The rate that connects two figures
Given a starting value, an ending value and the years between them, there is exactly one constant annual rate that links them. This calculator finds it. It is the standard way to describe growth in revenue, users, property values or an investment.
The formula
Worked example: 10,000 grows to 16,000 over 5 years
- Total growth: 60%
- Compound annual rate: 9.86%
- Total divided by years would give 12%
The 2.14-point gap is compounding. Growth in year five works on a base 46% larger than year one, so a smaller rate reaches the same endpoint.
Checking the answer
| Year | Opening | Growth at 9.86% | Closing |
|---|---|---|---|
| 1 | 10,000 | 986 | 10,986 |
| 2 | 10,986 | 1,083 | 12,069 |
| 3 | 12,069 | 1,190 | 13,259 |
| 4 | 13,259 | 1,307 | 14,567 |
| 5 | 14,567 | 1,436 | 16,003 |
The absolute growth rises every year while the rate never moves. That is the whole idea, and it is why the simple average always overstates.
What a single rate cannot tell you
The formula uses only the first and last values. Three very different businesses produce the same 9.86%:
- Steady growth of roughly 10% every year
- +60% in year one, then flat for four years
- Flat for four years, then +60% in year five
Only the first is a growth business. The other two are a good year and a recent inflection, and an investor should price them differently. Always look at the series alongside the rate.
What this calculator leaves out
Inflation, and any money added or removed between the two endpoints. If capital was injected in year three, part of the growth was bought rather than earned, and this rate credits it to performance.
Working the formula backwards
The same relationship answers three other questions. Fix any three of the four variables and the fourth follows.
To find the ending value: end = begin × (1 + rate)years. At 9.86% for another five years, 16,000 becomes 25,600. To find how long a target takes: years = log(end/begin) / log(1 + rate). Reaching 20,000 from 16,000 at this rate takes 2.4 years.
Comparing against a benchmark
A 9.86% compound rate is only meaningful next to something. Broad equity markets have returned roughly 7% a year in real terms over long periods, and general inflation has run near 2 to 3%.
So 9.86% nominal is roughly 7% real — respectable, and close to what a passive index would have delivered over the same window with no effort. For a business, the comparison is different again: 9.86% revenue growth is solid for a mature company and weak for an early-stage one.
The rule of 72 as a sanity check
Divide 72 by the rate and you get the years to double. At 9.86% that is 7.3 years, so 10,000 should reach roughly 20,000 by year seven and change.
The table above has it at 16,003 after five years, which is on track. If a quoted growth rate and the doubling time it implies do not line up with the actual figures, one of the numbers is wrong — usually the years, which get rounded or counted inclusively.
Related calculators
- CAGR calculator — the same figure under its finance name
- Revenue growth calculator — year-on-year rather than compounded
- Rule of 72 — how long this rate takes to double the value