The funnel and AARRR
Write a funnel as five counts and four step rates, price a 10% lift at each stage, and pick the stage where that lift is cheapest and fastest to read.
On this page
A funnel is a count at each stage a customer passes through and the rate between each pair of stages. It answers the question growth meetings circle: where the next dollar or engineer should go. Dave McClure named the stages in "Startup Metrics for Pirates" (opens in a new tab) (2007) — acquisition, activation, retention, referral, revenue, AARRR — and the names matter less than the habit of writing a number beside each one. This module takes revenue before referral, because referral is the loop back to the top.
One month of the invoicing app
The running example for this module is an invoicing app for freelancers and small agencies. Anyone can use it free; the paid plan is $50 a month at 80% gross margin, so a paying customer contributes $40 a month. Every figure in this module is in US dollars and is an assumption you can replace with your own. The company spends $50,000 a month on paid search and paid social, which brings 100,000 visits. That is $0.50 a paid visit, the bottom of the $0.50-to-$5 click range in the arithmetic a marketer carries rather than its $2 default, because most of this spend buys broad social traffic. The cheaper visits convert worse: 2.4% of this funnel's sign-ups end up paying, against the 20% module 0's chain assumes, which is why this company's paid CAC is $521 and not that chain's $333. Visitors who arrive without a paid click are counted separately, in blended versus paid CAC.
One month of paid visits:
- Acquisition: 100,000 visits become 4,000 sign-ups (4%).
- Activation: 1,200 of them send a first invoice within seven days (30%).
- Retention: 480 are still sending invoices in month 3 (40% of the activated).
- Revenue: 96 move to the paid plan (20% of the retained).
- Referral: some retained users bring in someone new, the loop back to the top.
Every stage needs a written definition before it gets a number. Activation here means a first invoice sent within seven days, the action after which users who stay start to look different from users who leave; "logged in twice" would inflate the count without predicting anything. Activation is the stage most often left undefined.
The stages multiply
Paying customers are the product of the visits and the four rates:
paying = visits × sign-up × activation × retention × paid
96 = 100,000 × 0.04 × 0.30 × 0.40 × 0.20
Because the stages multiply, a 10% relative lift at any one stage lifts paying customers by 10%: 96 becomes 105.6, about ten more a month, whichever rate moved. At the $521 a customer costs today, worked in CAC, LTV and payback, ten customers a month is what $5,000 a month of paid spend buys, so a project that delivers a 10% lift is worth up to $5,000 a month for as long as the lift lasts.
So the question is never which stage is worst, but where a 10% lift is cheapest and soonest seen. It is the habit the system-design course calls back-of-the-envelope estimation: turn the argument into a product of a few numbers, then argue about the numbers.
The mistake: fixing the stage with the lowest rate
The 4% sign-up rate looks like the problem, because 96 of every 100 visitors leave, and a team that reads the funnel that way spends the quarter on the landing page and the paid budget. But the size of a rate says nothing about the cost of moving it, and the top of the funnel hides two traps.
The first is that buying the lift with traffic is a recurring cost: ten percent more visits is $5,000 a month more paid spend, and more in practice, because a channel's next visit costs more than its last. The lift lasts exactly as long as the spend.
The second is that the stages are independent only while the people moving through them stay the same kind of people. A page that persuades more browsers to sign up adds sign-ups who activate less often. A 15% lift in sign-ups that drops activation from 30% to 27% delivers 1.15 × 0.90 = 1.035: a 3.5% lift in paying customers, not 15%. The multiplication holds; the assumption that the other rates hold does not.
The fix is to price every candidate lift the same way: what it costs, how long it lasts, what it does to the stage after it, and how quickly it can be measured. The exercise which funnel stage to fix works three proposals through those four questions.
Where a lift is cheapest and fastest to read
Measurement speed is the factor teams forget. Each stage sees a different monthly volume, which decides how long a test takes to tell a real lift from a lucky month:
| Stage | Seen each month | A 10% relative lift |
|---|---|---|
| Sign-up rate | 100,000 visits | 4.0% to 4.4% |
| Activation | 4,000 sign-ups | 30% to 33% |
| Month-3 retention | 1,200 activated | 40% to 44% |
| Paid conversion | 480 retained | 20% to 22% |
An onboarding test sees 4,000 sign-ups a month and reads within weeks. An upgrade-prompt test sees 480 users a month, and 20% against 22% on samples that size takes months to tell apart from noise; reading an experiment works the sample sizes. Every 10% is worth the same ten customers, so the stage that costs least and reads fastest wins. For most self-serve products that is activation: one-off engineering rather than recurring spend, a large monthly sample, and no change to who enters the funnel.
Referral: the loop back to the top
Referral is the one stage that feeds an earlier stage. Each month 480 users reach month 3 still active; if 5% refer one sign-up each, that is 24 sign-ups a month, 0.6% of the paid funnel's 4,000.
At the funnel's sign-up-to-paid rate of 2.4% (96 ÷ 4,000), 24 sign-ups add about 0.6 paying customers a month, roughly $300 of paid spend at $521 a customer. Negligible, and the arithmetic says how far from mattering: to equal a 10% lift anywhere else, referral has to add 400 sign-ups a month, which means 83% of the 480 retained users each referring one person, or the 5% who refer bringing 17 each. A referral credit will not move 5% to 83%.
The loop's summary is the viral coefficient, k, sign-ups produced per sign-up: here 24 ÷ 4,000 = 0.006, so the loop multiplies acquisition by 1 ÷ (1 − k) = 1.006. A k of 0.5 doubles every paid sign-up; one below 0.1 adds less than 11%. For this product referral is evidence that retained users like it, not a growth channel; AARRR and guardrails works the same five stages in product terms.
In practice
To the team: put five counts and four rates on one page every month, each with its definition, and price every proposal in one unit: paying customers a month, its cost, how long the lift lasts, and the weeks it takes to read. "Ten more customers a month is worth up to $5,000 a month of paid spend; the onboarding rebuild buys that once, the extra traffic buys it every month" settles most funnel arguments.
The mistake that costs money is fixing the stage with the lowest rate. The 4% at the top invites more spend, which buys a lift that ends when the spend does and often dilutes the stage after it.
Check yourself
1. An upgrade-prompt test lifts paid conversion from 20% to 22% on one month's 480 retained users. An onboarding test lifts activation from 30% to 33% on one month's 4,000 sign-ups. Both claim a 10% lift. Which do you act on first?
The onboarding result. Both are worth about ten paying customers a month if real, but the upgrade test moved 96 upgrades to about 106, and a count near 96 out of 480 varies by about √(480 × 0.2 × 0.8) ≈ 9 a month, so ten more is one ordinary month. The onboarding test added about 120 activations against a spread of √(4,000 × 0.3 × 0.7) ≈ 29: four times the noise. Ship onboarding; keep the upgrade test running.
2. An agency offers to double the sign-up rate from 4% to 8% with a new landing page for $40,000. What do you need to know before you say yes, and what is the deal worth if the claim holds?
If every later rate held, paying customers would double from 96 to 192 a month, worth about $50,000 a month of paid spend at $521 each, so $40,000 would be cheap. But a doubling at the top changes who arrives: if activation across all sign-ups halves to 15%, paying customers do not move (2 × 0.5 = 1). Run the page on half the traffic for a month and pay on activated sign-ups, not sign-ups.
3. A colleague proposes a referral credit and expects it to triple the share of retained users who refer, from 5% to 15%. Estimate the most it adds in a year.
480 × 15% = 72 referred sign-ups a month. At the funnel's 2.4% sign-up-to-paid rate that is about 1.7 paying customers a month, roughly 21 a year, worth about $11,000 of paid spend at $521 each, or $22,000 if referred users convert twice as well. Build it if it costs less; leave it out of the growth plan.