What CAGR tells you
The compound annual growth rate is the one constant yearly rate that would carry a starting value to an ending value over a given number of years. Real growth is bumpy; CAGR replaces the bumps with a smooth path so that different periods, investments or businesses can be compared on the same yearly footing.
The calculator works four ways:
- Growth rate — from a starting value, an ending value and the time between them (in years and months, or between two dates).
- From yearly returns — enter each year’s return and see the true compound rate next to the simple average of those returns.
- End value — what a starting value grows to at a given rate.
- Time to target — how many years it takes to reach a target at a given rate.
The values can be anything that grows or shrinks: revenue, a share price, a population, subscribers. If you want the return on an investment including fees and a net gain in money, the ROI calculator is built for that.
CAGR formula
CAGR = (V₁ ÷ V₀)^(1 ÷ t) − 1
CAGR = ((1 + r₁) × (1 + r₂) × … × (1 + rₙ))^(1 ÷ n) − 1
V₁ = V₀ × (1 + CAGR)^t
t = ln(V₁ ÷ V₀) ÷ ln(1 + CAGR)
- V₀
- starting value
- V₁
- ending value (or target)
- t
- number of years; months count as twelfths, leftover days as days ÷ 365
- r₁ … rₙ
- yearly returns as decimals (8% = 0.08)
The second formula is the geometric mean of the yearly growth factors. It is exactly the first formula applied to the value those returns produce, so both give the same answer for the same history.
Worked example
A shop’s yearly sales rise from 10,000 to 18,000 over 5 years.
- Growth multiple: 18,000 ÷ 10,000 = 1.8 (total growth of 80%)
- CAGR: 1.8^(1 ÷ 5) − 1 = 1.124746 − 1 = 12.47% a year
- Check: 10,000 × 1.1247 is 11,247.46 after one year, 12,650.54 after two, 14,228.64 after three, 16,003.61 after four and 18,000 after five.
Dividing the total growth by the years gives 80% ÷ 5 = 16%, which is too high: at 16% compounded, 10,000 would reach about 21,000 in five years, not 18,000.
Turned around: 10,000 growing at 8% a year reaches 14,693.28 after five years, and needs 9.01 years (rounded up, 9 years and 1 month) to double to 20,000. The rule of 72 gives almost the same answer: 72 ÷ 8 = 9 years.
Why the average of yearly returns overstates growth
Suppose an investment gains 50% one year and loses 50% the next. The average of the two returns is 0%, which sounds like breaking even. It isn’t:
- 10,000 × 1.5 = 15,000 after the gain
- 15,000 × 0.5 = 7,500 after the loss
You have lost a quarter of the money. The compound rate is √0.75 − 1 = −13.40% a year, and that figure, applied twice, does reproduce 7,500. A loss is taken from a larger base than the gain was applied to, so ups and downs of the same size leave you behind.
The same happens with less extreme numbers. Returns of 15%, −20%, 30%, 5% and −10% average 4% a year, but 10,000 actually becomes 11,302.20, a compound rate of 2.48%. Earning 4% every year would have produced 12,166.53. Mathematically, the arithmetic average is never lower than the compound rate, and the gap grows as returns swing more. The two agree only when every year’s return is the same.
When a fund or a pitch quotes an “average annual return”, check whether it is the arithmetic average or the compound (annualized) rate. Only the compound rate tells you what your money actually did.
What CAGR leaves out
- The path. Two investments with the same CAGR can have very different ups and downs along the way. CAGR says nothing about volatility or risk.
- Money added or withdrawn. CAGR assumes one starting value and one ending value. With regular contributions, use the investment calculator or a money-weighted return such as a spreadsheet’s XIRR function.
- Inflation. The rate is nominal. Subtracting inflation roughly gives the real growth; the inflation calculator shows what past money is worth today.
- Changes of sign. There is no compound rate from a negative value to a positive one (a loss turning into a profit), or from zero. The calculator says so instead of producing a number.
- Short periods. For less than a year, CAGR stretches a short result into a yearly one and can look far better or worse than it was.
To grow money forward at a fixed rate with regular deposits and different compounding frequencies, the compound interest calculator goes further.
Frequently asked questions
How do you calculate CAGR?
Divide the ending value by the starting value, raise the result to the power of 1 divided by the number of years, and subtract 1. Growing from 10,000 to 18,000 in 5 years gives 1.8^(1/5) − 1 = 12.47% a year.
Why is CAGR lower than the average annual return?
The average of yearly returns ignores that each year’s return applies to a different starting amount. A 50% gain followed by a 50% loss averages 0% but leaves you with 75% of your money, a compound rate of −13.40% a year. The compound rate is never higher than the arithmetic average.
Is CAGR the same as annualized return?
For a single amount invested at the start and valued at the end, yes: both are the constant yearly rate that links the two values. With deposits or withdrawals in between, an annualized money-weighted return such as XIRR is the right measure instead.
Can CAGR be calculated with negative numbers?
Only when both values have the same sign. From a loss of 100 to a loss of 150 over two years the calculator shows 22.47% a year, describing how the loss grew. From a negative value to a positive one, or from zero, no compound rate exists.
How long does it take to double at a given growth rate?
Divide the natural log of 2 by the natural log of 1 plus the rate. At 8% a year that is 0.6931 ÷ 0.0770 = 9.01 years. The rule of 72 (72 divided by the rate in percent) gives a quick estimate of about 9 years.
Sources
Last reviewed September 19, 2026