Calculator Inputs
Formula Used
Cumulative hazard: H(t) = -ln(S(t))
Average hazard from one survival point: h = -ln(S(t)) / t
Interval hazard: h = -ln(S2 / S1) / (t2 - t1)
Conditional event risk: q = 1 - (S2 / S1)
Here, S1 is starting survival probability, S2 is ending survival probability, and t2 - t1 is the interval length.
How to Use This Calculator
- Select single point mode or interval mode.
- Choose decimal or percent probability format.
- Enter survival probability values.
- Enter matching start and end times.
- Add optional standard errors for confidence limits.
- Press the calculate button.
- Review the result table above the form.
- Use CSV or PDF export for reports.
Example Data Table
| Scenario | Start Survival | End Survival | Start Time | End Time | Hazard Rate |
|---|---|---|---|---|---|
| Machine reliability | 1.00 | 0.80 | 0 | 12 | 0.018595 |
| Medical follow-up interval | 0.90 | 0.72 | 6 | 18 | 0.018595 |
| Warranty period | 0.95 | 0.88 | 1 | 3 | 0.038187 |
Understanding Hazard Rate
A survival probability tells how likely a subject is to remain event free past a chosen time. The hazard rate tells the instant event pressure behind that survival value. It is useful when failure risk changes over time. Engineers use it for parts. Actuaries use it for life tables. Medical analysts use it for relapse, death, or recovery studies.
Why This Calculator Helps
This calculator converts survival probability into cumulative hazard, average hazard, interval hazard, and conditional event risk. It supports one time point or two survival points. A single point gives the average rate from time zero. Two points give the rate inside a chosen interval. That is helpful when risk is not constant across the full study. The tool also reports the remaining survival ratio. This ratio shows how much survival remained between the starting and ending observations.
Interpreting the Results
A higher hazard means a stronger event rate per unit time. A hazard of 0.05 per month does not mean five percent failed every month. It is an instantaneous rate. For a small interval, it may look close to a probability. For a long interval, the difference matters. Cumulative hazard is easier to add across periods. Survival is easier to explain to readers. The formula links both measures with a natural logarithm. When survival drops, cumulative hazard rises. When survival stays near one, hazard remains small.
Best Practices
Enter survival values between zero and one. Do not enter percentages unless you choose the percent input option. Keep time units consistent. If your time is in years, the rate is per year. If your time is in days, the rate is per day. Use interval mode when you have survival at two visits, inspections, or ages. Use single point mode when only one survival probability is known. Review the table before exporting. The CSV file helps with spreadsheets. The report file helps with records. This calculator is a guide. It does not replace statistical modeling, censoring adjustment, or peer review. Always compare results with the source study design. Document assumptions before sharing. Note whether rates are constant or interval based. Small data changes move hazards greatly when survival is very low or near zero.
FAQs
What is hazard rate?
Hazard rate is the instant event rate at a given time or inside an interval. It is not exactly the same as probability, especially across longer time periods.
What is survival probability?
Survival probability is the chance that a subject, part, customer, or patient remains event free beyond a chosen time point.
Can I enter percentages?
Yes. Select the percent format, then enter values like 80 for 80 percent. Select decimal format for values like 0.80.
What does interval mode calculate?
Interval mode calculates the hazard rate between two survival observations. It uses the survival ratio and the time difference between both observations.
Why is natural logarithm used?
The natural logarithm links survival and cumulative hazard. The relationship is H(t) = -ln(S(t)), which is standard in survival analysis.
Can hazard rate be negative?
A true hazard rate should not be negative. A negative result can appear when the ending survival estimate is higher than the starting estimate.
What time unit does the answer use?
The answer follows your time input. If you enter months, the hazard is per month. If you enter years, it is per year.
Are confidence limits required?
No. They are optional. Add standard errors only when your survival estimates include them from a valid statistical source.