Survival Analysis Calculator

Survival analysis studies the time until an event occurs. The event might be death, relapse, equipment failure, customer churn, recovery, or any clearly defined endpoint. Unlike ordinary averages, survival methods can use information from subjects whose event has not been observed by the end of follow-up. Those observations are censored rather than treated as failures or discarded. This calculator uses the Kaplan–Meier product-limit estimator. At each distinct event time, it counts the subjects still at risk immediately before that time and the events occurring at that time. The conditional chance of surviving the interval is (n − d) / n, where n is the risk set and d is the number of events. Multiplying that factor by all preceding factors produces the cumulative survival probability. The estimate changes only at event times; a censored observation reduces later risk sets but does not directly lower survival. Enter survival times in the first field and matching status indicators in the second. Use 1 when the event occurred and 0 when the observation was censored. The first time corresponds to the first indicator, the second time to the second indicator, and so on. Times must be non-negative and may use any consistent unit, such as days, months, years, operating hours, or customer billing cycles. The output retains that same unit. The result table shows every observed time, the number at risk, events, censored observations, and cumulative survival. When events and censoring share a time, events are evaluated using the full risk set at that time before those observations leave the set. This is a conventional treatment for grouped observations. The median survival time is the earliest time at which estimated survival is at or below 0.5. If the curve never reaches 0.5, the median is reported as not reached rather than extrapolated. Censoring must be non-informative for a simple Kaplan–Meier estimate to be interpreted reliably. In practical terms, subjects who are censored should not systematically have a different future event risk solely because they were censored. The estimator also does not adjust for age, treatment, exposure, or other covariates. Comparing curves formally may require a log-rank test, while adjusted analysis commonly uses a Cox proportional hazards model. Use the table as a transparent descriptive estimate, not as a substitute for study design or clinical judgment. Small risk sets near the end of follow-up produce unstable tail estimates, and this compact calculator does not display confidence intervals. For research reporting, pair survival probabilities with uncertainty intervals, state the censoring rules and time origin, and use validated statistical software for inferential conclusions.