CAGR Calculator Guide: Formula, Examples & When to Use It
Compound annual growth rate (CAGR) summarizes multi-year performance into one yearly figure—with clear limits when cash flows, day counts, or arithmetic averages enter the picture.
CAGR Calculator Guide: Formula, Examples & When to Use It
Updated May 2026 · ~8 min read
CAGR answers a narrow but useful question: what constant yearly growth rate would connect a starting value to an ending value across n periods? This guide states the formula with plain-language examples (including declines), explains when two-point CAGR misleads, contrasts geometric growth with arithmetic averages of yearly labels, and links to StockCalc tools so you can check your math.
When CAGR is the right lens
- Comparing long horizons: you need one summary growth rate between two balances at known dates.
- Evaluating strategies: you want a single annualized figure comparable across investments with different paths.
- Sanity-checking headlines: you verify whether a quoted “annual” figure matches start/end snapshots.
- No mid-period flows: you can treat the portfolio as buy-and-hold between the two snapshots—otherwise use money-weighted or IRR-style tools.
The formula
CAGR = (V_end ÷ V_start)^(1/n) − 1
V_start and V_end must be in consistent units; n is the number of periods (often years or fractional years). When V_end < V_start, CAGR is negative. CAGR smooths the path—it does not describe volatility along the way.
Worked examples (illustrative numbers)
Example A — five-year growth
- Start value $10,000, end value $16,105, horizon 5 years.
- CAGR = (16105 ÷ 10000)^(1/5) − 1 ≈ 10.0% per year (rounded).
Example B — quick sanity check
- Doubling in ~7 years implies CAGR ≈ 10% (rule of 72 sketch).
- If endpoints disagree with intuition, recheck inputs—especially splits and reinvestment assumptions.
Example C — negative CAGR (decline)
- Start value $10,000, end value $5,905, horizon 5 years.
- Ratio = 0.5905; CAGR = 0.5905^(1/5) − 1 ≈ −10.0% per year (rounded).
- Same formula as gains: when V_end < V_start, CAGR is negative but still a smoothed annualized figure, not the path.
Choosing n (horizon) consistently
CAGR is only as honest as the period you plug in. Use the same day-count convention for both endpoints (e.g., both month-end statements, or both trade dates). If you mix “purchase on Jan 5” with “valuation on Dec 31,” decide whether n should be full calendar years, 365-day chunks, or something else—and keep it consistent when comparing two investments. For sub-year horizons, n can be a fraction (e.g., 2.5 years); the math still uses the same ratio-and-root pattern.
When cash flows break the two-point story
CAGR summarizes only a starting value, an ending value, and a count of periods. If you contribute or withdraw along the way, the endpoints alone no longer describe “how the portfolio grew.” In that setting, practitioners use time-weighted or money-weighted returns, or an IRR / XIRR-style solve on dated cash flows. StockCalc’s stock return calculator helps standardize price-and-dividend math; for irregular flows, pair intuition with an IRR guide or spreadsheet XIRR.
CAGR vs arithmetic average of yearly returns
Arithmetic mean of annual percentages can overstate growth when volatility is present. Sketch: +50% then −40% over two years multiplies wealth by 1.5 × 0.6 = 0.9, so the annualized CAGR linking those endpoints is roughly −5.1%, while the simple average of the two yearly labels is +5%. For decision-making, prefer the geometric story (CAGR between endpoints, or proper return aggregation) when you care about compounded wealth.
For definitions and related reading, see the CAGR glossary entry and CAGR vs absolute return. Then use the calculator below to reproduce the arithmetic on your own numbers.
Common mistakes
- Treating CAGR as the realized path—many journeys hit the same endpoints with very different drawdowns.
- Mixing cash flows into V_start/V_end without modeling contributions or withdrawals explicitly.
- Confusing CAGR with arithmetic average annual return—those differ unless volatility is zero.
- Using CAGR alone to rank assets without considering risk, liquidity, and taxes.
- Comparing two investments when their horizons use different day-count conventions (calendar vs trade date vs month-end).
- Reporting CAGR from a cherry-picked trough to a peak without labeling the window.
Try the calculator
Use the interactive calculator to plug in your numbers and see results instantly—without redoing the math by hand.
Open Stock Return calculator →FAQ
What is CAGR and how is it different from total return?
CAGR is a smoothed annualized growth rate between two values; total return includes dividends, timing, and cash flows along the full holding period.
What formula does StockCalc use for CAGR?
Our calculators apply the standard ratio-and-root definition consistent with the expression shown above, using the inputs you provide for starting value, ending value, and horizon.
When should investors use CAGR vs average annual return?
Use CAGR when you care about annualized growth between two endpoints; arithmetic averages of yearly returns can overstate growth when volatility is present.
What are common mistakes when interpreting CAGR?
Ignoring intermediate risk, mixing unrelated cash flows into the endpoints, or assuming future smooth growth because past CAGR looked steady.
Can CAGR be negative?
Yes. Whenever the ending value is below the starting value over a positive horizon, the ratio inside the formula is below 1 and CAGR is negative—still a smoothed rate, not the drawdown path.
What if I added or withdrew money during the period?
Two-point CAGR no longer describes “performance” of the strategy alone. Use time-weighted or money-weighted returns, or model dated cash flows with IRR/XIRR-style tools.
How should I pick n for partial years?
Express start and end on the same basis and set n to the elapsed time in consistent units (e.g., 2.5 years). Match that convention when comparing investments.
Does StockCalc provide personalized investment advice?
No. Pages and calculators are educational; they do not consider your individual circumstances.
Related calculators
Educational Disclaimer
This article is for educational and informational purposes only and should not be considered investment, financial, tax, or legal advice. Market information may change over time, and readers should verify important details independently before making financial decisions.