Every loop comes down to two numbers. K is how many new customers each customer brings. Cycle time is how many days pass between a customer's first order and the first order of the person they brought. Get both from your own file before you believe any growth story, including the ones in this book.

K, measured honestly

K is invites sent per customer times the share of invites that become customers. Two invites each and a 10% conversion gives a K of 0.2: every ten customers bring two more.

Count the second half strictly. A customer is someone who completed a first order that wasn't refunded, not a signup and not a code redemption on a cancelled cart. Signups inflate K the same way opens inflated email.

Viral software can run above 1, where every user brings more than one more and growth feeds itself. A consumer brand shipping boxes almost never does. Assume yours is somewhere between 0.05 and 0.4 until the file says otherwise.

Below one, a loop is a discount

When K is under 1, each customer you buy brings a chain that ends: K customers in the first turn, K×K in the second, and so on. The chain adds up to 1 ÷ (1 − K) customers per customer bought. At K = 0.2 that's 1.25. At 0.5 it's 2.

That changes what your acquisition really costs. Spread the paid cost and the rewards over everyone the chain brings, and the blended cost per customer is:

blended cost = acquisition cost × (1 − K) + reward per referred customer × K

Say acquisition costs $40, K is 0.2 and each referred customer costs $20 in rewards across both sides. Blended cost is $40 × 0.8 + $20 × 0.2: $32 plus $4, or $36. The loop took 10% off every customer you buy.

Below one, a loop is a discount on every customer you buy.

That framing keeps the loop honest in a budget meeting. It won't replace paid acquisition. It lowers its price, and it tells you exactly how much the reward can grow before the discount disappears: at K = 0.2, a reward above the acquisition cost itself makes the blend worse, not better.

Cycle time decides when it pays

David Skok, a venture investor, published the standard formula on his For Entrepreneurs blog. Customers after t days, starting from a seed, with K and a cycle time ct:

customers(t) = seed × (K^(t ÷ ct + 1) − 1) ÷ (K − 1)

Run it on 1,000 seed customers:

Two things jump out. At K = 0.5, halving the cycle time gets you to the same 2,000 customers sooner, and no further. Below 1, cycle time decides when the loop pays, not how much. Above 1, the same halving turns 25,075 customers into 101,845 by day 365. That's why software founders obsess over cycle time and DTC operators should obsess over K first.

Cycle time still matters to you for one reason: cash. A loop whose referred customers arrive in 20 days pays back inside the month you spent on the seed. One that takes 200 days pays back in a different fiscal year, after some of the inviters have churned.

Retention is inside K

Invites per customer isn't a fixed trait. It's a rate times a lifetime. A customer who stays active for a year has twelve months of moments to bring someone; one who churns after the first order has a week.

That's why the same referral program shows a K of 0.05 at one brand and 0.3 at another. The second brand usually doesn't have a better referral page. It has customers who stick around long enough to use it. Retention Is the Fuel works through this.

Run it on your numbers

Do this

• Compute K and cycle time from last quarter's orders, counting completed first orders only.
• Put the blended cost on the same slide as acquisition cost at the next budget meeting.