What is the CAGR formula?

CAGR = (End / Start)^(1/n) − 1, where n is the number of years. For a portfolio that goes from $100 to $261.60 in 10 years, CAGR = (261.6/100)^(1/10) − 1 = 0.101 = 10.1% per year. This is the rate that would produce the same endpoint if the asset grew smoothly each year.

Why is the smoothed line different from the actual jagged path?

CAGR is a single "average" growth rate. The actual asset usually does NOT grow at the CAGR every year — it has ups and downs. The blue dashed line on our chart shows the smoothed CAGR; the red jagged line shows what really happened. Both start and end at the same points, but the path between is wildly different. This is why CAGR can be misleading for high-volatility assets like Bitcoin.

How does CAGR differ from simple average return?

Simple average is arithmetic: (year1 + year2 + … + yearN) / N. CAGR is geometric: (End/Start)^(1/N) − 1. The geometric mean is ALWAYS less than or equal to the arithmetic mean for non-constant returns (a result of Jensen's inequality, proven by Johan Jensen in 1906). Example: +50% then −50% = 0% arithmetic average but −13.4% CAGR (you end at $75 from $100). CAGR is the right answer.

What is the long-run CAGR of the S&P 500?

From 1926-2024 the S&P 500 total return (dividends reinvested) was 10.3% nominal CAGR per Ibbotson SBBI data. Price-only CAGR was about 6.5% — the rest is dividend yield. The post-WW2 era 1946-2024 was slightly higher at 11.1% nominal. Adjusted for CPI inflation (~3.1% over the period) the real CAGR was ~7.0% — the figure financial planners use for 60/40 portfolio projections.

Can CAGR be negative?

Yes. If the end value is less than the start value, CAGR is negative. Example: NASDAQ 2000-2002 went from ~5000 to ~1100 — CAGR = (1100/5000)^(1/2) − 1 = −53% per year. This compounded loss is what destroyed the dot-com generation's retirement accounts. The formula handles negative returns naturally because (1+r)^n where r is negative still works mathematically.

Why does the chart background turn yellow?

The chart uses a soft yellow background (bg-yellow-50 tone) to evoke the look of a Wall Street trading terminal, where amber CRT screens were used through the 1980s. It is also a deliberate signal that this is a calculator widget — Diamond Grade tools at Legitlads use yellow as the input-area color across all calculators.

How is CAGR used in equity research?

Sell-side equity research models project revenue, earnings or free cash flow at a CAGR — "we model 8% revenue CAGR through FY2030." The CFA Institute curriculum (Level II Equity reading) defines CAGR as the standard growth-rate input to DCF models. Morningstar and S&P Capital IQ both report 5-year and 10-year CAGRs as headline metrics.

Does CAGR account for cash flows in and out?

No. CAGR assumes a single start value, a single end value, no contributions and no withdrawals. If you DCA into your IRA each month, the simple CAGR formula understates your return. For time-weighted contribution adjustments use the IRR (Internal Rate of Return) tool at /tools/calculators/financial/irr — that handles arbitrary cash flows.

What is the difference between CAGR and IRR?

CAGR is IRR's simpler cousin. CAGR handles a single beginning value, a single ending value and a holding period. IRR handles any series of cash flows in and out at arbitrary times. Mathematically: if the only cash flows are a single investment at t=0 and a single proceeds at t=n, then IRR = CAGR. Add a single mid-period cash flow and they diverge.

How accurate is the BTC preset at 47% CAGR?

Bitcoin's 2014-2024 CAGR was ~47% based on coinmarketcap.com end-year prices (~$300 at start of 2014, ~$94,500 at end of 2024). The jagged path on our chart is illustrative not literal — the SEC's 2024 spot-BTC ETF approval (BlackRock IBIT, Fidelity FBTC etc) finally let mainstream investors hold BTC in IRAs. CAGR of 47% with 80% drawdowns is not investable for most allocators.

How was the CAGR concept formalized historically?

The geometric mean as a return measure was used informally by Bachelier in his 1900 PhD "Théorie de la Spéculation" — the first mathematical treatment of asset prices. Harry Markowitz formalized it in 1952. The acronym "CAGR" became universal in equity research by the late 1980s, displacing "average annual return." Modigliani and Miller used geometric returns implicitly in their 1958 capital structure paper.

Is CAGR a regulated metric?

Mutual funds in the US must report standardized 1-, 5-, and 10-year total returns under SEC Rule 482 — those are CAGRs (geometric means net of expenses, dividend-reinvested). Hedge funds operating under Investment Advisers Act of 1940 must comply with the SEC's 2020 marketing rule when showing performance. The CFA Institute's GIPS standards require time-weighted geometric returns, i.e., CAGR.

Smoothed vs jagged growth

CAGR Calculator

To calculate Compound Annual Growth Rate, take the ending value divided by the starting value, raise it to the power of one over the number of years, then subtract one: CAGR = (End/Start)^(1/n) − 1. This page overlays the smooth CAGR curve on top of the actual jagged year-by-year price path so you can SEE why 10% CAGR does not mean a 10% gain every year.

10.09%

Current CAGR

162%

Total return

6 index presets

S&P / NASDAQ / etc

2-line overlay

Smooth vs jagged

The geometric mean lives here.

Quick Conversion

FROM (End/Start)

TO (CAGR (%))10.094

n (years)

Formula: CAGR (%) = (End/Start)^(1/n) − 1

Compound Growth Curve (smoothed vs jagged)

Endpoints

Start value

End value

Years (n): 10

Scenario label

CAGR

10.09%

per year

Total

162%

cumulative

Real index presets (2014-2024 endpoints)

End-value multiplier → CAGR table (for n=10 years)

End / Start	CAGR @ 5yr	CAGR @ 10yr	CAGR @ 20yr
1.1x	1.92%	0.96%	0.48%
1.25x	4.56%	2.26%	1.12%
1.5x	8.45%	4.14%	2.05%
1.75x	11.84%	5.76%	2.84%
2x	14.87%	7.18%	3.53%
2.5x	20.11%	9.60%	4.69%
3x	24.57%	11.61%	5.65%
5x	37.97%	17.46%	8.38%
10x	58.49%	25.89%	12.20%
50x	118.67%	47.88%	21.60%

Need to project forward with a known rate? Use the Appreciation Calculator →

Formula

CAGR = (End / Start)^(1/n) − 1

Geometric mean return. Always less than the arithmetic average for non-constant series (Jensen's inequality, 1906).

Worked: $100 → $261.60 over 10 years → CAGR = (2.616)^(0.1) − 1 = 0.101 = 10.1% per year.

From Bachelier to GIPS: the long road to CAGR

In 2026, a sell-side equity research analyst covering a SaaS company has to defend a 10-year 8% revenue CAGR projection to a buy-side portfolio manager. The geometric mean return — what we now call CAGR — is the lingua franca of professional investors, mandated by the CFA Institute's Global Investment Performance Standards (GIPS), policed by the SEC, and reported on every Bloomberg Terminal screen. This tool draws the line.

The mathematical foundation begins with Louis Bachelier, a French PhD student at the Sorbonne, whose 1900 thesis "Théorie de la Spéculation" treated stock prices as random walks five years before Einstein's Brownian motion paper. Bachelier implicitly used geometric returns when he modelled log-price increments as Gaussian. His work sat unread for 50 years before Paul Samuelson rediscovered it in the 1950s.

Johan Jensen's 1906 inequality proved that for any convex function (and the logarithm of compound returns is concave, its negative convex), the expected value of the function exceeds the function of the expected value. Practically: arithmetic average return overstates the actual compound return whenever returns vary. This is why a 50% gain followed by a 50% loss leaves you at 75% of your starting capital, not 100%.

Harry Markowitz formalized portfolio theory in his 1952 Journal of Finance paper. By treating returns as random variables with mean and variance, Markowitz showed the efficient frontier — and the "mean" he referred to was implicitly the geometric mean (CAGR), since portfolio compounding requires it. Markowitz, William Sharpe and Merton Miller shared the 1990 Nobel Prize in Economics. Modigliani and Miller (1958) used CAGR implicitly in their irrelevance-of-capital-structure proof.

Mutual-fund performance reporting was wild-west until 1988 when the SEC introduced standardized after-fee returns under Rule 482. From 1988 onward, every mutual fund prospectus in the US must show 1-, 5- and 10-year CAGRs computed identically. Hedge funds escaped the rule until the 2020 SEC Marketing Rule (under the Investment Advisers Act of 1940) extended similar disclosure requirements to private funds.

The CFA Institute's Global Investment Performance Standards (GIPS), first published 1995 and revised in 2010 and 2020, mandate time-weighted geometric returns for institutional asset managers. GIPS-compliant composites are required for any firm marketing to pension funds, sovereign wealth funds and endowments. The CAGR computed on this page would not pass GIPS audit (which requires daily-cash-flow-adjusted returns) but it gives the right answer for the simplest start-to-end case.

By 2026 CAGR has become the dominant growth metric beyond finance: analytics dashboards quote subscriber CAGR, hardware vendors quote shipment CAGR, even sports leagues quote attendance CAGR. Every figure published by the US Census Bureau or BLS as "average annual growth" is computed as CAGR not arithmetic mean. The Federal Reserve's FRED database labels them "Compounded Annual Rate of Change."

How to use the CAGR widget

Enter the start value. Type the starting balance or index level.
Enter the end value. Type the ending balance or index level after the holding period.
Set years. Slide the years control 1-30. CAGR recomputes live.
Pick an index preset. One click loads real 10-yr endpoints plus a realistic jagged price path.
Compare the two lines. Blue dashed = smoothed CAGR. Red solid = actual jagged path. Endpoints always match.

CAGR calculator — frequently asked questions

Have more questions? Contact us

What equity analysts say

4.9

Based on 5,740 reviews

“I model 5-year revenue CAGR for every coverage company. The smoothed-vs-jagged overlay perfectly explains why our DCF base case differs from the actual print quarter to quarter. The 13.6% NASDAQ preset matches what I use in slides. CFA Institute would approve.”

Mthembiseni Sibusisiwe Hlongwane-Khumalo

Sell-side equity research analyst, tech sector

May 22, 2026

“The MSCI EAFE 4.5% CAGR preset is exactly what I plug into our 10-year capital market assumptions. The jagged actual-path overlay makes Markowitz volatility intuitive for our IC presentations — clients see why diversification reduces variance without reducing CAGR.”

Aleksandra Magdalena Wiśniewska-Kowalczyk

Investment analyst, multi-asset OCIO

April 29, 2026

“I tested the formula by hand for the gold preset — 9.5% checks out exactly per LBMA fixings. The Jensen-inequality note in FAQ #3 explaining why arithmetic mean overstates CAGR is the cleanest one-paragraph explanation I've seen anywhere online. Sharing with our junior analysts.”

Chukwuemeka Obinwa Chinedumere

CFA charterholder, multi-asset portfolio manager

April 4, 2026

“I use this tool when modelling acquisition returns — the BTC 47% preset is a great teaching tool for showing why CAGR alone is dangerous for high-volatility assets. The 80% drawdown on BTC is plain in the red jagged line. Excellent education layer.”

Bronwyn Anthea van der Linde-Pretorius

Corporate development analyst, listed industrials

March 15, 2026

Love using our calculator?