How to use this CAGR calculator
The tool has two modes, switched by the chips above the inputs.
- Find CAGR, the default mode. Enter a beginning value (what your investment was worth at the start), an ending value (what it is worth now, or was worth at the end) and the number of years it was invested. You can use decimals, so 18 months is 1.5 years.
- Find years needed, the reverse calculation. Enter a beginning value, a target ending value you want to reach, and a desired CAGR, and the tool works out how many years it would take to get there at that steady rate.
The results update instantly as you type. In Find CAGR mode you will see your CAGR as a percent per year, your total growth across the whole period, and the growth multiple, which shows how many times your money grew. In Find years needed mode you will see the number of years required and the same growth multiple, plus a chart of the implied growth curve.
How CAGR is calculated
Compound annual growth rate is the single, steady yearly rate that would turn your beginning value into your ending value over the period. The formula is the ending value divided by the beginning value, raised to the power of one over the number of years, minus one: CAGR = (ending value / beginning value) ^ (1 / years) - 1. Multiply the result by 100 to read it as a percent. Because the exponent uses the number of years, CAGR accounts for compounding, the way each year's growth builds on the last.
It helps to know how CAGR differs from total return. Total return, or total growth, is simply how much the value changed across the whole period: ending value divided by beginning value, minus one, times 100. It ignores time, so a 150% total return looks the same whether it took two years or twenty. CAGR fixes that by spreading the gain evenly across the years, giving you a per-year figure you can fairly compare against savings rates, index funds or other investments held for different lengths of time. CAGR is a smoothed average, though, so it hides the ups and downs that happened along the way.
The Find years needed mode runs the same relationship in reverse. Instead of solving for the rate, it solves for the exponent: years = log(target value / beginning value) / log(1 + CAGR). Given a beginning value, a target ending value and the steady yearly rate you expect, this tells you how long it should take to get from one to the other. A CAGR that points the wrong way, for example a positive rate asked to shrink toward a lower target, has no valid answer, so the tool flags it instead of showing a number.
A worked example
Suppose you invested $10,000 and five years later it was worth $25,000. The growth multiple is 25,000 / 10,000 = 2.5x, and the total growth is (2.5 - 1) x 100 = 150%. To find the CAGR, raise 2.5 to the power of 1/5 and subtract one: 2.5 ^ 0.2 = 1.2011, so the CAGR is about 20.11% per year. In other words, a steady 20.11% annual return would have grown $10,000 into $25,000 over five years, even though the real returns may have jumped around from one year to the next.
Running that same example through Find years needed checks out the reverse formula: with a$10,000 beginning value, a $25,000 target and a 20.11% desired CAGR, the growth multiple is again 2.5x, and years = log(2.5) / log(1.2011) ≈ 0.9163 / 0.1832 ≈ 5 years, matching the period from the first example.
Frequently asked questions
How do you calculate CAGR?
CAGR is the ending value divided by the beginning value, raised to the power of one over the number of years, then minus one. Multiply by 100 to show it as a percent. For example, $10,000 growing to $25,000 over 5 years is a CAGR of about 20.11% per year.
What is the difference between CAGR and total return?
Total return is the overall percent change across the whole period and ignores time. CAGR smooths that change into a single steady yearly rate, so you can compare investments held for different lengths of time on equal footing.
Is CAGR the same as the actual yearly return?
No. CAGR is a smoothed average. Real returns swing up and down year to year, but CAGR shows the constant rate that would have produced the same final value, hiding the volatility along the way.
What is a good CAGR?
It depends on the asset and the risk taken. As a rough benchmark, the long-run stock market has returned roughly 7% to 10% per year, so a CAGR well above that usually came with higher risk.
How do I find out how many years it takes to reach a target?
Switch to the "Find years needed" mode, then enter a beginning value, a target ending value and the CAGR you expect. The tool solves years = log(target value / beginning value) / log(1 + CAGR). If the rate points the wrong way for that target, for example a positive rate asked to shrink toward a lower value, there is no valid number of years, and the tool explains why instead of guessing.
This tool is for general information only and is not financial advice.
Related: ROI Calculator, Compound Interest Calculator, Inflation Calculator, Percentage Calculator.