Calculation results
| Hazard Ratio (Exp/Control) | ||
| 95% Confidence Interval | ||
| 95% Left-Sided Interval | ||
| 95% Right-Sided Interval | ||
| P-value | ||
| Χ2 |
Created by CalculatorOK Team · Last updated: Apr 15, 2025
Hazard Ratio Calculator
What a hazard ratio tells you
A hazard ratio compares how fast an event happens in two groups across the timeline of a study. It comes from survival analysis, where the timing of an event matters as much as whether the event occurs at all. Clinical researchers, epidemiologists, biostatisticians, and medical writers rely on it to summarize treatment effects in oncology trials and cohort studies.
An HR of 2 means the exposed group carries twice the instantaneous risk. An HR of 1 means the risks are identical, while values on either side tell you which direction the effect runs.
The formula behind the number
The hazard ratio is simply the ratio of hazard rates: the event rate in the exposed group divided by the event rate in the control group. Imagine a trial where controls log 40 events per 100 person-years while the treated arm logs 20 events per 100 person-years. Dividing 20 by 40 gives a hazard ratio of 0.50, so treated patients accumulate risk at half the pace of controls.
Values below 1 favor the treatment, while values above 1 point to added risk. Keep in mind the standard model assumes the ratio between the two rates stays reasonably steady over time, an idea statisticians call proportional hazards.
Getting results you can trust
Getting a result takes two quick steps. Enter your survival figures into the Raw data field, listing each subject's follow-up time and event status, then choose the Confidence level, typically 95 percent, and press Calculate. The output reports the Hazard Ratio (Exp/Control), the 95% Confidence Interval, the left-sided and right-sided 95 percent intervals, and the P-value. A smart habit is checking whether the interval spans 1; when it does, the data cannot rule out equal risk, so describe any observed difference as uncertain.
Frequently Asked Questions
What does a hazard ratio of 2 mean?
It means the exposed group experiences the event at twice the instantaneous rate of the control group at any moment. If controls fail at 10 events per 100 person-years, the exposed group fails at 20.
Is a hazard ratio of 1 good?
A hazard ratio of exactly 1 means no difference in instantaneous risk between the groups. In a trial comparing two drugs, HR 1.00 suggests neither drug changes the event rate relative to the other.
How is a hazard ratio different from relative risk?
Relative risk compares total proportions of people with an event at the end of a study, while the hazard ratio compares ongoing rates. A study with HR 0.50 halves the instantaneous risk, but the final proportions depend on follow-up length.
Does the confidence interval matter for hazard ratios?
Yes, a 95 percent confidence interval shows the range where the true hazard ratio likely sits. If the interval runs from 0.35 to 0.85, it excludes 1, so the difference is statistically significant at the 0.05 level.
What data do I need to calculate it?
You need survival data for both groups, meaning each subject's follow-up time and whether the event occurred. For example, 50 treated patients and 50 control patients with their event times produce a hazard ratio and a P-value.