How this calculation works
Some followed units have not failed when observation ends. Treating those right-censored records as failures or discarding them entirely changes the estimated survival experience. Kaplan–Meier uses their observed time while keeping their unknown later outcome unknown. This page builds the product-limit survival table from individually entered records. It displays the risk set, events and censoring at each distinct observed time, making the accounting inspectable.
S(t) = product over event times [1 − events at t/subjects at risk immediately before t]A worked example
Four subjects begin at risk. At time one, one event and one censoring give a survival factor three quarters, with two subjects remaining for later times. An event among those two at time two multiplies survival by one half, yielding 0.375. The final subject is censored at time three, leaving survival unchanged and a product-limit median of two time units.
Good to know
Independent subjects and non-informative right censoring are important assumptions. Informative loss to follow-up, competing events and changing cohort composition require more complete analysis. No confidence bands, hazard-ratio comparison or treatment-effect conclusion is provided. The calculation is a descriptive survival estimate and does not supply clinical or maintenance recommendations.
Reference: NIST — Kaplan Meier product limit estimator (opens in a new tab) ↗
What this calculation answers
Some followed units have not failed when observation ends. Treating those right-censored records as failures or discarding them entirely changes the estimated survival experience. Kaplan–Meier uses their observed time while keeping their unknown later outcome unknown.
This page builds the product-limit survival table from individually entered records. It displays the risk set, events and censoring at each distinct observed time, making the accounting inspectable.
The Weibull survival quantiles and conditional remaining life calculator evaluates a supplied parametric lifetime model. Kaplan Meier instead estimates observed survival while retaining right-censored follow-up.
Use the right input conventions
Each row needs a nonnegative follow-up time and status one for an observed event or zero for right censoring. Subjects start follow-up together; delayed entry is not represented.
Events at a time are evaluated before removing subjects censored at that same time. Tied records are grouped, so row order does not arbitrarily change the risk set or survival decrement.
Interpret the result
Survival changes only at event times. A censoring time reduces future risk sets but does not itself cause a survival drop. The final observed survival is not an extrapolation beyond follow-up.
The median is the first event time where estimated survival is at most one half. If the curve never reaches that level, the page reports that the median is not reached rather than assigning the last follow-up time.
Work through the example
Four subjects begin at risk. At time one, one event and one censoring give a survival factor three quarters, with two subjects remaining for later times.
An event among those two at time two multiplies survival by one half, yielding 0.375. The final subject is censored at time three, leaving survival unchanged and a product-limit median of two time units.
Where the model stops
Independent subjects and non-informative right censoring are important assumptions. Informative loss to follow-up, competing events and changing cohort composition require more complete analysis.
No confidence bands, hazard-ratio comparison or treatment-effect conclusion is provided. The calculation is a descriptive survival estimate and does not supply clinical or maintenance recommendations.
A few questions, answered
Should a right-censored record be counted as a failure?
No. It contributes observed time and remains at risk until censoring, but no event is assumed afterward.
What changes in the comparison?
Change the tied censoring record into an observed event and follow the risk-set consequences.