Monthly growth to annual

Compound a monthly rate up to a yearly one, or break a yearly one down.

Convert
% / month
% / year
annual growth rate

Annual = (1 + monthly) ^ 12 − 1  ·  Monthly = (1 + annual) ^ (1/12) − 1


Why you cannot just multiply by 12

This is the single most common error in growth reporting. If a metric grows 5% month over month, the annual growth rate is not 60%. It is 79.59%, because each month compounds on top of the last.

(1.05) ^ 12 − 1 = 0.7959 = 79.59%

The gap widens fast. At 2% monthly the naive answer is 24% and the real one is 26.8%. At 10% monthly the naive answer is 120% and the real one is 213.8%. Anyone presenting a multiplied-by-twelve figure for a fast-growing metric is understating it substantially, and anyone checking the arithmetic will notice.

The formulas

Annual = (1 + monthly) ^ 12 − 1
Monthly = (1 + annual) ^ (1/12) − 1

They are inverses of each other, which is why this page runs in both directions. The second is the one people reach for less often and need just as much: if a plan calls for 40% growth this year, the monthly rate that gets you there is 2.84%, not 3.33%.

Where this comes up

The honest caveat

Annualizing a single month assumes that month repeats twelve times. It almost never does. A strong January for a business with January seasonality annualizes into a number that will not survive contact with February.

Use this conversion when the monthly rate is an average over several months, or a deliberate planning assumption. Treat a single observed month as a rough indication, not a forecast. If your metric is seasonal, compare each month against the same month last year instead — that comparison is already annual and needs no conversion.

Questions

What about negative monthly growth?

It works the same way, and the compounding cuts in the same direction. A 5% monthly decline is a 45.96% annual decline, not 60%. Losses compound more gently than the naive multiplication suggests, which is the mirror image of the gains case.

Is this the same as CAGR?

Closely related. CAGR annualizes growth between two values over a period; this page annualizes a rate that is already expressed per month. If you have a starting and ending value instead of a rate, use the main CAGR calculator.

What about weekly or quarterly rates?

Same structure, different exponent: 52 for weekly, 4 for quarterly. So a 3% quarterly rate annualizes to (1.03) ^ 4 − 1 = 12.55%.

Does this account for churn?

No. It converts whatever net rate you feed it. If your 5% monthly figure is already net of churn, the annualized result is too. If it is gross growth, the annualized number is gross as well, and will overstate where you actually land.