How to Calculate CAGR

1.What CAGR is

CAGR is the constant annual rate that takes a starting value to an ending value over t years if growth compounded once per year. It is not the average of yearly returns, and it hides the path in between — volatility, deposits, and withdrawals disappear. Use it to compare two holding periods on equal terms, not as a forecast. Start and end must be positive; years must be positive.

2.The formula

CAGR = (V_end / V_start)^{1/t} − 1. V_start is the beginning value, V_end is the ending value, and t is the number of years. The result is a decimal rate; the CAGR calculator scales it to a percent. After t years at that constant rate, V_start × (1 + CAGR)^t equals V_end. The same identity powers the CAGR calculator on this site.

\[ \mathrm{CAGR} = \left(\frac{V_{\text{end}}}{V_{\text{start}}}\right)^{1/t} - 1 \]

3.Worked example

Take $10,000 growing to $16,105 over 5 years — the same defaults as the CAGR calculator. The ratio is 16105 / 10000 = 1.6105. Raise that to 1/5 and subtract one: 1.6105^{0.2} − 1 ≈ 0.10, or about 10% per year. Checking the other way, 10000 × (1.10)^5 ≈ 16,105.

\[ \mathrm{CAGR}=\left(\frac{16105}{10000}\right)^{1/5}-1\approx 0.10 \]

4.Smoothed growth staircase

Move start value, end value, and years to see the constant annual rate update and the staircase rebuild. Each step is one year at that smoothed CAGR — not the actual year-by-year path. This is a teaching widget — no deposits, no fees, no full calculator chrome. Open the CAGR calculator when you want the standalone tool.

5.Open the full calculator

The CAGR calculator uses the same (V_end / V_start)^{1/t} − 1 identity, the same $10,000 / $16,105 / 5-year example, and the same limitation that taxes and fees are omitted. Browse other finance tools if you need ROI, compound interest, or APY next.