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Relative Risk Calculator

Find the relative risk from a 2×2 table.

How it is calculated

Relative risk (risk ratio) compares the chance of an outcome in an exposed group with the chance in an unexposed group: RR = [a ÷ (a + b)] ÷ [c ÷ (c + d)]. Cell a = exposed with the outcome, b = exposed without, c = unexposed with the outcome, d = unexposed without. The first fraction is the risk in the exposed group, the second the risk in the unexposed group. RR = 1 means no difference, above 1 means higher risk with exposure and below 1 means lower. Counts cannot be negative, each group must contain someone, and c must be above zero. The result has four decimals, with no confidence interval.

Worked example

Exposed group: 20 with the outcome out of 100 (20 + 80), so the risk is 0.20. Unexposed group: 10 out of 100 (10 + 90), risk 0.10. RR = 0.20 ÷ 0.10 = 2.0000. The exposed group has twice the risk.

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Common mistakes

  • Using the odds ratio formula (a·d)/(b·c) in place of RR; with common outcomes the two values differ.
  • Entering the group totals in b and d rather than the numbers without the outcome.
  • Swapping the exposed and unexposed rows, which gives the reciprocal of the true RR.
  • Using RR on case-control data, where the group sizes are chosen by the researcher and the risks cannot be estimated.
  • Putting zero in c; the unexposed risk is then zero and the ratio is undefined.

Sources

About this calculator

This calculator computes relative risk (RR), also called the risk ratio, from a 2×2 contingency table of exposed/unexposed groups and outcome/no-outcome counts: RR = [a/(a+b)] / [c/(c+d)], where a and b are the exposed group with and without the outcome, and c and d are the unexposed group with and without the outcome. An RR of 1 means no difference in risk between groups; RR of 2 means the exposed group has double the risk.

Relative risk is the standard measure reported in prospective cohort studies and randomized controlled trials to quantify how much an exposure — a drug, a risk factor, a behavior — changes the probability of an outcome, and it's distinct from odds ratio, which is used in case-control studies.

Epidemiologists and public health researchers analyzing cohort study data, clinicians interpreting drug trial results, and biostatistics students learning the difference between relative risk and odds ratio all use this calculation.

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Comments (1)

  • Editorial team

    Relative risk only makes sense when the table comes from following groups forward, as in a cohort study or a trial, where the group sizes reflect real risk. In a case-control study the counts are chosen by the researchers, so the ratio of those fractions does not estimate risk and an odds ratio is the usual measure instead. The tool also shows no confidence interval, so small counts can look more decisive than they are. Which kind of study does your table come from?

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