Relative Risk from a 2×2 Table Calculator
Compute relative risk with a 95% confidence interval from the raw event counts in exposed and unexposed groups.
How it works
RR = (a ÷ n₁) ÷ (c ÷ n₂) · 95% CI = exp(ln RR ± 1.96 · √(1/a − 1/n₁ + 1/c − 1/n₂))
Relative risk compares the probability of an outcome between an exposed and an unexposed group by dividing one risk by the other. RR = 1 means no difference; above 1 the exposure raises risk, below 1 it lowers it. The confidence interval is built on the log scale because the sampling distribution of RR is skewed, then exponentiated back — an interval that excludes 1 signals a statistically significant association at the 5% level.
Worked example
With 30 of 100 events in the exposed group and 15 of 100 in the unexposed group, risks are 30% and 15%, so RR = 0.30 ÷ 0.15 = 2.0. The 95% CI is exp(ln 2 ± 1.96 × 0.283) ≈ 1.15 to 3.49 — it excludes 1, so the doubling is significant.
Sources: Relative risk — Wikipedia
Frequently asked questions
How does relative risk differ from the odds ratio?
Relative risk divides two probabilities; the odds ratio divides two odds. When the outcome is rare the two are close, but for common outcomes the odds ratio exaggerates the effect, so RR is preferred whenever risks can be estimated directly (as in cohort studies).
What does a relative risk of 1 mean?
It means the outcome is equally likely in both groups — the exposure carries no association with the event. A confidence interval that straddles 1 means the data are consistent with no effect.
Why is the confidence interval computed on a log scale?
Ratios are bounded below by zero but unbounded above, so their distribution is skewed. Taking logarithms makes it roughly symmetric, so the standard ± 1.96·SE construction works; exponentiating returns an asymmetric interval on the original scale.
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Educational statistics tool, not medical advice.