The formulas
CAGR is derived by working backward from the total growth over the whole period to a single annual rate:
CAGR = (Ending value / Starting value)^(1 / years) − 1
Raising the total growth ratio to the power of one-over-years is what “undoes” however many years of compounding to isolate the single rate that, applied repeatedly, produces that ratio. It’s the same math as compound interest, run in reverse: instead of a rate you already know, you’re solving for the rate that must have applied.
The calculator’s other two questions run the same formula the other way round:
Ending value = Starting value × (1 + rate)^years
Years = ln(Target / Starting value) ÷ ln(1 + rate)
With dates instead of a number of years, the years are the days between the two dates divided by 365.
A worked example
Say $100.00 grew to $200.00 in 5 years.
- Divide the ending value by the starting value: 200 ÷ 100 = 2. It doubled.
- Raise that to the power of 1 ÷ 5 = 0.2: 20.2 = 1.1487.
- Subtract 1: 0.1487, a CAGR of 14.87% a year.
Growing 14.87% every year gets there exactly:
| After | Value |
|---|---|
| 1 year | $114.87 |
| 2 years | $131.95 |
| 3 years | $151.57 |
| 4 years | $174.11 |
| 5 years | $200.00 |
Dividing the 100% total return by 5 years would say 20% a year, which overstates it: at 20% a year, $100.00 would become $248.83, not $200.00. Enter these numbers in the calculator above and you'll get the same 14.87%.
Why CAGR smooths out a bumpy path
A real investment, business, or metric rarely grows at a constant rate: some years are up sharply, some are flat, some go backward. CAGR ignores all of that internal variation and reports only the beginning and ending points, as if growth had been perfectly smooth. That’s exactly what makes it useful for comparison (it reduces a messy multi-year story to one number) and exactly what it can’t tell you (how volatile or risky the actual path was to get there). Two investments can have an identical CAGR while one moved in a straight line and the other swung wildly.
That’s also why a single CAGR can hide a lot. Comparing several periods that end on the same date, such as the last 1, 3 and 5 years, shows whether growth has been speeding up or slowing down: a fund with a strong 5-year CAGR and a weak 1-year one tells a different story from one that’s steady across all three.
Reading the chart and the yearly table
The chart and the table show what the value would be at each point if it had grown at exactly the CAGR every year: a smooth path with the same start and end as your real numbers. With values in between, the chart also marks where the investment really was on those dates, so you can see how far the real path strayed from the smooth one.
With dates, the table can count years from your start date, or follow calendar years (January to December). In rupees it can also follow India’s financial year (April to March). A first or last row that isn’t a full year says how long it covers.