CAGR Calculator

1. Enter the value at the start of the period in Beginning value. It must be greater than 0.
2. Enter the value at the end of the period in Ending value. 0 is allowed here.
3. Enter how many years lie between the two values in Period. Decimals such as 2.5 are allowed.
4. Select Calculate to see the compound annual growth rate, the total growth rate and the growth multiple.
5. Select Reset example to go back to the values shown when the page opened.

The beginning value and the ending value must be the same kind of number. They do not have to be money: revenue, assets, subscribers or any other value that changes over time works just as well. The unit itself is never used in the calculation, so you only need to enter both values in the same unit.

The values shown when the page opens are a hypothetical example chosen to show how the calculation works. They are not a real product return or a market forecast. This calculator holds no return, tax or fee figures of its own.

CAGR is short for compound annual growth rate. It takes the total change between a beginning value and an ending value and spreads it evenly, as if the value had changed by the same rate every year.

For example, if 10,000 becomes 12,100 over 2 years, the total change is 21% and the CAGR is 10%. Growing by 10% in the first year and 10% again in the second year gives 1.1 × 1.1 = 1.21, which is the same 21% in total. It does not mean the value really rose by 10% each year. Starting from the same 10,000, a value that jumped 50% to 15,000 in the first year and then fell about 19% to end at exactly 12,100 has a completely different path, yet because the beginning and ending values match, the CAGR is still 10%.

That is why CAGR is useful for comparing results over periods of different lengths on the same scale, and why it cannot show how much the value moved up and down along the way.

These are the formulas this calculator uses. Following them in order lets you check the result by hand.

CAGR(%) = [ (V₁ ÷ V₀) ^{1 ÷ t} − 1 ] × 100

• V₀: beginning value (the value at the start of the period, greater than 0)
• V₁: ending value (the value at the end of the period, 0 or more)
• t: period in years (greater than 0)

The supporting results shown with it come from these formulas.

• Total change = ending value − beginning value
• Growth multiple = ending value ÷ beginning value
• Total growth rate (%) = (growth multiple − 1) × 100

Intermediate values are never rounded. Only the numbers on screen are tidied up to four decimal places. A very small non-zero rate that would round to zero is written as “less than 0.0001%” rather than a false 0%.

These are the same values the calculator shows when the page opens. Both the values and the period are a hypothetical example, not a real product return or a market forecast.

1. Beginning value 10,000, ending value 12,100, period 2 years
2. Total change = 12,100 − 10,000 = +2,100
3. Growth multiple = 12,100 ÷ 10,000 = 1.21×
4. Total growth rate = (1.21 − 1) × 100 = 21%
5. CAGR = (1.21^{1 ÷ 2} − 1) × 100 = 10%

To check the last line, multiply 1.1 by itself: 1.1 × 1.1 = 1.21, the same multiple you started with. In other words, the result is the same as growing 10% a year for 2 years.

CAGR starts from the ratio of the ending value to the beginning value. When there is nothing to divide by, or when the ratio cannot be read as a growth rate, this calculator does not calculate anything rather than invent a number.

• A beginning value of 0 cannot be calculated. There is nothing to divide by, and a value that starts at 0 cannot be said to have grown by any multiple.
• An ending value of 0 can be calculated. If the beginning value and the period are both greater than 0, the result is exactly −100%, meaning the entire value was lost.
• If the beginning and ending values are equal, the result is exactly 0%. Nothing changed, and the answer stays 0% no matter what period you enter.
• A period of 0 cannot be calculated. Stating a rate per year means dividing by the period, and dividing by 0 is not possible.
• Negative values are not calculated. A ratio taken against a negative number cannot be read as a growth rate. Two negative values also produce a positive ratio, but calling that growth reverses its meaning entirely, so it is refused.
• Values that change sign (+ to − or − to +) are not calculated either. Because negative numbers are refused outright, sign changes are filtered out naturally. A move from a loss to a gain cannot be expressed as a multiple, so CAGR has no meaning for it.
• Empty fields, letters, values above 1,000,000,000,000,000 and periods longer than 100 years are not calculated either, and the calculator tells you which field is wrong and why.
• Even inside the allowed range, an extreme combination of a very small beginning value and a very large ending value can exceed what a number can represent. In that case no truncated result is shown and the calculator says it cannot be calculated.

• CAGR is an equivalent annual rate that smooths the whole change; it does not mean the value actually changed by that rate every year.
• It cannot show volatility — how far the value rose or fell in between is invisible.
• Intermediate deposits and withdrawals are not reflected. This calculator compares two points in time only, so money added or taken out along the way is not part of the result.
• CAGR is not IRR or XIRR. When there are several cash flows the answers differ, and this calculator does not provide IRR or XIRR.
• Taxes are not automatically included.
• Fees are not automatically included.
• Inflation is not automatically included.
• Exchange rates are not automatically included.
• No statutory tax rate, fee rate or market data is ever guessed or applied automatically.
• Results are informational estimates based only on the values you enter.
• They do not guarantee any return and are not investment, legal or tax advice. No specific product is recommended.
• A past CAGR does not mean the same rate will continue into the future.
• Intermediate values are not rounded; only the numbers on screen are rounded for display.
• Results may differ from other services, because details such as how a period is counted in days can be defined differently.
• Your inputs are calculated only in this browser and are never sent to or stored on a server.

CAGR and an overall investment return answer different questions, so it helps to know which one you actually need.

• CAGR (this page) compares two points in time and the period between them. Money added or withdrawn in between is not part of the calculation, which is why the same CAGR can come from very different paths.
• A total investment return asks how much you got back compared with everything you put in. If contributions were made during the period, the growth in value came partly from those contributions and partly from performance, and CAGR cannot separate the two.
• IRR and XIRR take every cash flow and its date into account. When there were several deposits or withdrawals, that is the measure you need. This calculator does not provide it.

If nothing was added or withdrawn in between, CAGR and a simple annualised return describe the same thing. To look forward instead of back, the Compound Interest Calculator lets you enter a principal, an expected annual return and a period. Putting the CAGR you found here into that expected-return field shows what the same pace would look like if it continued, but a past growth rate does not mean the same rate will continue, and that calculator is a hypothetical simulation that guarantees nothing.

This calculator looks backwards, restating a change that has already happened as an annual rate. To look forward instead, the Compound Interest Calculator takes a principal, an expected annual return and a period and shows how a balance could grow. It is a hypothetical simulation and guarantees no return.

Growth on money you invest and interest on money you borrow are the same compounding idea seen from two directions. The Loan Repayment Calculator estimates the monthly payment, total payment and total interest of a fixed-rate loan with equal monthly payments, using only the figures you enter.

• Compound Interest Calculator — project how a balance may grow
• Loan Repayment Calculator — estimate a monthly payment