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CAGR Calculator

Find the compound annual growth rate: the steady yearly rate that turns a beginning value into an ending value over a set number of years.

Level: Grades 10–11

  • Common Core standard HSF.LE.A.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Printable worksheet

CAGR Calculator

Know the answer you need? Pick an input to work backward.

Inputs

The value at the start. Must be above zero.

Fractions are fine, for example 2.5.

Result

Compound annual growth rate

11.29%

Growing from 10,000 to 19,000 over 6 years is a compound annual growth rate of 11.29%.

Total growth
90%
Growth multiple
1.9 ×

See the step-by-step solution ↓

Value each year at a steady CAGR
Value each year at a steady CAGR
YearValue
010,000
111,129.07
212,385.62
313,784.05
415,340.37
517,072.4
619,000

Step-by-step solution

  1. Divide the ending value by the beginning value. This growth multiple tells you how many times bigger it got

    19,00010,000=1.9

  2. Raise the multiple to the power 1 ÷ years. This undoes the compounding and gives the growth factor for one year

    1.916=1.112907

  3. Subtract 1 and multiply by 100 to turn that factor into a percent per year

    1.112907−1×100=11.2907%

  4. For comparison, find the total growth over the whole period

    1.9−1×100=90%

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

Please note: Results are estimates for planning and comparison. Lenders, banks, and tax authorities may round differently or include fees not modeled here, so confirm figures with your provider before deciding.

What this calculator does

Find the one steady yearly growth rate that gets you from a starting value to an ending value. That rate is the compound annual growth rate, or CAGR. It smooths an up-and-down history into one number. Think of a portfolio, a company's sales or a town's population over several years. CAGR is the same-every-year rate that would land on exactly the same result. It includes compounding, where each year's growth builds on the last.

Enter the beginning value, the ending value and the number of years. You'll get the CAGR and the total growth over the whole period. For a whole number of years, you'll also see a table of the value each year along that smooth path.

Where it's used

Why this math matters outside the classroom:

  • Investment growth. A portfolio that grows from $10,000 to $20,000 in 8 years has a compound annual growth rate of about 9.05%.
  • Company revenue. Analysts summarize revenue that rose unevenly over five years with one steady yearly rate that reaches the same end figure.
  • Population trends. Planners describe a town that grew from 20,000 to 25,000 residents over a decade with a single yearly growth rate.
  • Comparing two periods. Converting each period's growth to an annual rate lets a 3-year gain and a 7-year gain be compared fairly.

Grade level and standards: Grades 10–11; Common Core State Standards for Mathematics HSF.LE.A.2. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Enter the beginning value: the starting balance, price, revenue or count. It must be above zero.
  2. Enter the ending value at the end of the period.
  3. Enter the number of years between them. Fractions such as 2.5 are fine.
  4. Read the CAGR, the total growth and the growth multiple.

What the inputs mean

Beginning value
Any positive amount, in any unit, as long as the ending value uses the same unit. A start of zero or below has no growth rate you can work out.
Ending value
The value at the end of the period. Zero is allowed and gives −100%. Negative values aren't allowed.
Number of years
The length of the period in years. For a period given in months, divide by 12.

Formula and method

growth multiple = ending value ÷ beginning value
CAGR % = (growth multiple^(1 ÷ years) − 1) × 100
total growth % = (growth multiple − 1) × 100

The growth multiple is how many times bigger the value got. Raising it to the power 1 ÷ years is the same as taking the years-th root. Here's why that works. Say a value grows at a rate r each year (as a decimal) for n years. It ends up multiplied by (1 + r)^n. CAGR runs that backwards. Take the n-th root of the overall multiple to get the yearly factor, then subtract 1.

Averaging the yearly percent changes would give a different number, and usually a higher one. That's because a plain average ignores compounding. CAGR is the rate that actually connects the starting and ending values.

Worked example

A business had revenue of 10,000 six years ago and 19,000 this year.

  1. Growth multiple: 19,000 ÷ 10,000 = 1.9.
  2. Yearly factor: 1.9^(1/6) = 1.112907.
  3. CAGR: (1.112907 − 1) × 100 = 11.29% a year.
  4. Total growth: (1.9 − 1) × 100 = 90% over the six years.

Result: Revenue grew at a compound annual rate of about 11.29% a year, for 90% growth in total.

Understanding the result

CAGR describes a smooth average path, not the real one. A value that jumped 40% one year and fell 10% the next can have the same CAGR as one that grew steadily.

A negative CAGR means the value shrank on average each year. A CAGR of −100% means it fell to zero.

Use CAGR to compare things measured over different lengths of time, such as two funds with five-year and eight-year records.

Assumptions and limitations

  • Growth is compounded once a year at a steady rate.
  • Only the starting and ending values matter. Values in between are ignored.
  • No money is added or taken out during the period. For investments with deposits or withdrawals, CAGR can make the true return look higher or lower than it was.
  • Results aren't rounded along the way. The rate is shown to two decimal places.
  • The beginning value must be above zero. Growth from zero, or from a negative figure such as a loss, has no compound rate.
  • CAGR hides the ups and downs (volatility). Two series with the same CAGR can carry very different risk.
  • A high CAGR over a short period rarely continues. It describes the past; it isn't a forecast.

Frequently asked questions

Why can't the beginning value be zero or negative?

CAGR divides the ending value by the beginning value and then takes a root. You can't divide by zero. With a negative start, the ratio either flips sign or the root has no real answer, so the result wouldn't mean anything. For a business that went from a loss to a profit, describe the change in dollars instead.

How is CAGR different from the average annual growth rate?

The simple average adds up each year's percent change and divides by the number of years. It ignores compounding, so it usually comes out higher. For example, +50% then −50% averages 0%. But the value actually fell 25%, a CAGR of about −13.4%.

Can I use months instead of years?

Yes. Divide the number of months by 12 and enter that as years. The result is still a yearly rate. If you'd rather have a monthly rate, enter the number of months in the years box. The answer will then be per month.

Is CAGR the same as annualized ROI?

They use the same formula. CAGR is the usual name for growth of any value over time. Annualized ROI (return on investment) is the name for an investment's yearly return. The ROI calculator also shows the total return in dollars.

How this calculator is checked

Method: Standard compound annual growth rate definition: (ending ÷ beginning)^(1/years) − 1, derived from value × (1 + r)^n. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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