How to use the word-of-mouth spread calculator
Word of mouth is often modelled as a geometric chain in which each generation brings in the next. Enter the people you told directly as the initial reach and the new people one person brings in as the spread rate r: generation 2 is initial reach × r, generation 3 is initial reach × r squared, and so on. The table lists every generation up to the count you enter, and the cumulative figure is the sum of the rounded numbers shown in that table.
One condition matters a great deal. If the spread rate is 1 or more, the geometric series does not converge. Assuming every person keeps bringing in at least one more means the audience grows without limit, so a single "total spread" figure has no value at all. In that case the calculator says the series does not converge instead of printing a number. In reality the addressable audience is finite and contacts overlap, so unbounded spread never happens.
When the spread rate is below 1 the theoretical total is initial reach × 1 ÷ (1 − spread rate). Generations are capped at 20, and the label says so whenever the cap or whole-number rounding is applied. No industry average spread rate is built in: take it from your own referral history.
Frequently asked questions
Divide the number of people who arrived through referrals by the number of people who sent a referral. Referral code or invite link reporting for a fixed period gives the most reliable figure.
No. The model assumes each generation reaches new people, so overlapping contacts are not filtered out. Treat the result as an upper bound rather than deduplicated net reach.