# CAGR Calculator | Compound Annual Growth Rate

> Calculate compound annual growth rate from a start value, end value and years, or work backward to the value a target growth rate reaches. Free tool.

URL: https://raziel.co/tools/cagr-calculator

Find the compound annual growth rate between two values, or flip it around and see what a starting amount grows to at a given rate.

## Results

CAGR

13.99%

$10,000 to $25,000 over 7 years, compounded once a year.

**Total growth**

150.0%

**Multiple**

2.50x

End / start

**Gain or loss**

$15,000

**Annual rate**

13.99%

**Ending value**

$25,000

**Time to double**

5.3 years

At this rate

Value over time at a constant rate

TodayYear 2Year 4Year 7

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The math

## How CAGR is *calculated*

CAGR answers one question: what constant yearly rate turns the starting value into the ending value? Divide the end by the start to get the total multiple, then take the root for the number of years, which spreads that growth evenly across them.

1. **Multiple.** End divided by start. Growing from $10,000 to $25,000 is 2.5x.
2. **Annualize.** Raise the multiple to the power of 1 divided by the number of years.
3. **Subtract one** to turn the yearly multiple into a rate.

Reverse mode runs the same formula forward: start x (1 + rate) raised to the number of years.

CAGR = (end / start) ^ (1 / years) - 1 Target value = start x (1 + CAGR) ^ years Doubling = ln(2) / ln(1 + CAGR)

### Assumptions and simplifications

- Assumes no money was added or withdrawn between the two dates. For contributions and distributions, use XIRR.
- Compounds once a year. The chart shows a smooth path; real values move up and down around it.
- Not adjusted for inflation, taxes or fees.

Worked example

### $10,000 growing to $25,000 in 7 years

**End / start**

$25,000 / $10,000 = 2.50x

**Raised to 1 / years**

2.50 ^ (1/7)

**Total growth**

150.0%

**Check**

$10,000 x (1 + 13.99%)^7 = $25,000

CAGR**13.99%**

## Further reading

- [Raziel Learn MOIC vs IRR: Which Number to Trust on an Angel or LP Statement](https://raziel.co/learn/moic-vs-irr)

## Frequently Asked Questions

Common questions about the CAGR calculator and the math behind it.

### What is CAGR?

Compound annual growth rate is the steady yearly rate that would take a starting value to an ending value over a period, if growth compounded once a year. It smooths out the ups and downs in between, so you can compare investments or businesses that grew unevenly over different periods.

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

A simple average of yearly returns overstates growth when returns are volatile. Up 50% one year and down 50% the next averages 0%, but you end with 75% of what you started with, a CAGR of about -13.4%. CAGR always reflects what actually happened to the money from start to finish.

### What is the difference between CAGR and IRR?

CAGR only looks at a starting and an ending value. IRR (and XIRR) accounts for money added or withdrawn along the way, at the dates it moved. For a single investment with no cash flows in between, the two are the same. If you contributed or withdrew money, use the XIRR calculator instead.

### Can I use fractional years?

Yes. Enter 2.5 for two and a half years, or divide the number of days by 365 for an exact holding period. The rate is still annualized.

### How does the reverse mode work?

Switch to "Target value" and enter a starting amount, a growth rate and a number of years. The calculator compounds the start value forward, start x (1 + rate) ^ years, to show where it ends up.

Related tools

## More free *calculators*

[All tools](https://raziel.co/tools)

- [Returns IRR Calculator Annualized return from any series of dated cash flows. Open calculator](https://raziel.co/tools/irr-calculator)
- [Returns MOIC Calculator Multiple on invested capital, realized and unrealized. Open calculator](https://raziel.co/tools/moic-calculator)
- [Returns XIRR Calculator Excel-matching XIRR from cash flows on any dates. Open calculator](https://raziel.co/tools/xirr-calculator)