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Risk Ratio (Relative Risk) Calculator

Compare event risk between two groups and calculate the relative risk ratio.

How it is calculated

For each group the tool first computes the risk: risk = events / total people in the group. The risk ratio is then RR = risk(exposed) / risk(control). You enter four counts: events and group total for the exposed group, events and group total for the control group. Totals must be above zero, and events cannot be negative or larger than their group total. The two risks are also shown as percentages, and RR is shown with two decimals. If the control group has no events, the ratio would require division by zero, so no result is shown. The tool gives a point estimate only: no confidence interval or p-value, so it cannot say whether a difference is statistically meaningful.

Worked example

In a hypothetical study, 24 of 300 people in the exposed group had the outcome, and 12 of 400 people in the control group had it. Exposed risk: 24 / 300 = 8.00%. Control risk: 12 / 400 = 3.00%. Risk ratio: 0.08 / 0.03 = 2.67. The outcome was about 2.67 times as common in the exposed group as in the control group. A value of 1.00 would mean equal risk. With only 12 control events, this estimate could be quite uncertain.

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Common mistakes

  • Entering the group sizes as the number of events, or leaving out the people without events from the total. The totals must include everyone in the group, both with and without the outcome.
  • Confusing the risk ratio with the odds ratio. This tool divides risks (events / total), not odds (events / non-events), so the numbers will differ, especially when the outcome is common.
  • Reading a ratio of 2.67 as a 267% increase. The increase is 167%, since a ratio of 1.00 means no increase.
  • Swapping the groups. Putting the control group in the exposed fields gives the inverse ratio (0.38 instead of 2.67).

About this calculator

The risk ratio, also called relative risk, compares the probability of an event between two groups: it is the risk in the exposed group (events divided by total people in that group) divided by the risk in the unexposed or control group. A risk ratio of 1.0 means no difference between groups, a value above 1.0 means the exposed group is more likely to experience the event, and a value below 1.0 means the exposure appears protective.

Epidemiologists and clinical researchers use risk ratios in cohort studies and randomized controlled trials, where the absolute number of people at risk from the outset is known — this distinguishes it from the odds ratio, which is used instead in case-control studies where the group sizes are chosen by the researcher rather than reflecting the true population at risk.

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