What is the formula for compound annual growth rate?

CAGR = (ending value / starting value)^(1 / elapsed years) - 1. Multiply by 100 to write it as a percentage. For 100 to 133.1 over three years: (133.1/100)^(1/3)-1 = 0.10, or 10%. The tool substitutes your known figures into the formula.

Can I calculate CAGR from elapsed months or less than one year?

Yes. Choose Months, then the elapsed years are months / 12. For known values of 100 and 110 over six months, CAGR is (110/100)^(1/0.5)-1 = 21%. This is a mathematical annual equivalent of the observed change, not a claim that it repeats. With 36 elapsed months, use three elapsed years.

How do I calculate CAGR in Excel or with RRI?

Put starting value in A2, ending value in B2 and elapsed years in C2. Enter =(B2/A2)^(1/C2)-1 and format the result as a percentage. For positive endpoints, =RRI(C2,A2,B2) expresses the same compound-period rate when C2 counts years. If C2 holds elapsed months, use =(B2/A2)^(12/C2)-1 or =RRI(C2/12,A2,B2). The worksheet is not created or downloaded here.

How do I calculate a three-, four- or five-year CAGR?

Use the same two-endpoint formula and enter 3, 4 or 5 as the elapsed years. There are three intervals from the start of year one to the start of year four, even though four year labels appear. Count elapsed intervals, not the number of table rows.

Does CAGR work with negative numbers, zero values or losses?

The starting value must be positive. A smaller nonnegative ending value produces a negative CAGR; 100 to 81 over two years gives -10%. A zero ending value gives -100% for any positive duration. A negative starting or ending value is refused because an ordinary real compound growth factor cannot represent that path. Use a suitable alternative metric when endpoints cross zero.

Is CAGR the same as the average annual growth rate?

CAGR is a geometric compound equivalent between endpoints. AAGR usually means the arithmetic mean of each annual growth percentage, so it needs the annual observations and can differ from CAGR. Average Calculator handles supplied arithmetic or geometric lists; this page does not infer a missing year-by-year history.

Can I use this for nonfinancial values or a known index return?

Yes, as endpoint arithmetic on a consistent unit, such as a count or an index level. You must supply the observed endpoints and elapsed duration. No S&P 500, VOO, stock, crypto or other price history is fetched, and the result does not judge whether growth is good or forecast a future value.

Can I reverse CAGR to calculate an ending value or include deposits?

This page solves the rate from known endpoints. APY Calculator applies a supplied annual rate to a starting amount over a duration and can add regular deposits. Irregular dated investments require a cash-flow method such as IRR or XIRR, which this endpoint formula does not calculate.

How do I calculate CAGR from a known total percentage in Excel?

A known total percentage P corresponds to ending value / starting value = 1 + P, using the decimal percentage. For a 33.1% total increase over three years, (1 + 0.331)^(1/3)-1 = 10%. If D2 is the total percentage formatted as a percentage and C2 holds elapsed years, use =(1+D2)^(1/C2)-1. In this calculator use starting value 1 and ending value 1.331. A list of individual yearly percentages is a different input; do not substitute their arithmetic mean for the compounded total.

What CAGR doubles a known starting value over ten years?

Use an ending value twice the starting value and ten elapsed years. (2/1)^(1/10)-1 is about 7.177346%. This is the rate implied by those chosen endpoints and duration; it does not predict that an investment will double.

CAGR Calculator

Enter known starting and ending values in the same unit, then the elapsed duration in years or months. This page opens on 100 to 133.1 over three years, giving a 10% compound annual growth rate. CAGR connects the endpoints with one equivalent annual factor; it does not show intermediate fluctuations, dated cash flows or a forecast.

Compound annual growth rate10%100 to 133.10 over 3 years · equivalent annual compound rate

Total endpoint change = (133.1 − 100) ÷ 100 = 33.1%CAGR = (133.1 ÷ 100)^(1 ÷ 3) − 1 = 10%

Calculate

Starting value

Ending value

Elapsed duration

Duration unit

Use known endpoints in the same units and select the elapsed duration unit. CAGR is an equivalent compound rate, without costs or interim cash flows.

A total return is not a yearly one. 64% over three years is 17.9% a year, because the yearly figure is the compound one: the rate that, applied three times over, turns 12,500 into 20,500. Dividing the total by the years gives a different arithmetic average. ROI keeps its yearly figure hidden for periods under a year; CAGR can explicitly calculate an annual equivalent from a known part-year duration. Neither is a forecast.

Backward looking, on purpose. Every box is a figure you already have, and there is none here for a growth assumption, a market average or money added part way through. Browser double-precision arithmetic, rounded for display. ROI subtracts only the costs you enter; CAGR uses the known endpoints and elapsed duration. Tax, fees not entered, dated cash flows and account terms are not inferred, and neither calculation forecasts future results.

Common questions

What is the formula for compound annual growth rate?: CAGR = (ending value / starting value)^(1 / elapsed years) - 1. Multiply by 100 to write it as a percentage. For 100 to 133.1 over three years: (133.1/100)^(1/3)-1 = 0.10, or 10%. The tool substitutes your known figures into the formula.
Can I calculate CAGR from elapsed months or less than one year?: Yes. Choose Months, then the elapsed years are months / 12. For known values of 100 and 110 over six months, CAGR is (110/100)^(1/0.5)-1 = 21%. This is a mathematical annual equivalent of the observed change, not a claim that it repeats. With 36 elapsed months, use three elapsed years.
How do I calculate CAGR in Excel or with RRI?: Put starting value in A2, ending value in B2 and elapsed years in C2. Enter =(B2/A2)^(1/C2)-1 and format the result as a percentage. For positive endpoints, =RRI(C2,A2,B2) expresses the same compound-period rate when C2 counts years. If C2 holds elapsed months, use =(B2/A2)^(12/C2)-1 or =RRI(C2/12,A2,B2). The worksheet is not created or downloaded here.
How do I calculate a three-, four- or five-year CAGR?: Use the same two-endpoint formula and enter 3, 4 or 5 as the elapsed years. There are three intervals from the start of year one to the start of year four, even though four year labels appear. Count elapsed intervals, not the number of table rows.
Does CAGR work with negative numbers, zero values or losses?: The starting value must be positive. A smaller nonnegative ending value produces a negative CAGR; 100 to 81 over two years gives -10%. A zero ending value gives -100% for any positive duration. A negative starting or ending value is refused because an ordinary real compound growth factor cannot represent that path. Use a suitable alternative metric when endpoints cross zero.
Is CAGR the same as the average annual growth rate?: CAGR is a geometric compound equivalent between endpoints. AAGR usually means the arithmetic mean of each annual growth percentage, so it needs the annual observations and can differ from CAGR. Average Calculator handles supplied arithmetic or geometric lists; this page does not infer a missing year-by-year history.
Can I use this for nonfinancial values or a known index return?: Yes, as endpoint arithmetic on a consistent unit, such as a count or an index level. You must supply the observed endpoints and elapsed duration. No S&P 500, VOO, stock, crypto or other price history is fetched, and the result does not judge whether growth is good or forecast a future value.
Can I reverse CAGR to calculate an ending value or include deposits?: This page solves the rate from known endpoints. APY Calculator applies a supplied annual rate to a starting amount over a duration and can add regular deposits. Irregular dated investments require a cash-flow method such as IRR or XIRR, which this endpoint formula does not calculate.
How do I calculate CAGR from a known total percentage in Excel?: A known total percentage P corresponds to ending value / starting value = 1 + P, using the decimal percentage. For a 33.1% total increase over three years, (1 + 0.331)^(1/3)-1 = 10%. If D2 is the total percentage formatted as a percentage and C2 holds elapsed years, use =(1+D2)^(1/C2)-1. In this calculator use starting value 1 and ending value 1.331. A list of individual yearly percentages is a different input; do not substitute their arithmetic mean for the compounded total.
What CAGR doubles a known starting value over ten years?: Use an ending value twice the starting value and ten elapsed years. (2/1)^(1/10)-1 is about 7.177346%. This is the rate implied by those chosen endpoints and duration; it does not predict that an investment will double.

Browser double-precision arithmetic, rounded for display. ROI subtracts only the costs you enter; CAGR uses the known endpoints and elapsed duration. Tax, fees not entered, dated cash flows and account terms are not inferred, and neither calculation forecasts future results.