CAGR calculator

What is CAGR and how is it calculated?

The compound annual growth rate is the single yearly rate that, compounded every year, turns a start value into an end value over a period. The formula is CAGR = (end value / start value)^(1 / years) - 1. It ignores everything that happened in between and describes the trip as if it had been perfectly smooth.

With the default inputs, $10,000 grows to $18,000 in five years. The end is 1.8 times the start, and 1.8^(1/5) - 1 = 12.47% a year. Check it forward: $10,000 x 1.1247 five times over lands back on $18,000. Total growth was 80%, but the yearly rate is not 80 / 5 = 16%, because each year's growth builds on the last.

The second tab runs the formula in reverse: end value = start value x (1 + CAGR)^years. At 8% a year, $10,000 becomes $14,693.28 after five years, total growth of 46.93%.

How do you calculate CAGR by hand?

Four steps, using the defaults:

1. Divide the end value by the start value: 18,000 / 10,000 = 1.8.
2. Divide 1 by the number of years: 1 / 5 = 0.2.
3. Raise the result of step 1 to the power from step 2: 1.8^0.2 = 1.12475.
4. Subtract 1 and show it as a percentage: 0.12475, or 12.47%.

Step 3 needs a calculator with a power key (often marked y^x or x^y). Without one, use logarithms: the natural log of 1.8 is 0.58779; divide by 5 to get 0.11756; the exponential of that is 1.12475, the same as step 3. The working under the result shows each step with your own numbers.

Here is the steady path those numbers describe, next to a straight line between the same two values:

The compound path starts slower and catches up at the end, which is the shape the chart beside the result draws.

How do you calculate CAGR in Excel and Google Sheets?

Both have a function built for it. Excel's is RRI(nper, pv, fv), which Microsoft's documentation says returns an equivalent interest rate for the growth of an investment; nper is the number of periods, pv the starting value and fv the ending value. Google Sheets uses the same name and order, RRI(number_of_periods, present_value, future_value). For the defaults:

=RRI(5, 10000, 18000) returns 0.1247, or 12.47% formatted as a percentage. The longhand version, =(18000/10000)^(1/5)-1, gives the same answer and works in any spreadsheet.

Two details matter. First, RRI returns a rate per period in whatever unit nper is in. Microsoft's own example, =RRI(96, 10000, 11000), uses 96 months and returns 0.0009933, a monthly rate; the same growth over eight years is 1.20% a year. Second, Google's documentation notes that the number of periods and the present value must be greater than 0, and that a future value of 0 returns -1, or -100%. For dates in cells, Excel's YEARFRAC(start_date, end_date, 1) turns them into years on an actual/actual day count, which can differ slightly from the anniversary count this page uses.

Why is CAGR lower than the average yearly return?

An arithmetic average of yearly returns ignores compounding, so it overstates growth whenever returns vary. Take five years of returns of +20%, -10%, +15%, +5% and -5%:

The average of the five returns is 5.00% a year. The CAGR from $10,000 to $12,388.95 is only 4.38%. The extreme case makes the point: a 50% gain followed by a 50% loss averages 0%, yet $100 becomes $150 and then $75, a CAGR of -13.40%. The CAGR is the rate that actually reproduces the end value from the start value.

The same logic separates CAGR from simple growth per year. On the defaults, 80% total over five years is 16% a year divided evenly, against a CAGR of 12.47%. The calculator shows both in the tiles under the result.

Can you calculate CAGR with a negative or zero starting value?

No, and a calculator that returns a number in those cases is returning something that is not a growth rate. The formula divides the end by the start and takes a root of the result. With a start of zero, the division has no answer: any rise from nothing is an infinite percentage. With a negative start, or a negative end, the ratio is negative: for most periods it has no real root, and where one exists it does not describe growth. With both negative, the ratio turns positive and the formula gives a figure, but it reads a shrinking loss as a decline, which is backward.

This comes up with company earnings, which can move from a loss to a profit. Suppose a business went from a loss of $20,000 to a profit of $15,000 over four years. This calculator says the CAGR is not defined, and instead reports the change in money, $35,000, and the average change a year, $8,750. Workaround formulas that shift both values by the size of the loss do produce a percentage, but it depends on the size of the shift you pick, so it is not a CAGR either.

Two practical routes: measure from the first year with a value above zero, or describe the change in money, as the calculator does. An end value of exactly zero is defined: it is a CAGR of -100%.

What is a value worth at a given CAGR? The reverse calculation

Choose End value from a CAGR to project forward. The tab also shows how many years it takes to double at that rate, ln 2 / ln(1 + CAGR). At 8% that is 9.01 years; at the default 12.47% from the first tab it would be 5.90 years.

Reading it the other way round is often more useful. The CAGR needed to double a value depends heavily on the time allowed:

A projected end value is arithmetic on a rate you supply, not a forecast. A past CAGR describes one stretch of history, and the next stretch can be faster, slower or negative.

Worked examples in pounds, euros and dirhams

The house rose 24% in total, which sounds large until it is spread over six years: 3.65% a year. The dirham portfolio lost 16% in total, a CAGR of -5.65%, so a negative CAGR simply means steady decline. For the reverse, £5,000 at 6% a year for ten years projects to £8,954.24, and €20,000 at 5% a year for seven years to €28,142.01.

The currency selector changes only the formatting. A CAGR is a percentage, so the same two values give the same rate in any currency.

CAGR over 3, 5 or 10 years, or between two dates

The number of years is the exponent, so getting it right matters as much as the two values. From the end of 2020 to the end of 2025 is five years, not six, even though six year-end figures are involved. Count the gaps between values, not the values.

For values on specific days, choose Start and end dates. The calculator counts whole years from anniversary to anniversary of the start date and adds the part year left over by actual days. With the default dates, 15 January 2020 to 15 July 2025, that is 5.4959 years, and growth from $10,000 to $18,000 becomes a CAGR of 11.29%: the extra half year lowers the yearly rate from 12.47%.

The start point can move the answer a lot. If the start value had been $9,000 instead of $10,000, the same $18,000 end would give 14.87% a year over five years; at $11,000 it would give 10.35%. When you read a quoted CAGR, check which years it starts and ends on.

What CAGR leaves out, and common mistakes

• Volatility. Two investments with the same CAGR can have had very different journeys, one smooth and one with a deep fall in the middle.
• Money added or taken out. CAGR assumes nothing was added or withdrawn. For a plan with regular contributions, use the IRR calculator with each flow, or the ROI calculator for a single purchase with income and costs.
• Inflation. CAGR is in money terms; the real return calculator converts it into growth in buying power.
• Counting the values instead of the years. Six year-end values span five years.
• Using a month count as years. RRI with months returns a monthly rate.
• Treating a past CAGR as a projection. It is a summary of one period.

Glossary

CAGR: the steady yearly rate that compounds a start value into an end value. Start value and end value: the two measurements the rate connects. Multiple: end value divided by start value. Total growth: the multiple minus 1, as a percentage. Arithmetic average return: the plain average of yearly returns, which ignores compounding. Doubling time: the years needed to double at a given rate. RRI: the spreadsheet function that returns the equivalent rate per period between two values.

Frequently asked questions

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