CAGR Calculator — Compound Annual Growth Rate
Calculate compound annual growth rate (CAGR) from a beginning value, ending value, and number of years. Reverse-solve for required end value or time horizon. Compare CAGR across multiple investments side by side.
Quick Presets
Solve For
What Is the CAGR Calculator — Compound Annual Growth Rate?
CAGR — Compound Annual Growth Rate — is the single most useful number for comparing investments that grow at different speeds over different time periods. This calculator solves all four forms of the CAGR equation: given any three of the four variables (start value, end value, CAGR, years), it calculates the fourth.
- ›Four solve modes — calculate CAGR, end value, start value, or required years. Switch instantly between modes with the radio buttons.
- ›Year-by-year growth table — see the exact value, annual gain, and cumulative return for every year up to 30. Scrollable for long horizons.
- ›Rule of 72 — instantly shows how many years it takes to double at the calculated CAGR. A quick sanity check that's been used by investors for centuries.
- ›Investment comparison panel — enter 2–3 investment names and CAGRs side by side to see which grows the most over any time horizon. Results are ranked automatically.
- ›Simple annual return — shown alongside CAGR to illustrate the difference between compounded and non-compounded growth. The gap widens dramatically over long periods.
- ›Preset scenarios — one-click loading of S&P 500 historical average, Berkshire Hathaway, savings account, and US real estate for instant benchmarking.
Formula
CAGR Formula
CAGR = (End Value / Start Value)^(1 / Years) − 1
Solve for End Value
End Value = Start Value × (1 + CAGR)^Years
Solve for Start Value
Start Value = End Value / (1 + CAGR)^Years
Solve for Years
Years = log(End Value / Start Value) / log(1 + CAGR)
Rule of 72
Years to double ≈ 72 / CAGR%
| Symbol | Name | Description |
|---|---|---|
| CAGR | Compound Annual Growth Rate | The year-over-year growth rate that, if constant, produces the observed total growth |
| Start Value | Beginning Value | The initial investment or value at the start of the period |
| End Value | Ending Value | The final value at the end of the measurement period |
| Years | Number of Years | The length of the investment period in years (decimals allowed) |
| n | Exponent | Same as Years — used in the formula (1 + CAGR)^n |
| 72 | Rule of 72 constant | An approximation: divide 72 by the CAGR percentage to estimate years to double |
How to Use
- 1Select a solve mode: Choose what you want to calculate: CAGR (given start, end, years), end value (given start, CAGR, years), start value (given end, CAGR, years), or years (given start, end, CAGR).
- 2Enter the known values: Fill in the three inputs that correspond to your chosen mode. The field for the variable being solved is hidden automatically.
- 3Try a preset: Click S&P 500, Berkshire, Savings, or Real Estate to load real-world benchmarks instantly and see what growth looks like at each rate.
- 4Click Calculate or press Enter: Results appear immediately: the main solved value, total return %, absolute gain, simple annual return, and Rule of 72.
- 5Review the year-by-year table: Expand the growth table to see how your investment compounds year by year, with each year's value, annual gain, and cumulative return.
- 6Use the comparison panel: Expand "Investment Comparison" to enter 3 investments with their CAGRs. Click Compare to see a ranked table showing which grows most over your target horizon.
- 7Interpret the results: Focus on: (1) how CAGR differs from simple annual return over long periods, (2) the Rule of 72 as a doubling sanity check, and (3) how small CAGR differences compound into massive value differences over decades.
Example Calculation
$10,000 invested at the S&P 500 historical average (10.7% CAGR) for 30 years
Given: Start = $10,000 | CAGR = 10.7% | Years = 30
Step 1: Apply the CAGR formula
End Value = $10,000 × (1 + 0.107)^30
End Value = $10,000 × (1.107)^30
End Value = $10,000 × 20.855
End Value = $208,550
Step 2: Total return
Total Return = ($208,550 / $10,000) − 1 = 1,985% (≈ 20x)
Step 3: Rule of 72
Years to double = 72 / 10.7 ≈ 6.7 years per doubling
In 30 years: ~4.5 doublings → 2^4.5 ≈ 22.6x — consistent
Step 4: Simple annual return comparison
Simple annual = 1,985% / 30 = 66.2% (not compounded)
CAGR (10.7%) vs simple (66.2%) — compounding is the difference
| Year | Value | Annual Gain | Cumulative Return |
|---|---|---|---|
| 1 | $11,070 | +$1,070 | 10.7% |
| 5 | $16,660 | +$1,597 | 66.6% |
| 10 | $27,756 | +$2,660 | 177.6% |
| 20 ★ | $77,010 | +$7,388 | 670.1% |
| 30 | $208,550 | +$19,986 | 1,985% |
The compounding effect: CAGR vs simple annual return
A 10.7% simple annual return on $10,000 would give $10,000 + 30 × $1,070 = $42,100. The CAGR calculation gives $208,550 — nearly five times more. The difference is compounding: returns earned in year 1 generate their own returns in year 2, and so on. Over 30 years this snowballing effect becomes the dominant force in wealth building.
Understanding CAGR — Compound Annual Growth Rate
What is CAGR and Why It Matters
CAGR — Compound Annual Growth Rate — is the rate at which an investment would have grown each year if it grew at a perfectly steady rate. Real investments never grow at a constant rate; they have good years and bad years. CAGR smooths this out into a single comparable number that tells you the effective annual growth rate regardless of the path taken.
Why does this matter? Because without CAGR, comparing investments is almost impossible. If Investment A grew 40% over three years and Investment B grew 25% over two years, which performed better per year? CAGR answers this precisely: A = 11.87%/yr, B = 11.80%/yr — nearly identical, not obvious at all.
- ›CAGR is the standard metric used in earnings calls, fund factsheets, and analyst reports.
- ›It neutralizes the effect of different time periods, making any two investments directly comparable.
- ›CAGR captures the effect of compounding — making it far more meaningful than simple averages.
- ›It can be negative (when investments lose value) or very high (early-stage businesses, crypto).
CAGR vs Average Annual Return — A Critical Difference
The most common mistake when evaluating investments is confusing CAGR with the average (arithmetic mean) of annual returns. They are fundamentally different:
| Year | Return | Value |
|---|---|---|
| Year 1 | +50% | $15,000 |
| Year 2 | −50% | $7,500 |
| Average annual return | 0% (arithmetic mean) | — |
| CAGR (actual) | −13.4% per year | $7,500 from $10,000 |
The arithmetic average return is 0% — suggesting you broke even. But CAGR correctly shows −13.4%/yr: you actually lost 25% of your investment. Volatility destroys compounding. This is the volatility drag effect, and it is why low-volatility investments often outperform high-volatility ones with the same arithmetic mean return.
The geometric mean vs arithmetic mean
CAGR is the geometric mean of annual returns. The arithmetic mean always equals or exceeds the geometric mean (this is Jensen's inequality). The more volatile the returns, the larger the gap. For a portfolio with standard deviation σ, the relationship is approximately: CAGR ≈ arithmetic mean − σ²/2. This is why reducing volatility — even without changing average returns — directly improves long-term wealth.
The Rule of 72
The Rule of 72 is a mental math shortcut: divide 72 by the annual growth rate to estimate the number of years required to double an investment. At 10% CAGR: 72 ÷ 10 = 7.2 years to double. At 6%: 12 years. At 3%: 24 years.
- ›Accurate within 1–2% for rates between 2% and 30% — the range covering most real investments.
- ›Works in reverse: if something doubles in 8 years, its CAGR is approximately 72 ÷ 8 = 9%.
- ›Can estimate how many times an investment doubles: 30 years at 10% → 30 ÷ 7.2 ≈ 4.2 doublings → 2^4.2 ≈ 18.4x.
- ›The exact formula is log(2) / log(1 + r) ≈ 0.693/r. "72" in the rule accounts for the approximation error.
- ›For continuous compounding, use 69.3 instead of 72.
How to Use CAGR for Investment Comparison
CAGR lets you compare investments that differ in size, time period, or both. The comparison panel in this calculator makes this concrete: enter any 3 investments and see exactly how they diverge over your target horizon.
- ›Benchmark comparison: compare your portfolio's CAGR against the S&P 500 (historically ≈10.7%) to evaluate whether active management adds value.
- ›Asset class comparison: US real estate ≈8.6%, bonds ≈4–5%, savings ≈4.5%, international stocks ≈7–8%. CAGR puts all on equal footing.
- ›Business growth: a company growing revenue at 15% CAGR for 10 years grows 4x in size — impressive compared to 7% CAGR (2x) or 25% CAGR (9x).
- ›Future value planning: use the "end value" mode to project what your current savings will be worth at retirement under different assumed rates.
Common Pitfalls When Comparing Investments
- ›Survivorship bias: index funds that track "the market" include all companies including failures. Funds that quote their CAGR may have excluded underperforming periods or funds.
- ›Different start dates: a 10-year CAGR starting in 2009 (after the financial crisis) looks much better than one starting in 2007. Always compare CAGRs over identical periods.
- ›Fees and taxes: CAGR figures are often quoted before fees (expense ratios, management fees) and taxes. A 10% gross CAGR fund with 1.5% fees returns 8.5% net — compounding the difference over 30 years produces a 40%+ gap in final wealth.
- ›CAGR ≠ future returns: past CAGR is a description of history, not a guarantee. The S&P 500's 10.7% historical CAGR includes extreme bull markets that may not repeat.
- ›Ignoring risk: two investments with identical CAGR can have vastly different volatility. CAGR alone does not measure risk — always also consider standard deviation or drawdown.
Frequently Asked Questions
What does CAGR mean and how is it different from a regular annual return?
Key differences:
- ›CAGR is the geometric mean of returns — it compounds correctly
- ›Arithmetic average ignores the sequence of returns and always overstates real growth
- ›CAGR gives the actual rate that transforms start value into end value over n years
- ›For volatile investments, the gap between CAGR and arithmetic mean can be enormous
Use CAGR when comparing investments or projecting future values. Never use arithmetic average for multi-year growth analysis.
How do I calculate CAGR manually?
Step-by-step manual calculation:
On most calculators, use the y^x key: enter 1.8, press y^x, enter 0.1667, press =, then subtract 1.
What is a good CAGR for an investment?
Reference benchmarks (approximate long-term historical):
- ›Cash / savings account: 3–5% CAGR
- ›US Treasury bonds: 4–5% CAGR
- ›US real estate (price appreciation only): 8–9% CAGR
- ›S&P 500 (price + dividends): 10–11% CAGR
- ›Small-cap stocks: 11–13% CAGR (higher volatility)
- ›Berkshire Hathaway (1965–2024): ≈19.8% CAGR — exceptional outlier
Always compare CAGR over the same time period and adjust for fees, inflation, and risk.
How accurate is the Rule of 72?
Rule of 72 accuracy by rate:
- ›2% CAGR → exact: 35.0 yr | Rule of 72: 36.0 yr (error: +1 yr)
- ›6% CAGR → exact: 11.9 yr | Rule of 72: 12.0 yr (error: +0.1 yr)
- ›10% CAGR → exact: 7.3 yr | Rule of 72: 7.2 yr (error: −0.07 yr)
- ›20% CAGR → exact: 3.8 yr | Rule of 72: 3.6 yr (error: −0.2 yr)
- ›50% CAGR → exact: 1.7 yr | Rule of 72: 1.44 yr (error: −0.26 yr)
For continuous compounding, use 69.3 instead of 72. The Rule of 72 overestimates at very low rates and underestimates at very high rates.
Can CAGR be negative?
Negative CAGR occurs when end value < start value:
- ›CAGR = (7000/10000)^(1/5) − 1 = −6.9% per year (lost 30% total in 5 years)
- ›Common in: individual stocks in decline, crypto bear markets, bond funds during rate hikes
- ›A negative CAGR of −10% means you lose 10% of whatever balance remains each year
- ›After 10 years at −10% CAGR: $10,000 → $3,487 (not $0 — it's exponential decay)
The calculator handles negative CAGRs correctly in all four solve modes.
What is the difference between CAGR and IRR?
When to use CAGR vs IRR:
- ›CAGR: single lump-sum investment with one start and one end point
- ›IRR: multiple cash flows — monthly contributions, dividends reinvested, partial withdrawals
- ›CAGR is simpler and widely used for fund reporting and benchmarking
- ›IRR is more accurate for evaluating real investment portfolios with irregular cash flows
- ›Both use the same underlying mathematics — IRR generalizes CAGR to multiple periods
How does CAGR relate to compound interest?
The relationship between CAGR and compound interest:
- ›Both use the formula: Value = Principal × (1 + rate)^years
- ›Compound interest: the rate is given (contractual) and you calculate the future value
- ›CAGR: the start and end values are given (observed) and you solve for the rate
- ›For monthly compounding: effective annual rate = (1 + r/12)^12 − 1 (slightly higher than nominal)
- ›The calculator uses annual compounding — the standard for CAGR calculations