Growth rates and compounding

In his 2012 essay “Startup = Growth”, Paul Graham wrote: “A good growth rate during YC is 5-7% a week.” He called 10% a week exceptional. He wrote that 1% a week is a sign that a team does not yet know what to do.

Five percent sounds small. A store that sells 5% more this week than last week does not make the news. But a startup measures growth week after week, and each week starts from a bigger number. This lesson shows what that does to the numbers.

Predict first

Revenue grows 5% each week for one year (52 weeks). How many times larger is it at the end of the year?

Type a guess before you continue. A guess first, even a wrong one, makes the answer easier to remember.

A growth rate for one period

A growth rate is the percentage change from one period to the next:

Growth rate
  = This month ÷ Last month − 1
  = $46K ÷ $40K − 1
  = 15%

Founders give growth for three periods: week over week (WoW), month over month (MoM), and year over year (YoY). Use the same kind of number for each period: revenue, active users, or orders. Say which number and which period you mean.

Growth compounds

Compound growth applies each period’s rate to a bigger base. At 10% a month, $100K becomes $110K in month 2. In month 3, the 10% applies to $110K, so revenue becomes $121K, not $120K.

After 12 months at 10% a month, revenue is 1.1^12 = 3.14 times bigger. That is growth of 214% in the year, not 120%. The difference between the two numbers grows each month.

To convert a rate between periods, raise (1 + rate) to the number of short periods in the long period. In the formulas, w is the weekly rate and m is the monthly rate:

From a weekly rate:
Monthly rate    = (1 + w)^(52÷12) − 1
Yearly multiple = (1 + w)^52

From a monthly rate:
Yearly multiple = (1 + m)^12

Weekly growth	Monthly growth	Yearly multiple
1%	4.4%	1.68x
2%	9.0%	2.80x
5%	23.5%	12.64x
7%	34.1%	33.73x
10%	51.1%	142.0x

Worked example · step 1 of 4

Convert 7% a week into a monthly rate and a yearly multiple

1
Count the weeks in a month
A year has 52 weeks and 12 months. A month is not exactly 4 weeks.
```
Weeks in a month = 52 ÷ 12
                 = 4.33
```

The converter shows the same rate for a week, a month, and a year. The chart puts compound growth next to the common mistake of added rates. Try 10% a month for 2 years. Then try 7% a week.

Converter

Growth rates compound

Enter a growth rate for a week, a month, or a year. See the same rate for the other periods, and see the revenue curve.

Growth rate

From −10% to 15% a week.

The rate is for one

Revenue this month$10K

Time span

Each week: 5%
Each month: 23.5%
Each year: 1,164%
Yearly multiple: 12.64x

Revenue each month

Compound growth
Rates added, not compounded

5% a week is 23.5% a month and 1,164% a year. In one year, revenue grows from $10K to $126.43K a month.

If you add the rates and do not compound them (5% × 52 = 260% a year), you get $36K a month after one year. Compound growth gives 3.51x that amount, because each week grows a larger base.

Work it out

Revenue grows 2% each week for one year. How many times larger is it at the end of the year?

Churn compounds against you

Revenue growth is a net number. Each month, new sales and upgrades add revenue, and churn removes revenue. The growth rate that you report is the difference.

Northwind has $40K of MRR. Each month, new sales add MRR equal to 8% of the month before. Compare two cases after 12 months. In the first case, no customers leave. In the second case, Northwind loses 3% of its MRR to churn each month, so net growth is 5% a month:

No churn: $40K × 1.08^12 = $100.7K
3% churn: $40K × 1.05^12 =  $71.8K

A churn of 3% a month removes approximately $29K of MRR from the end result. The loss compounds, like the growth. The lesson Unit economics shows how churn also decreases the value of each customer.

Doubling time

A second way to read a growth rate is the time that revenue takes to double. The doubling time is a number of weeks or months, so it is easy to compare with a plan. In the formula, r is the growth rate for one period:

Doubling time = log(2) ÷ log(1 + r)

Growth rate	Doubling time
7% a week	10.2 weeks
5% a week	14.2 weeks
10% a month	7.3 months
3x a year (a T2D3 “triple”)	7.6 months
22% a year	3.5 years

For rates of less than approximately 20%, the “rule of 72” gives a quick estimate. Divide 72 by the rate in percent. At 10% a month, 72 ÷ 10 = 7.2 months, which is close to the exact 7.3 months.

What YC and investors look for

Graham’s 5% to 7% a week is a target for the time of a YC batch. In March 2025, Garry Tan, the CEO of YC, told CNBC that the Winter 2025 batch as a whole grew approximately 10% a week.

Graham also showed what such a rate does over years. $1,000 of monthly revenue that grows 5% a week becomes approximately $25 million a month after 4 years. The example shows why a small weekly rate is a big claim.

CMGR: an honest average

Monthly growth is not steady. To give one average for many months, use the CMGR (compound monthly growth rate). The CMGR is the steady monthly rate that turns the first month into the last month. In the formula, n is the number of months between the first month and the last month:

CMGR = (Last ÷ First)^(1 ÷ n) − 1

Here is revenue for seven months, in thousands of dollars: 20, 30, 33, 45, 50, 70, 80. The six monthly growth rates are 50%, 10%, 36%, 11%, 40%, and 14%. Their simple average is 27.0%. The CMGR is lower:

CMGR = (80 ÷ 20)^(1 ÷ 6) − 1
     = 4^(1 ÷ 6) − 1
     = 26.0%

a16z writes: “The CMGR will be smaller than the simple average in a growing business.” The simple average gives too much weight to big jumps from small bases. Thus give the CMGR.

Work it out

Revenue grew from $50K a month to $200K a month in 12 months. What is the CMGR?

Growth paths: T2D3 and Q2T3

Investors also use paths for ARR over five years. In February 2015, Neeraj Agrawal of Battery Ventures named the T2D3 path. It starts after a SaaS company has product-market fit and $2M of ARR. Then ARR must triple twice and double three times:

$2M → $6M → $18M
    → $36M → $72M → $144M

In 2025, Bessemer gave an update for AI startups that it calls “Shooting Stars”: Q2T3, which is quadruple twice, then triple three times. The average Bessemer Shooting Star got approximately $3M ARR in year 1, then approximately $12M, $40M, and $103M. Those are multiples of 4.0x, 3.3x, and 2.6x. Bessemer writes in a footnote that it does not have five years of data yet.

Each path has a monthly rate. The table converts each yearly multiple:

Multiple in one year	Monthly rate	Weekly rate
2x (a “double”)	5.9%	1.34%
3x (a “triple”)	9.6%	2.14%
4x (a “quadruple”)	12.2%	2.70%

The paths show the best companies. They do not show a typical company.

Why do growth rates fall as a company gets bigger?

A rate is a percentage of the base. A company with $100K of ARR can double with $100K of new sales. A company with $100M of ARR must sell $100M more to double. Thus the paths go from a triple to a double, and the Bessemer averages fall from 4.0x to 2.6x.

Quiz · question 1 of 5

Test what you learned

Your startup grows revenue 5% each week for one year. Approximately how many times larger is it after the year?

In this lesson you will learn