Your two values
The starting figure — revenue, users, market size, anything that compounds.
The figure at the end of the period.
The elapsed time, not the number of data points. Five annual figures span four years.
Compound annual growth rate
20.11%
Growing at this constant rate turns $1,000,000 into $2,500,000 over 5.00 years.
Total growth
150.00%
2.500× over the whole period
Doubling time
3.78 yrs
Exact, not the rule of 72
Annual multiplier
1.20112×
If this rate continued
A straight extrapolation from your ending value — shown because it is the projection people build anyway, and it is better made explicit than assumed. Nothing guarantees a past rate persists.
| Year | Projected value |
|---|---|
| +1 | $3,002,811 |
| +2 | $3,606,750 |
| +3 | $4,332,155 |
| +4 | $5,203,458 |
| +5 | $6,250,000 |
Read this alongside the answer
- CAGR smooths the path completely: a business that fell 40% and then tripled shows the same CAGR as one that grew steadily. Read it alongside the year-by-year series, never instead of it.
Step-by-step solution for your numbers
Including the check that matters most: compounding the rate back over the period must return your ending value exactly. That step is the arithmetic proof the answer is right.
Step 1: Divide the ending value by the beginning value
- Formula
- ratio = ending ÷ beginning
- Your numbers
- $2,500,000.00 ÷ $1,000,000.00
- Result
- 2.500000×
This is the total multiple over the whole period, before annualising.
Step 2: Take the n-th root, where n is the number of years
- Formula
- annual multiple = ratio^(1/n)
- Your numbers
- 2.500000^(1 ÷ 5.00) = 2.500000^0.200000
- Result
- 1.20112443
The root undoes the compounding: it finds the single yearly multiplier that repeats n times to produce the total ratio.
Step 3: Subtract 1 to convert the multiplier into a growth rate
- Formula
- CAGR = ratio^(1/n) − 1
- Your numbers
- 1.20112443 − 1
- Result
- 0.20112443
Step 4: Express the rate as a percentage
- Formula
- CAGR% = CAGR × 100
- Your numbers
- 0.20112443 × 100
- Result
- 20.11%
Step 5: Check the result by compounding it back
- Formula
- beginning × (1 + CAGR)^n should return the ending value
- Your numbers
- $1,000,000.00 × (1 + 0.20112443)^5.00
- Result
- $2,500,000.00
Recomputing the ending value from the rate is the arithmetic proof that the answer is right.
Step 6: Find the doubling time at this rate
- Formula
- t = ln(2) / ln(1 + CAGR)
- Your numbers
- t = 0.693147 ÷ ln(1 + 0.201124) = 0.693147 ÷ 0.183258
- Result
- 3.78 years
Exact doubling time — the "rule of 72" is a shortcut that drifts several percent away from this at high rates.
The formula
CAGR = (ending / beginning)^(1/n) − 1
t_double = ln(2) / ln(1 + CAGR)
n is the number of years elapsed between the two values. The second line is the exact doubling time at that rate — the figure the rule of 72 approximates.
What CAGR is good for, and what it conceals
CAGR is a geometric mean, and that is precisely why it is the right average for a rate that compounds. The arithmetic mean of +50% and −50% is zero, which would suggest you broke even; in reality a value that rises by half and then falls by half has lost a quarter of its worth. CAGR reports that honestly, at about −13.4% a year.
What it cannot do is describe the journey. Two businesses with identical endpoints have identical CAGRs, whether one grew steadily and the other collapsed and recovered. Treat it as a summary statistic to be read beside the underlying series, and be suspicious of any growth story told entirely through a single compound rate.
Two mechanical errors account for most wrong CAGRs in circulation, and both are easy to avoid. Counting data points rather than elapsed years inflates the denominator and understates the rate. And computing growth from a very small base produces a percentage that is technically correct and practically meaningless — going from $1,000 to $100,000 is a 900% annual rate over two years, which tells you far less than the two raw numbers do.
Over a long span, part of any nominal growth rate is simply rising prices. To convert both endpoints into the same period's dollars before computing a real growth rate, use the inflation adjustment calculator
Methodology and sources
The calculation is the standard geometric-mean growth rate, computed in double precision directly from the two values and the elapsed period. The page also compounds the resulting rate back over the period and shows that it reproduces your ending value — a self-check that makes an arithmetic error visible rather than plausible.
Doubling time is computed exactly from natural logarithms rather than through the rule of 72, which drifts by several percent at higher rates.
No market or company data is embedded in this page: both values are yours to supply. Where the figures come from matters more than the arithmetic does, so the sources below are the primary federal series to take them from — audited filings for company revenue, and official industry accounts for the sector comparison that gives a growth rate its meaning. All arithmetic runs in your browser; nothing you enter is transmitted or stored.
Primary sources
U.S. Securities and Exchange Commission
EDGAR full-text search — company filingsAudited revenue and segment figures from 10-K and 10-Q filings are the primary source for a growth rate on any US public company — preferable to a secondary summary, which may restate or reclassify.
U.S. Bureau of Economic Analysis
GDP by IndustryOfficial value-added and gross-output series by industry, the standard denominator when comparing a company’s growth against its sector.
U.S. Census Bureau
Economic CensusBenchmark revenue and establishment counts by industry, collected every five years — the reference series for measuring long-run industry growth.
Links go to the publishing agency, so you always read the current figure rather than a copy of it. This page embeds no agency data of its own.
Common questions
How many years should I enter?
The elapsed time between the two values, not the number of figures you have. Annual revenue for 2020 through 2025 is six data points but five years of growth. Entering six there is the single most common mistake in a CAGR, and it understates the rate.
Why can’t I start from zero or from a loss?
Because CAGR is built on the ratio of the two values, and dividing by zero or by a negative number has no meaningful compound rate — the result would be infinite or imaginary. Growth from a near-zero base is better described in absolute terms, or by naming the base explicitly, than by a percentage that can be made arbitrarily large by shrinking the starting point.
What does CAGR hide?
The path. A business that fell 40% and then tripled produces the same CAGR as one that grew steadily every year, and the two are not remotely the same investment. CAGR is a summary of the endpoints only, so it should be read next to the year-by-year series rather than instead of it.
Is CAGR the same as average annual growth?
No, and the difference is not small. The simple average of +50% and −50% is zero, but a value that rises 50% then falls 50% has lost a quarter of its worth — its CAGR is about −13.4% a year. CAGR is a geometric mean, which is the correct way to average a rate that compounds.
How accurate is the rule of 72?
It is a mental shortcut, not the answer. At 10% growth the rule says 7.2 years to double; the exact figure is 7.27. The gap widens as rates rise. This page reports the exact doubling time from natural logarithms, so there is no need for the approximation.
Should I project forward at the same rate?
Only with stated reasons. The projection shown here is a straight extrapolation, included because it is the calculation people perform anyway and it is safer made explicit. A past rate persisting into the future is an assumption that needs its own evidence — market saturation, competition and base effects all tend to pull realised growth below a historical CAGR.
Should I adjust for inflation first?
If you are comparing purchasing power or growth across a long span, yes. A nominal CAGR includes general price increases; a real one strips them out. Convert both endpoints into the same period’s dollars first, then compute the rate on the adjusted figures.
This page does the arithmetic. We check the numbers you put into it.
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