CAGR Calculator — Compound Annual Growth Rate
Compute the compound annual growth rate using CAGR = (EV / BV)1/n − 1. Solve for CAGR, ending value, beginning value, or number of periods. Includes step-by-step math, a live growth trajectory schematic, and companion metrics including absolute return, average annual return, doubling time, and future value projections.
CAGR is the smoothed growth rate
CAGR represents the constant annual rate at which an investment, revenue, or metric would have grown if it had grown at a steady rate from BV to EV over n years. In reality, growth is rarely smooth — some years are up, some down — but CAGR reduces the entire trajectory to a single, comparable number. This makes it ideal for comparing investments, companies, or metrics of different sizes and time spans on a level playing field. A CAGR of 10.41% means the value grew as if it had compounded at 10.41% every year, even if the actual path was volatile.
CAGR is a geometric mean, not arithmetic
CAGR is mathematically the geometric mean of the annual growth factors minus 1: CAGR = (Π(1 + rᵢ))^(1/n) − 1. If you average the annual percentage returns arithmetically, you will get a higher number — often significantly higher in volatile investments. For example, an investment that gains 50% in year 1 and loses 33.3% in year 2 ends flat. The arithmetic mean return is (+50 − 33.3)/2 = 8.35%, but the true CAGR is 0%. CAGR is the honest measure because it accounts for the compounding effect of losses.
CAGR ignores volatility and timing
A key limitation: CAGR says nothing about the path taken between BV and EV. Two investments can have identical CAGRs but very different risk profiles — one smooth, one volatile. Additionally, CAGR does not capture intermediate cash flows: if you add or withdraw money along the way, CAGR of the initial investment is misleading. For investments with cash flows, use IRR (internal rate of return) or TWR (time-weighted return) instead. CAGR is best for measuring the growth of a lump-sum investment with no intermediate transactions.
Rule of 72 for quick estimates
The Rule of 72 is a mental shortcut for estimating doubling time: years to double ≈ 72 / CAGR(%). For example, at CAGR = 10%, doubling takes about 7.2 years. At CAGR = 7%, about 10.3 years. The rule is accurate to within a few percent for rates between 5% and 15%, which covers most realistic investment scenarios. This calculator provides the exact doubling time using the formula tdouble = ln(2) / ln(1 + CAGR), which is slightly more precise than the Rule of 72.
How to Use This Calculator
The CAGR formula links the beginning value, ending value, and number of periods. Pick what you want to compute, and the calculator solves for the remaining quantity.
1. Choose what to solve for
Pick CAGR, EV, BV, or n from the toggle. The calculator rearranges CAGR = (EV/BV)^(1/n) − 1 for whichever variable you choose.
2. Use realistic presets
Presets cover typical scenarios: BV from $100 to $10M, EV from $12,100 to $100,000, and n from 1 to 20 years. The default ($10K → $20K over 7 years) gives CAGR ≈ 10.41%.
3. Match units consistently
BV and EV must be in the same units (both dollars, both index points, etc.). n must be in years for annualized CAGR — if your data are in months, divide by 12; if in quarters, divide by 4.
4. Read the result and verdict
The result card shows CAGR as a percentage. A colour-coded verdict classifies growth from decline (below 0%) through flat, modest, moderate, strong, and exceptional (above 25%).
5. Check the schematic and chart
The schematic shows the CAGR-compounded trajectory compared with a linear growth reference. The chart plots CAGR vs. ending value at fixed BV and n.
6. Switch to Advanced for depth
Advanced mode adds a detailed growth trajectory chart, a sensitivity check, and companion metrics including total return, doubling time, future value projections, and comparison with arithmetic mean return.
What This Tool Offers
Built around the standard CAGR formula CAGR = (EV/BV)1/n − 1, the fundamental measure of compound annual growth.
Four-way solving
Solve for CAGR, ending value, beginning value, or number of periods. The calculator rearranges the formula for whichever variable you choose.
Live growth schematic
A growth trajectory chart comparing CAGR compounding with linear growth, showing BV and EV markers and year intervals.
Growth verdict
Each result is classified from decline (below 0%) through flat, modest, moderate, strong, and exceptional (above 25%).
Companion investment metrics
Total return, absolute gain, doubling time, future value projections, arithmetic mean comparison, and Rule of 72 estimate.
Dual comparison charts
CAGR vs. ending value at fixed BV and n, plus a growth trajectory chart comparing CAGR compounding vs. linear growth.
Reference tables
Typical CAGRs by investment type, doubling time lookup, and a full variable reference table.
Reference Tables & Conversions
Typical CAGR values by asset class, doubling time lookup, and the Rule of 72.
Doubling time lookup (Rule of 72)
Typical CAGRs by Investment Type
Historical long-term CAGRs across different asset classes and economies. Past performance does not predict future returns.
| Investment / Metric | Typical CAGR | Period | Notes |
|---|
Comparison of Return Metrics
Different ways to measure performance. CAGR is the most appropriate for comparing long-term compounding growth.
| Metric | Formula | What it measures | Best for |
|---|---|---|---|
| CAGR | (EV/BV)^(1/n) − 1 | Constant annual compounded rate | Long-term performance comparison |
| Total Return | (EV − BV) / BV | Overall percentage gain or loss | Single-period comparison |
| Arithmetic Mean | Σrᵢ / n | Average of periodic returns | Statistical analysis; overstates compounding |
| IRR | Solve NPV = 0 | Rate for cash-flow investments | Portfolio with contributions/withdrawals |
| TWR | Chain-linked subperiod returns | Manager performance independent of cash flows | Fund manager evaluation |
| Logarithmic Return | ln(EV/BV) | Continuously-compounded return | Academic finance; additive over time |
Variable Reference
| Symbol | Meaning | Typical range | Notes |
|---|---|---|---|
| CAGR | Compound annual growth rate | −100% to +∞ | Expressed as annual percentage |
| BV | Beginning value | > 0 | Starting amount |
| EV | Ending value | > 0 | Final amount |
| n | Number of years | > 0 | Periods between BV and EV |
| EV/BV | Growth ratio | > 0 | Total multiple |
| FV | Future value projection | — | BV × (1 + CAGR)^t |
What Does CAGR = (EV / BV)1/n − 1 Measure?
The Compound Annual Growth Rate is the constant annual rate at which an investment, revenue, portfolio, or metric would have grown if it had compounded smoothly from its beginning value to its ending value over a specified number of years. It transforms any total growth into a single annualized percentage, making it easy to compare investments or business performance across different sizes, time frames, and starting points. CAGR is the standard metric used by investors, analysts, and business leaders to evaluate long-term growth, and it is the correct average for any quantity that compounds over time.
CAGR Formula
The defining relationship is:
Rearranged to solve for the other three quantities:
BV = EV / ( 1 + CAGR )n
n = ln( EV / BV ) / ln( 1 + CAGR )
The equivalent future value formula for projecting forward:
Doubling time (exact):
Rule of 72 approximation:
CAGR Variables
| Symbol | Meaning | Notes |
|---|---|---|
| CAGR | Compound annual growth rate | Constant annual rate |
| BV | Beginning value | Starting amount (must be > 0) |
| EV | Ending value | Final amount (must be > 0) |
| n | Number of periods | In years for annual CAGR |
| FV | Future value | Projected value at time t |
| tdouble | Doubling time | Years to double the investment |
How Each Variable Affects CAGR
CAGR increases when the ending value increases (at fixed BV and n), decreases when the beginning value increases (at fixed EV and n), and decreases when the number of periods increases (at fixed BV and EV). In words: a higher final value or a lower starting value means a higher growth rate; a longer time frame means a lower annual rate for the same total growth. This last point is why comparing investments over different time horizons requires CAGR — a 100% total return over 5 years (CAGR ≈ 14.9%) is very different from a 100% total return over 20 years (CAGR ≈ 3.5%).
An important subtlety: CAGR is a geometric mean, not an arithmetic mean. If returns are volatile, the arithmetic mean of annual returns will always be higher than CAGR. For example, returns of +50%, −33.3%, +50%, −33.3% have an arithmetic mean of 8.35% but a CAGR of 0% (because the ending value equals the beginning value). CAGR measures the actual compounded performance of a lump-sum investment and should be the standard for reporting long-term returns.
CAGR Calculation Examples
CAGR = (20,000 / 10,000)1/7 − 1 = 21/7 − 1
CAGR = 1.1041 − 1 = 0.1041 = 10.41%
EV = 1,000 × (1.15)10 = 1,000 × 4.0456 = $4,045.60
BV = 50,000 / (1.08)20 = 50,000 / 4.6610 = $10,727.36
n = ln(15,000 / 5,000) / ln(1.116) = ln(3) / ln(1.116) = 1.0986 / 0.1097 = 10.01 years
Frequently Asked Questions
CAGR is the geometric mean of annual growth factors minus 1, while "average return" usually refers to the arithmetic mean of periodic returns. They are not the same, and the arithmetic mean is always higher unless all returns are identical. For example, consider returns of +50% and −50% over two years. The arithmetic mean return is (50 + (−50))/2 = 0%, but the true CAGR is −13.4% (because $100 × 1.50 × 0.50 = $75, so CAGR = (75/100)^(1/2) − 1 = −13.4%). The arithmetic mean ignores the effect of compounding and therefore overstates the actual performance. Always use CAGR (or its equivalent, the geometric mean return) to report annualized performance.
No. CAGR ignores the path taken between BV and EV. Two investments can have identical CAGRs but very different volatility. Investment A might grow steadily at 8% every year; Investment B might alternate between +30% and −15%. Both could produce the same CAGR, but Investment A is much less risky. To evaluate risk-adjusted performance, combine CAGR with volatility measures like standard deviation, Sharpe ratio, Sortino ratio, or maximum drawdown. CAGR is a return metric, not a risk metric.
CAGR assumes no intermediate cash flows — it measures the growth of a lump-sum investment held for the entire period. If you add money or withdraw money during the period, CAGR becomes misleading because the ending value reflects those external transactions, not just the underlying investment return. For investments with cash flows, use IRR (internal rate of return) which solves for the discount rate that makes the net present value of all cash flows equal to zero. Alternatively, use TWR (time-weighted return) to measure the performance of the underlying investment independent of cash flow timing. IRR and TWR are standard in fund accounting and portfolio management.
Yes. CAGR is negative when the ending value is less than the beginning value (EV < BV). For example, an investment that drops from $10,000 to $7,000 over 5 years has a CAGR of (7,000/10,000)1/5 − 1 = −6.85% per year. CAGR is bounded below by −100% (which would mean the investment lost all its value), but it can be arbitrarily positive. Negative CAGR is a critical signal that the investment is losing value over time — a persistent negative CAGR is a warning sign that requires intervention or a change in strategy.
It depends on context and asset class. Broad stock market indices (like the S&P 500) have historically returned about 7% CAGR after inflation (10% before inflation) over long periods. Bonds typically return 3–5% nominal. Real estate varies widely by market, averaging 3–7%. High-growth companies in tech may achieve 20–40% CAGR for a few years, but sustaining those rates long-term is very rare. For a retirement portfolio, a long-term CAGR of 6–8% is often considered realistic and sufficient. For a startup, 50%+ growth rates are often expected in early years. The right benchmark depends on the risk profile and the opportunity set available to the investor.
The Rule of 72 is a quick mental math shortcut for estimating how long it takes for an investment to double: doubling time ≈ 72 / CAGR(%). For example, at 6% CAGR, doubling takes about 12 years (72/6 = 12). The exact formula is tdouble = ln(2) / ln(1 + CAGR). The Rule of 72 is accurate to within a few percent for rates between 5% and 15%, which covers most realistic investment scenarios. It is slightly inaccurate at very low rates (because the base of natural log changes) and very high rates. Use it for quick estimates; use the exact formula for precision.
Absolutely. CAGR is not limited to financial investments — it applies to any quantity that grows or shrinks multiplicatively over time. Common applications in business: revenue CAGR (comparing business growth rates), user CAGR (measuring user base expansion), website traffic CAGR (measuring audience growth), and market size CAGR (comparing market growth rates). For any metric where you have a beginning value, ending value, and time period, CAGR gives you a clean, annualized growth rate that is comparable across companies, time periods, and industries.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| CAGR | Compound annual growth rate | % |
| Ending Value | Final investment value | currency |
| Beginning Value | Initial investment value | currency |
| n | Number of years |
What it means
The Compound Annual Growth Rate (CAGR) is the average annual growth rate of an investment over a specified time period, assuming compounding. It is calculated from the beginning and ending values and the number of years, smoothing out volatility. CAGR is widely used to compare historical returns of investments, to assess business growth, and to set performance benchmarks. Unlike the arithmetic mean, it accurately reflects the geometric progression of growth. Understanding CAGR is essential for investors and managers to evaluate performance over multiple periods and to forecast future growth.
Worked example
CAGR – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Beginning Value | 10000 |
| Ending Value | 20000 |
| n | 5 |
| Parameter | Value |
|---|---|
| Beginning | 5000 |
| Ending | 15000 |
| n | 10 |
Common mistakes
- CAGR: The constant annual growth rate that would produce the same ending value.
- n: The number of years – ensure it matches the period between beginning and ending values.
- Exponent: Raise the ratio to the power (1/n) – not multiply by n.
- Ending and Beginning Values: Use the same time‑consistent values (e.g., end‑of‑period values).
- CAGR assumes steady growth – it is a geometric mean.
Applications
Compound Annual Growth Rate (CAGR) measures the annualised growth rate of an investment over a specified period, smoothing out volatility. It is widely used in finance, marketing, and business to compare historical growth rates across companies, industries, and time periods. Investors use CAGR to assess portfolio performance, to benchmark against indices, and to set return expectations. Corporate managers use it to evaluate revenue, earnings, and asset growth. By calculating CAGR, professionals can understand the consistent annual growth that would have been needed to achieve the total change, making it a clear and comparable metric. It is essential for performance reporting and strategic planning.
- Investment portfolio performance measurement and benchmarking
- Revenue and earnings growth analysis for companies
- Market growth and industry trend analysis
- Setting realistic growth targets and forecasting
- Performance reporting to stakeholders
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