CAGR Calculator (Compound Annual Growth Rate)
CAGR (Compound Annual Growth Rate) is the average rate at which an investment would have grown each year, compounded, to move from its beginning value to its ending value over a given period.
- Closed-form: (FV/PV)^(1/n) - 1
- CAGR, total return and growth multiple
- Compare investments of different lengths
CAGR Calculator (Compound Annual Growth Rate)
Enter your numbers and press Calculate
How CAGR is calculated
CAGR is obtained with a closed-form formula, without iterating year by year:
CAGR = (ending value / beginning value)^(1 / years) - 1
The result is expressed as a percentage by multiplying by 100. Alongside CAGR, this tool computes two related metrics:
Total return = (ending value / beginning value) - 1, the cumulative growth over the whole period (not annualized).
Growth multiple = ending value / beginning value, how many times the capital multiplied.
The key is the n-th root of the ratio: it converts total growth into the equivalent annual rate that, compounded over n years, produces that same growth. That is why CAGR is always lower than the total return when the period lasts more than one year.
Worked example: an investment of 10,000 that ends up worth 20,000 after 7 years. Multiple = 20,000 / 10,000 = 2. Total return = 2 - 1 = 100%. CAGR = 2^(1/7) - 1 = 0.104090 = 10.4090%. In other words, that capital grew at a compounded rate of 10.41% per year.
Source: the standard definition of CAGR in financial mathematics (the compound annual growth rate formula). It is a universal formula and does not depend on any jurisdiction or official rates.
CAGR examples with the same formula
Four scenarios computed with the exact same formula the tool uses:
- Double in 7 years: 10,000 -> 20,000 over 7 years. CAGR = 2^(1/7) - 1 = 10.41%. Total return = 100%. Multiple = 2.
- No change: 1,000 -> 1,000 over 5 years. CAGR = 1^(1/5) - 1 = 0%. Total return = 0%. Multiple = 1. If the value does not change, CAGR is zero no matter how much time passes.
- 10x growth: 10,000 -> 100,000 over 10 years. CAGR = 10^(1/10) - 1 = 25.89%. Total return = 900%. Multiple = 10. Even though the capital multiplied tenfold, the compounded annual pace is 25.89%, far below the 900% total.
- Loss: 50,000 -> 40,000 over 4 years. CAGR = 0.8^(1/4) - 1 = -5.43%. Total return = -20%. Multiple = 0.8. CAGR can be negative when the ending value is lower than the beginning value.
The pattern is clear: the longer the period, the more CAGR separates from the total return, because compounding spreads that growth over more years.
How to use the calculator step by step
Step 1: enter the beginning value of the investment (the capital at the start of the period). It must be greater than zero, because the formula divides by it.
Step 2: enter the ending value of the investment (the capital at the end of the period). If it is lower than the beginning value, CAGR will be negative; that is correct and signals an annualized loss.
Step 3: enter the number of years in the period. Decimals are accepted if the period is not a whole number of years (for example 2.5 years). It must be greater than zero.
Step 4: review the results. CAGR is the compounded annual rate as a percentage; total return is the cumulative growth over the whole period; and the multiple shows how many times your capital multiplied.
Tip: use CAGR to compare investments of different lengths on equal footing. One that doubled in 7 years (10.41% CAGR) grew faster than one that doubled in 10 years (7.18% CAGR), even though both have the same 100% total return.
Important notice: this calculator provides an indicative estimate for informational and educational purposes. CAGR describes the historical growth of capital and does not guarantee future returns; it is not financial or investment advice. For real decisions, consider inflation, taxes, fees and risk, and consult a qualified adviser.
About this calculator
It is the go-to metric for comparing investments of different lengths because it smooths out volatility: it turns uneven growth into a single equivalent annual rate. This calculator applies the standard closed-form formula: CAGR = (ending value / beginning value) raised to the power of (1 / number of years), minus 1. Enter the beginning value, the ending value and the number of years in the period and you instantly get the CAGR as a percentage, the cumulative total return over the period and the growth multiple (how many times your capital multiplied). Unlike the arithmetic average of yearly returns, CAGR reflects the effect of compounding, so it is the rate that truly describes how capital grew. This is an indicative estimate for informational purposes and is not investment advice.
Frequently asked questions
What is CAGR and what is it for?
CAGR (compound annual growth rate) is the single annual rate at which capital would have grown, compounded, to move from its beginning value to its ending value over a given period. It is used to compare investments of different lengths on equal footing, because it smooths volatility and expresses all the growth as one annual pace. It is computed as (ending value / beginning value) raised to (1 / years), minus 1.
How does CAGR differ from total return?
Total return is the cumulative growth over the whole period: (ending value / beginning value) - 1. CAGR annualizes that growth: it spreads it across the years of the period by taking the n-th root. So if capital doubles (100% total return) over 7 years, CAGR is 10.41%, not 14.3%. CAGR is always lower than total return when the period exceeds one year, because it accounts for compounding.
Can CAGR be negative?
Yes. When the ending value is lower than the beginning value, the ratio is below 1 and CAGR comes out negative, indicating an annualized loss. For example, going from 50,000 to 40,000 over 4 years gives a CAGR of -5.43%: the capital fell at a compounded rate of 5.43% per year. The calculator correctly shows negative values when there is a loss.
What values do I need to enter?
Just three: the beginning value (capital at the start), the ending value (capital at the end) and the number of years in the period. The beginning value and the years must be greater than zero. The values can be in any currency or unit, because CAGR depends only on the ratio of ending to beginning, not on the currency. If the period is not whole, enter decimals (for example 3.5 years).
What is the exact CAGR formula?
CAGR = (ending value / beginning value)^(1 / number of years) - 1. The result is multiplied by 100 to express it as a percentage. It is a closed-form formula: it does not require iterating year by year or knowing the intermediate values, only the beginning, the ending and the duration. It is the standard definition of compound annual growth rate in financial mathematics, valid in any country and for any asset.