Relative Risk Calculator

Enter a 2x2 table of events and non-events for the exposed and control groups to compute the relative risk (risk ratio), the risk in each group, and a 95% confidence interval.

Quick Facts

Formula
RR = [a/(a+b)] / [c/(c+d)]
Risk in the exposed group divided by risk in the control group; RR = 1 means no difference.

Your Results

Calculated
Relative risk (RR)
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Risk ratio, exposed vs control
Risk in exposed group
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a / (a + b)
Risk in control group
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c / (c + d)
95% confidence interval
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Log-based interval for RR

Ready

Enter your 2x2 counts and press Calculate.

What relative risk measures

Relative risk (RR), also called the risk ratio, compares how often an outcome happens in an exposed group versus an unexposed control group. It answers a simple question: does being exposed to something — a drug, a treatment, a behavior, a risk factor — make the outcome more or less likely, and by how much?

You build it from a 2×2 table of counts:

  • a = events (the outcome occurred) in the exposed group
  • b = non-events in the exposed group
  • c = events in the control group
  • d = non-events in the control group

The formula

The risk in each group is the number of events divided by the group total:

Risk in exposed = a / (a + b)  ·  Risk in control = c / (c + d)

Relative risk is the ratio of those two risks:

RR = [a / (a + b)] / [c / (c + d)]

For example, if 30 of 100 exposed subjects have the outcome (risk = 0.30) and 15 of 100 control subjects do (risk = 0.15), then RR = 0.30 / 0.15 = 2.0 — the exposed group has twice the risk.

How to read the number

  • RR = 1 — no association. The outcome is equally likely in both groups.
  • RR > 1 — the exposure is associated with increased risk. RR = 2.0 means double the risk; RR = 1.5 means 50% higher risk.
  • RR < 1 — the exposure is associated with reduced risk (often a protective effect). RR = 0.75 means a 25% lower risk.

The 95% confidence interval

A single RR is a point estimate from one sample. The confidence interval shows the range of values compatible with your data. This tool uses the standard log method: the standard error of ln(RR) is √(1/a − 1/(a+b) + 1/c − 1/(c+d)), and the 95% interval is exp(ln(RR) ± 1.96 × SE). If the interval does not include 1, the association is statistically significant at the 5% level; if it straddles 1, the data are also consistent with no effect.

Relative risk vs. odds ratio

Relative risk needs the total number at risk in each group, so it applies to cohort studies and randomized controlled trials. Case-control studies, which sample by outcome rather than by exposure, cannot estimate true risks and report the odds ratio instead. When the outcome is rare, the odds ratio closely approximates RR; when the outcome is common, the odds ratio overstates the effect and should not be read as a risk ratio.

Frequently Asked Questions

What is relative risk?
Relative risk (the risk ratio, RR) is the probability of an outcome in an exposed group divided by the probability of that outcome in an unexposed control group: RR = [a/(a+b)] / [c/(c+d)]. It quantifies how much more (or less) likely the outcome is when the exposure is present.
How do I interpret a relative risk of 2.0?
An RR of 2.0 means the exposed group is twice as likely to experience the outcome as the control group. An RR of 0.5 means half as likely (a protective effect), and an RR of 1.0 means the exposure makes no difference.
How is relative risk different from the odds ratio?
Relative risk compares probabilities (events ÷ group total); the odds ratio compares odds (events ÷ non-events). They agree closely when the outcome is rare, but the odds ratio exaggerates the effect when the outcome is common. Relative risk requires knowing the total at risk in each group, so it comes from cohort studies and trials, not case-control studies.
Why does my confidence interval include 1?
A 95% interval that contains 1 means the data are consistent with no real difference between the groups — the result is not statistically significant at the 5% level. Wide intervals usually come from small samples or few events; increasing the sample size narrows the interval.

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