 7.18%/yr. - End value: compound the rate forward — $10,000 at 7.18% for 10 years lands back on ~$20,000.
- Years:
ln(end ÷ start) ÷ ln(1 + r)— how long a doubling takes at 7.18% (ten years; at 10% it's 7.3). - Start value: discount the end backwards — what you'd have needed to begin with.
The number's power is comparability: a 3-year fund result, a 7-year house appreciation, and a savings rate all reduce to the same per-year unit. Its weakness is the same smoothing — CAGR hides every drawdown along the way, which is exactly the property that makes marketing love it. Pair it with the path-aware metrics in ROI, CAGR, and drawdown before letting a single smooth percentage impress you, and remember the rule of 72 for mental checks: 72 ÷ rate ≈ years to double (72 ÷ 7.18 ≈ 10 ✓).
CAGR FAQ
What is the CAGR formula?
CAGR = (end ÷ start)1/years − 1. Doubling $10,000 to $20,000 over ten years is (2)0.1 − 1 = 7.18% a year — not 10%, because compounding does part of the lifting. CAGR is the smooth rate that would have produced your result; the actual path was bumpier.
How do I solve for the end value or the number of years instead?
Fill any three fields and leave the one you want blank. Start, rate, and years give the end value (start × (1 + r)years); start, end, and rate give the years (log-ratio divided by log-growth). The answer row labels itself with whichever quantity it solved.
Why is CAGR lower than my average yearly return?
Because arithmetic averages ignore compounding's cruelty: +50% then −50% "averages" 0% but leaves you down 25%. CAGR is the geometric answer — it only cares where you started, where you ended, and how long it took. The gap between the two is volatility drag, and the metrics article shows it eating a portfolio in a worked table.
Why can't CAGR handle a value that crosses zero?
The formula takes an nth root of end ÷ start, and no real growth rate turns a positive number into a negative one (or grows anything out of exactly zero). A value hitting zero is a −100%-per-year story at best. For sign-crossing journeys, describe the legs separately — a growth rate that spans a bankruptcy isn't a rate, it's an obituary.
How precise is the result?
CAGR is this site's one documented exception to exact rational arithmetic: an nth root is irrational, so it computes in double-precision floating point and displays at up to 4 decimal places — where the float error, around one part in 1015, sits eleven orders of magnitude below what's shown. Every other calculator here never touches a float; the methodology page records the exception.