How the model works

This projects two connected populations. Free users grow from organic signups and virality, the average number of new free users each existing free user brings in per month, and shrink as some convert to paid and others churn without converting. Paid customers then behave like a standalone churn model: they churn, expand, and get reactivated, with MRR tracked on its own path so expansion can lift revenue per account independent of raw headcount. Every conversion out of the free pool becomes an inflow into the paid pool at your average revenue per user.

How to read the results

When the viral coefficient R is smaller than conversion plus free churn combined, the free base settles into a steady size and paid MRR eventually levels off near the ceiling shown as a dashed line on the chart. When R is larger, the free base compounds on its own, so both the free count and MRR grow without a ceiling, even if you stopped organic marketing entirely. Lifetime value and customer lifetime describe the paid side only, using the same churn and expansion math as a standalone subscription business.

Caveats worth knowing

Real freemium funnels rarely hold a constant viral coefficient or conversion rate for years at a time; both tend to decay as easy channels saturate. This model also treats conversion as pulling from the current month's free base rather than modeling cohort age, so very fast-growing or shrinking funnels will drift from the simplified math over a long horizon. Treat the projection as a directional planning tool, not a committed forecast.