Calculator inputs
This page keeps a clean single-column flow, while the form uses three columns on large screens, two on medium screens, and one on mobile.
Example data table
This example illustrates a Kaplan-Meier style dataset and the running survival estimate.
| Time | At risk | Events | Censored | Estimated survival |
|---|---|---|---|---|
| 1 | 120 | 6 | 2 | 0.950000 |
| 3 | 112 | 7 | 3 | 0.890625 |
| 6 | 102 | 8 | 4 | 0.820723 |
| 10 | 90 | 10 | 5 | 0.729532 |
| 15 | 75 | 9 | 6 | 0.641988 |
| 20 | 60 | 8 | 5 | 0.556389 |
Formula used
1) Exponential survival model
Survival: S(t) = e-λt
Failure probability: F(t) = 1 - S(t)
Cumulative hazard: H(t) = λt
Hazard: h(t) = λ
Median survival: t0.5 = ln(2) / λ
Use this when hazard stays constant across time.
2) Weibull survival model
Survival: S(t) = e-(t / λ)k
Failure probability: F(t) = 1 - S(t)
Cumulative hazard: H(t) = (t / λ)k
Hazard: h(t) = (k / λ) × (t / λ)k-1
Median survival: t0.5 = λ × [ln(2)]1/k
Mean survival: E(T) = λ × Γ(1 + 1/k)
Use this when hazard changes over time.
3) Kaplan-Meier estimator
Step survival: S(ti) = S(ti-1) × (1 - di / ni)
Interval hazard: hi = di / ni
Greenwood variance component: Σ[di / (ni(ni - di))]
Cumulative hazard approximation: H(t) = -ln(S(t))
Use this for observed event data with censoring.
How to use this calculator
- Choose the estimation method that matches your data or assumption.
- Enter the target time where you want survival probability reported.
- Set a cohort size if you want expected counts of survivors and failures.
- For Exponential, enter the hazard rate. For Weibull, enter shape and scale.
- For Kaplan-Meier, paste rows as time, at-risk, events, censored.
- Set the graph horizon and time step for the plotted curve.
- Click Calculate survival to display the results above the form.
- Use the CSV and PDF buttons to export a summary and the curve.
FAQs
1) What does survival probability mean?
It is the estimated chance that a subject remains event-free beyond a chosen time. The event could be failure, churn, relapse, death, or any defined endpoint.
2) When should I use the exponential model?
Use the exponential model when the hazard is assumed constant across time. It is simple, interpretable, and useful for quick baseline checks or reliability studies.
3) Why would I choose the Weibull model instead?
The Weibull model is better when hazard changes over time. A shape below one suggests declining hazard, while a shape above one suggests increasing hazard.
4) What is Kaplan-Meier used for?
Kaplan-Meier estimates survival directly from observed interval data. It is widely used when you have censored observations and prefer a non-parametric step curve.
5) What does censoring mean in survival analysis?
Censoring means the exact event time is not fully observed. For example, a person may leave a study early or remain event-free when follow-up ends.
6) What is cumulative hazard?
Cumulative hazard summarizes total risk accumulated up to a time point. It is linked to survival through the relationship S(t) = e-H(t).
7) Why do expected survivors and failures depend on cohort size?
The model first estimates probabilities. Multiplying those probabilities by cohort size converts them into expected counts, which helps planning, forecasting, and resource allocation.
8) Are confidence intervals shown for every method?
This version applies confidence intervals to Kaplan-Meier results. Parametric models here report point estimates only, which keeps the page focused and easy to interpret.