CAGR Calculator
Calculator Use
The CAGR Calculator finds the compound annual growth rate. CAGR is the average rate of growth of an investment or business over a period of time, typically years.
What is CAGR?
CAGR is an acronym for Compound Annual Growth Rate. It is the average annualized growth rate of an investment or business.
CAGR calculates the average rate of growth for an investment across all time periods. By using this average it provides a "smoothed" rate of return, compounded yearly over time.
This CAGR Calculator finds CAGR percentage, beginning value of an investment, final value of an investment, or number of time periods. Enter three known variables and the calculator finds the fourth.
The CAGR Formula
Compound Annual Growth Rate Formula
CAGR % = ( (FV/BV)1/t - 1 ) x 100
Where:
- CAGR % = Compound Annual Growth Rate as a percentage
- BV = Beginning Value
- FV = Final Value
- t = Number of Years
Reading the CAGR formula in plain words, you would say the compound annual growth rate percentage equals the final value divided by the beginning value, raised to the power of 1 divided by the number of time periods, minus one, times 100.
When to Use CAGR
You can use the CAGR calculation to compare the average rate of return for different periods of growth for any given investment. You can also compare CAGR between investment options to evaluate their historic returns.
Using CAGR, the average or "smoothed" rate of return is helpful as it lets you assume steady growth across an investment period. However with periods of high volativity or large fluctuations in value, the average could be skewed toward the direction of those valuation spikes. So be aware of this factor when comparing CAGR across different investments.
If you'd like to calculate rate of return on any investment for a single year use our Return on Investment ROI Calculator. Input your initial value, final value, and 1 year for "Length of Investment."
CAGR is typically measured in years however you can use this CAGR Calculator to find the average rate of growth for other time periods.
You can calculate the annually compounded average rate of growth for periods of days, weeks, months or quarters by selecting your time period from the calculator menu. If you do the calculation by hand however, the exponent in the formula must be adjusted to account for your selected time unit. Read "Calculating CAGR from Monthly or Quarterly Data" below to understand how different time units affect the CAGR formula.
Use caution with time periods less than a year because in these cases the CAGR calculation may not be truly representative of long-term investment performance.
How to Calculate CAGR
You can calculate CAGR by hand using your own calculator. Use the CAGR formula above and plug in your numbers.
For example, say you wanted to evaluate the performance of a stock market index fund. Its current value is 424, and its value on the same calendar day 5 years ago was 376. What is the compound annual growth rate for this index fund?
Start with the CAGR formula, insert your numbers, and complete the calculation. The math is shown for you here:
CAGR % = ( (FV/BV)n/t - 1 ) x 100
CAGR % = ( (424/376)1/5 - 1 ) x 100
CAGR % = ( (1.22766)0.2 - 1 ) x 100
CAGR % = ( 1.02432 - 1 ) x 100
CAGR % = 0.02432 x 100
CAGR % = 2.432%
So the index fund averaged 2.432% growth in value over the past 5 years.
You can use the CalculatorSoup® CAGR Calculator to confirm your math anytime you do a CAGR calculation by hand.
Calculating CAGR from Monthly or Quarterly Data
You can use this calculator to find the compound average growth rate for periods less than a year. In the standard CAGR formula, time t is in years which means compounding is annual and occurs once per year, so n = 1.
If you want to calculate CAGR for a period of say 8 months you can still calculate what the average rate of return would be using the CAGR formula. You would need to change n/t to a ratio that still reflects annual compounding however.
CAGR % = ( (FV/BV)n/t - 1 ) x 100
Here:
- CAGR % = Compound Annual Growth Rate as a percentage
- BV = Beginning Value
- FV = Final Value
- n = Number of periods per year. For calculations in quarters n = 4, for months n = 12, for weeks n = 52, and for days n = 365.
- t = Number of periods in terms of the same unit used for n (quarters, months, weeks or days).
So if you have a period of 8 months, the CAGR formula remains the same but the exponent in the calculation is n/t = 12/8 = 1.5. Alternatively you could figure out what is 8 months as a decimal and then use that number as t to divide 1 in the standard 1/t exponent. So 8 months as a decimal is 8/12 = 0.666667. Dividing 1 by this number, 1/0.666667 = 1.5. This shows that you'd get the same number in the exponent with either method.
Reverse CAGR Calculator Formulas
Reverse CAGR calculations mean you know the CAGR percentage, but you want to instead calculate one of the other three variables: the beginning Value BV, the final value FV, or the number of time periods t.
You can use this calculator to do a reverse CAGR calculation by selecting which variable you want to calculate and entering the other three known values.
The reverse CAGR formulas are listed here. To simplify these formulas we have CAGR in decimal form (multiply % by 100), and time is in the standard years. The reverse CAGR formulas are:
Find Beginning Value BV
BV = FV / (CAGR + 1)t
Find Final Value FV
FV = BV x (CAGR + 1)t
Find Number of Periods t
t = ln(FV/BV) / ln(CAGR + 1), where ln is the natural log
Calculate CAGR in Excel
If you would like to use the CAGR formula in an Excel spreadsheet you can use the Excel CAGR formula:
=ROUND(((POWER((B2/B1),(1/B3))-1)*100),4)
Set up your Excel spreadsheet as shown below so that the cell references provided in our formula are valid. Once you understand how the formula works you can change the cell references to work with your own spreadsheet layout.
For the values given here the CAGR result in your test cell B4 should be 58.4893%.
| A | B | |
|---|---|---|
| 1 | Beginning Value | 100000 |
| 2 | Final Value | 1000000 |
| 3 | No. of Years | 5 |
| 4 | CAGR % | =ROUND(((POWER((B2/B1),(1/B3))-1)*100),4) |