CAGR Calculator - Compound Annual Growth Rate Calculator
Calculate the Compound Annual Growth Rate (CAGR), absolute return, return multiple, and total profit for an investment held over a set period.
AI Quick Summary
Definition & Purpose:
This calculator computes the Compound Annual Growth Rate (CAGR) — the constant annual rate an investment would need to grow at to go from its starting value to its ending value over a given holding period — along with the absolute return, return multiple, and total profit.
When to Use:
Use CAGR to compare the annualized performance of investments held for different lengths of time — a stock held 3 years and a property held 10 years can be compared fairly using CAGR, unlike raw absolute return.
Key Takeaway Insights:
- CAGR and absolute return answer different questions — absolute return says how much total gain occurred with no regard to time, while CAGR says what constant annual rate would have produced that same total gain, which is why CAGR is the right metric for comparing investments held over different periods.
- CAGR is a geometric average connecting only the starting and ending values in a smooth curve — it says nothing about what happened in between, so two investments with identical CAGR can have had completely different, even opposite, paths of gains and losses along the way.
- Doubling an investment's value produces a very different CAGR depending on how long it took — doubling in 2 years is a 41.4% CAGR, while doubling in 20 years is only about 3.5%, even though the absolute return (100%) is identical in both cases.
Investment Valuation
CAGR Calculation
Introduction
CAGR Calculator – Compound Annual Growth Rate Guide
The Compound Annual Growth Rate (CAGR) is one of the most widely used metrics for comparing investment performance, because it expresses growth as a single, time-adjusted annual rate rather than a raw total gain. This calculator computes CAGR, absolute return, return multiple, and total profit.
The CAGR Formula
CAGR = ≤ft((Final Value / Initial Value))^(1 / t) - 1
Multiply the result by 100 to express it as a percentage. Compare this against the simpler absolute return, which ignores time entirely:
Absolute Return = (Final Value - Initial Value / Initial Value) × 100
Worked Example
An investment growing from 10,000 to 20,000 over 5 years:
- CAGR: ≤ft(dfrac20,00010,000)^1/5 - 1 = 2^0.2 - 1 ≈ 0.148698, or 14.87%
- Absolute return: dfrac20,000 - 10,00010,000 × 100 = 100.00%
- Return multiple: dfrac20,00010,000 = 2.00x
- Total profit: 20{,}000 - \10,000 =10{,}000$
Why Time Matters So Much
The same 100% absolute return produces a very different CAGR depending on how long it took to achieve:
| Holding Period | Absolute Return | CAGR |
|---|---|---|
| 2 years | 100.00% | ≈ 41.42% |
| 5 years | 100.00% | 14.87% |
| 20 years | 100.00% | ≈ 3.53% |
Doubling an investment in 2 years reflects genuinely fast annual growth, while doubling it over 20 years reflects a much more modest pace — even though both describe identical total profit.
What This Calculator Does Not Include
To see year-by-year compounding rather than a single smoothed rate, see the Compound Interest Calculator.
Formula & Variables Explained
This tool utilizes standard equations formulated under standard rules.
Variables:
- Input parameter: Values supplied to resolve the output formula.
How to Calculate (Step-by-Step)
- Input the required parameters into the form.
- Click the calculate or auto-compute option.
- The outputs will refresh instantly with step-by-step variables.
Worked Examples Calculation
110,000 Growing to20,000 Over 5 Years
Initial Value = 10,000, Final Value =20,000, Holding Period = 5 Years
CAGR = (20,000 / 10,000)^(1/5) - 1 = 2^0.2 - 1 = 1.148698 - 1 = 0.148698, or 14.87%. Absolute Return = (20,000 - 10,000) / 10,000 × 100 = 100.00%. Return Multiple = 20,000 / 10,000 = 2.00x. Total Profit = 20,000 - 10,000 = $10,000.
CAGR = 14.87% | Absolute Return = 100.00% | Return Multiple = 2.00x | Total Profit = $10,000
2Same 100% Absolute Return, but Over 20 Years Instead of 5
Initial Value = 10,000, Final Value =20,000, Holding Period = 20 Years
CAGR = (20,000 / 10,000)^(1/20) - 1 = 2^0.05 - 1 ≈ 0.035265, or about 3.53% — dramatically lower than the 5-year scenario's 14.87%, even though the absolute return (100%) and total profit ($10,000) are identical in both cases.
CAGR ≈ 3.53% | Absolute Return = 100.00% | Return Multiple = 2.00x | Total Profit = $10,000
Real-World Applications
Widely used in student curriculum, professional projections, and quick estimations.
Limitations & Common Mistakes
- Entering incompatible unit formats (e.g. Mixing Metric and Imperial).
- Typographical mistakes in numeric entry fields.
CAGR smooths the entire holding period into a single constant rate and completely ignores interim volatility — an investment that fell sharply mid-period and later recovered can show the same CAGR as one that grew steadily the whole time.
Frequently Asked Questions (FAQ)
Q:What is the formula for calculating CAGR?
CAGR = ((Final Value ÷ Initial Value)^(1 ÷ t) − 1) × 100, where t is the holding period in years. This finds the single constant annual growth rate that, compounded over t years, would take the initial value to the final value.
Q:How does CAGR differ from Absolute Return?
Absolute Return measures total percentage gain with no regard to how long it took — doubling your money is a 100% absolute return whether it happens in 2 years or 20. CAGR incorporates the holding period, so it shows that doubling in 2 years reflects a much faster annual growth rate (about 41.4%) than doubling in 20 years (about 3.5%).
Q:Why is CAGR preferred over a simple average of annual returns?
A simple arithmetic average of yearly returns can be misleading because of compounding — if an investment loses 50% in year one and gains 50% in year two, the arithmetic average is 0%, but the actual money went from 100 to 50 to 75, a real 25% loss. CAGR correctly reflects this as a negative compound annual return rather than a flat 0%.
Q:Can CAGR be negative?
Yes. If the final value is lower than the initial value, the formula produces a negative CAGR, reflecting a compound annual loss over the holding period rather than a gain.
References & Citations
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