# Free investment return and CAGR calculator

> Enter your starting and ending values to find the annualized return (CAGR), or enter a rate and starting value to project how much an investment will grow.

Calculate the compound annual growth rate (CAGR) of any investment, or project a future value at a given annual rate. Includes total return, total gain, and the Rule of 72 doubling time.

**Interactive version:** https://onlinecalculator.me/finance/investment-return/
**Category:** Finance

## How to use

1. Choose **Calculate CAGR** to find the annualized growth rate, or **Project value** to forecast future value at a given rate.
2. In CAGR mode, enter your starting and ending investment values and the number of years between them.
3. In project mode, enter your starting value, expected annual rate, and time horizon.
4. Read the annualized rate, final value, total percentage return, and Rule of 72 doubling estimate.

## The formulas

**CAGR (Calculate mode):**

```
CAGR = (FV / PV)^(1/n) - 1
```

**Future value (Project mode):**

```
FV = PV × (1 + r)^n
```

**Total return:**

```
Total return% = (FV / PV - 1) × 100
```

Where `PV` = initial value, `FV` = final value, `r` = annual rate as a decimal, `n` = years.

## Worked example

$10,000 invested, grew to $20,000 over 10 years:

- CAGR = (20,000 / 10,000)^(1/10) - 1 = 2^0.1 - 1 ≈ **7.18%**
- Total return: (20,000 / 10,000 - 1) × 100 = **100%**
- Total gain: **$10,000**
- Years to double at 7.18%: 72 / 7.18 ≈ **10 years**

## Notes

- CAGR smooths out volatility. An investment with a CAGR of 7% may have had years of 20% gains and years of 10% losses — the rate tells you the equivalent steady compounding that produces the same result.
- This calculator does not account for taxes, fees, or dividends unless you include them in your final value.
- The Rule of 72 doubling time is an approximation; the calculator displays the precise figure alongside it.

## Frequently asked questions

### What is CAGR and how is it calculated?

CAGR stands for Compound Annual Growth Rate — the steady annual rate that would take an investment from its starting value to its ending value over a given number of years. The formula is: CAGR = (FV / PV)^(1/n) - 1, where FV is the final value, PV is the initial value, and n is the number of years.

### How is CAGR different from average annual return?

Average annual return adds up yearly returns and divides by the count. CAGR uses the geometric mean, which accounts for compounding. For example, if an investment loses 50% one year and gains 100% the next, the average return is 25% but the CAGR is 0% — you are back to where you started. CAGR is a more accurate measure of real investment growth.

### What is the Rule of 72?

The Rule of 72 is a shortcut for estimating how long it takes an investment to double: divide 72 by the annual rate. At 7%, money doubles in roughly 72 / 7 ≈ 10.3 years. At 10%, it doubles in about 7.2 years. The rule is an approximation — the calculator also shows the precise doubling time using the same CAGR.

### How can I use this for S&P 500 planning?

The S&P 500 has historically returned about 10% annually before inflation (roughly 7% after inflation) over long periods. Use project mode, enter your starting investment, set the rate to 7% or 10%, and set your time horizon. The result is an estimate — actual returns vary significantly year to year and past performance does not guarantee future results.

### How do I share my calculation?

Press "Share with my numbers" to copy a URL that encodes your mode, values, rate, and years. Anyone opening the link sees your exact scenario pre-filled.

## Sources

- [Rate of return](https://en.wikipedia.org/wiki/Rate_of_return) — Wikipedia
- [Compound annual growth rate (CAGR)](https://en.wikipedia.org/wiki/Compound_annual_growth_rate) — Wikipedia

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