user churn

Also called: churned users, churn rate, user churn rate, customer churn rate, subscription churn, monthly churn rate

Users who stop using the product. For free products it is inferred from inactivity, so its definition (how long inactive) must be stated.

Churn is the loss of users or customers over a period, and churn rate is that loss as a share of who you had at the start:

$\text{churn rate} = \frac{\text{users at the start of the period who churned during it}}{\text{users at the start of the period}}$

New users gained during the period go in neither the numerator nor the denominator, so churn rate is simply $1 -$ the retention of the existing base over that period.

The hard part is deciding what counts as churned, and it differs by business model:

Subscription products have an explicit event: a subscription ended (cancelled and not renewed, or payment failed for good). Churn is observed, and you can split it into voluntary (cancelled) and involuntary (failed payment). Revenue churn, which weighs each loss by what the customer paid, is a separate metric.
Free products have no cancel button; people just stop coming back. Churn has to be inferred from inactivity, so you must state the rule: "a user active last month who wasn't active this month", or "no meaningful activity for 30 days". Choose the window from the product's usage rhythm: a weekly product might use 28 days, a monthly one 60. Some of these users will come back later ("resurrected" users), which a good report shows separately.

Churn is reported per period (usually per month), and monthly rates don't scale linearly to a year: a constant monthly churn $c$ leaves $(1-c)^{12}$ of the base after 12 months. For diagnosis, split churn by cohort age and segment: new users almost always churn faster than established ones, so a wave of new sign-ups can raise the overall churn rate while every cohort is behaving as usual.

Example

Free users (inactivity rule: active in the previous calendar month, not active this month). 10,000 people used Halves in June; 7,400 of them were active again in July.

Churned in July: $10000 - 7400 = 2600$ .
Churn rate: $2600 / 10000 = 26.0\%$ (the base's month-over-month retention is 74.0%).
July also brought 3,100 new users and 400 resurrected users, so July's active users are $7400 + 3100 + 400 = 10900$ . Growth in active users didn't mean low churn.

Halves Plus subscribers. 1,200 subscriptions were active on July 1; 84 of them ended in July (cancelled or payment failed); 150 new ones started.

Churn rate: $84 / 1200 = 7.0\%$ per month. The 150 new subscriptions don't change it.
At a steady 7% a month, the share of today's subscribers left after a year is $0.93^{12} \approx 0.419$ , so annual churn is about $1 - 0.419 = 58.1\%$ , not $12 \times 7\% = 84\%$ .

Common mistakes

No stated inactivity rule. "Churn is 26%" means nothing for a free product until you say what inactivity counts as churn.
Putting new users in the denominator. Dividing by the end-of-period or average base mixes acquisition into churn; use the start-of-period base.
Multiplying monthly churn by 12. Churn compounds; convert with $1 - (1-c)^{12}$ .
Calling a finished trip "churn". When a trip group ends, the user may simply have no bills until the next trip; separate group lifetime from user churn.
One churn rate for all ages. New cohorts churn faster; report churn by cohort age, or a surge of sign-ups will look like a product problem.