Hazard Ratio Calculator

Work out hazard ratio instantly with clear inputs, formula shown and shareable results.

About Hazard Ratio Calculator

The hazard ratio compares instantaneous event rates between groups. A value below 1 favours the treatment, and the confidence interval is built on the log scale because the ratio's sampling distribution is skewed.

Formulas

Hazard ratio

HR = (events₁/time₁) / (events₂/time₂)

Confidence interval

exp(ln HR ± 1.96·√(1/e₁ + 1/e₂))

Worked example

With the default values below, Hazard Ratio Calculator returns Hazard ratio of 0.57600000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Events in the treatment groupminimum 0: 30
Person-time in the treatment groupminimum 0: 500
Events in the control groupminimum 0: 50
Person-time in the control groupminimum 0: 480

Results

Hazard ratio: 0.57600000
95% confidence interval: 0.3663 to 0.9057
Treatment event rate: 0.06000000
Control event rate: 0.10416667

Step by step

1Values used
2Hazard ratio
3Confidence interval
4Hazard ratio= 0.57600000
595% confidence interval= 0.3663 to 0.9057
6Treatment event rate= 0.06000000
7Control event rate= 0.10416667

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 30 events in 500 person-years versus 50 in 480?

The rates are 0.06 and 0.1042, so HR ≈ 0.576 with a 95% interval of about 0.367 to 0.904.

How does it differ from relative risk?

Relative risk compares cumulative proportions; the hazard ratio compares instantaneous rates and accounts for time at risk.