Finance · 5 min read
How to Calculate CAGR
A constant annual rate that connects start to end
Compound annual growth rate (CAGR) smooths a multi-year path into one constant yearly rate. This tutorial walks through (V_end / V_start)^{1/t} − 1, a $10,000 / $16,105 / 5-year worked example, and a playground that builds the smoothed growth staircase as you change start, end, and years. Figures are illustrative; fees and taxes are omitted.
Written by the My Calculator Stack editorial team. About our methods
These figures are illustrative. Fees, taxes, and product-specific rules are omitted. This is not investment, tax, or financial advice.
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.
Inline playground
Illustrative — fees and taxes omitted
Smoothed annual rate
10.00%
Start $10,000.00 → end $16,105.00 over 5 years
(16105 / 10000)^(1/5) − 1 ≈ 10.00%
Illustrative only — a single start and end, no extra deposits, no fees or taxes.
Open the full CAGR calculator →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.
Try it yourself
Open the related calculator and put these formulas to work.