CAGR Calculator
Find the compound annual growth rate between a start and an end value, or solve for the start, the end or the years. Paste yearly returns to see why their simple average overstates the real growth.
How to Use
- Pick what to solve for: the CAGR, the starting value, the ending value or the number of years. The unknown field turns into the answer box.
- Enter the other three values. Years can be fractional, such as 2.5.
- Read the CAGR, the total return and the simple average a year, which shows how far off dividing by the years would be.
- To compare averages, choose From yearly returns and paste each year’s return in percent, such as 12, −8, 20.
- Use the chart to see the growth path; the red dashed line is what the wrong (simple or arithmetic) average would predict.
Worked Example
From a start and an end value. $10,000 grows to $25,000 in 8 years. The growth multiple is 25,000 ÷ 10,000 = 2.5. The CAGR is 2.51/8 − 1 = 12.1353% a year. Check: 10,000 × 1.1213538 = $25,000. At that rate the money doubles every ln 2 ÷ ln 1.121353 = 6.052 years.
From yearly returns. Returns of +12%, −8%, +20%, +5% and +15% average (12 − 8 + 20 + 5 + 15) ÷ 5 = 8.8%. Multiplying instead, 1.12 × 0.92 × 1.20 × 1.05 × 1.15 = 1.49305, so $10,000 became $14,930.50 and the CAGR is 1.493051/5 − 1 = 8.3465%, 0.4535 points below the average.
The common mistake: quoting the arithmetic average as the yearly growth. A +50% year then a −50% year averages 0%, which suggests you broke even. In fact $10,000 rose to $15,000 and fell to $7,500: a 25% loss, or −13.3975% a year. Only the CAGR, applied every year, reproduces the real ending value.
Show Work
Formulas
Two Averages, Two Answers
The arithmetic, geometric and harmonic means are the three classical “Pythagorean means” of Greek mathematics. For anything that grows by multiplying — money, populations, prices — the geometric mean is the right one, because each year’s change is applied to the result of the year before. The geometric mean of positive numbers is never above their arithmetic mean, which is why an average of yearly returns flatters any investment whose returns vary.
The difference matters enough that fund rules address it. In the United States, mutual fund performance in advertisements and prospectuses is quoted as an “average annual total return” worked out from a compound formula, P(1 + T)n = ERV — the initial payment P growing at rate T for n years to the ending redeemable value. That T is a CAGR.
About This Calculator
This calculator solves the CAGR equation for any of its four parts — the rate, the starting value, the ending value or the time — and checks each answer against the standard time-value functions. The yearly-returns mode puts the arithmetic and geometric averages side by side and draws what each one predicts. CAGR assumes no money was added or taken out; when there were deposits or withdrawals, use the IRR Calculator on the cash flows instead.
All calculations run in your browser; nothing you enter is sent to a server.
Estimates for planning and education — not financial, tax or legal advice.
Related tools: Rule of 72 Calculator, IRR Calculator, and ROI Calculator.
Frequently Asked Questions
What is CAGR?
The single yearly rate that, compounded, turns the starting value into the ending value. $10,000 that grows to $25,000 in 8 years has a CAGR of (25,000 ÷ 10,000)1/8 − 1 = 12.1353%: $10,000 × 1.1213538 = $25,000. It smooths out the ups and downs along the way.
Why can’t I just divide the total return by the years?
Because growth compounds. $10,000 to $25,000 is a 150% total return, and 150% ÷ 8 = 18.75%. But $10,000 growing at 18.75% a year for 8 years would reach $39,542.94, not $25,000. The rate that really fits is 12.1353%.
What is the difference between average return and CAGR?
The average (arithmetic mean) adds the yearly returns and divides; the CAGR (geometric mean) multiplies them. A +50% year followed by a −50% year averages 0%, yet $10,000 becomes $15,000 and then $7,500 — a CAGR of −13.3975% a year. The more the returns swing, the further the arithmetic average sits above the growth you actually got.
Can CAGR be negative?
Yes. An investment that falls from $10,000 to $8,000 over 3 years has a CAGR of −7.1682% a year. In that case the calculator shows the halving time instead of the doubling time.
Does CAGR work if I added or withdrew money?
No — it treats every change in value as growth. $10,000 plus a $5,000 deposit after a year, worth $17,000 after two years, looks like a 30.38% CAGR. Counting the deposit as money in, the real return is 7.7592% a year, which the IRR Calculator works out from the cash flows.
How do I use the CAGR Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Company revenue growth
Revenue rising from $2.4 million to $5.1 million in 5 years is a CAGR of 16.2711% a year.
Investment performance
A $10,000 holding worth $25,000 after 8 years grew 12.1353% a year, compounded.
Planning a target
To have $100,000 in 10 years at 6% a year, you need $55,839.48 today.
How long to double
$10,000 growing at 9% a year reaches $20,000 in 8.043 years.
User or audience growth
Going from 12,000 to 45,000 users in 3 years is a CAGR of 55.3616% a year.
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