Relative Risk Calculator — RR, ARD & 95% CI
Enter the event rate in the exposed (treatment) group and the event rate in the control (unexposed) group — along with group sizes for the confidence interval — to get the Relative Risk, Absolute Risk Difference, NNT and 95% CI instantly.
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%
Exposure increases risk (RR > 1) — 200% higher
- 1
Risk in exposed group
30 % ÷ 100 = 0.3 - 2
Risk in unexposed group
10 % ÷ 100 = 0.1 - 3
Relative Risk
0.3 ÷ 0.1 = 3RR > 1 means the exposed group has higher risk; RR < 1 means the exposure is protective.
How does this calculator work?
Relative Risk = event rate in exposed group ÷ event rate in unexposed group. RR > 1 signals harm; RR < 1 signals protection. The Absolute Risk Difference is the arithmetic gap between the two rates, and its reciprocal gives NNT. The 95% CI is computed via the log-normal method from group sizes.
Formula
How this is calculated
Relative Risk (also called Risk Ratio, RR) is the ratio of the probability of an event in the exposed group to the probability of that same event in the unexposed (reference) group. An RR of 1.0 means identical risk; RR > 1 means the exposure is associated with higher risk; RR < 1 means it is protective. Unlike the Odds Ratio, RR is directly interpretable as "how many times more (or less) likely" the event is.
This calculator takes the event rate (a percentage) in each group directly — ideal when you have summary statistics rather than raw cell counts. The Absolute Risk Difference (ARD) is the arithmetic difference between the two rates; its reciprocal is the Number Needed to Treat (NNT) when the exposure is beneficial, or Number Needed to Harm (NNH) when harmful. Both RR and ARD are essential: an RR of 2 looks dramatic but if the background rate is 0.001% the ARD is still tiny.
The 95% confidence interval is derived from the log-normal method: ln(RR) ± 1.96 × SE, where SE = √(1/a − 1/n₁ + 1/c − 1/n₀). This approximation is valid when all four derived cell counts (a, b, c, d) are at least 5. When a CI cannot be computed (extreme rates or very small samples), the point estimate is still shown.
Frequently asked questions
Relative Risk divides two probabilities (proportion with event in exposed group ÷ proportion in unexposed group) and is directly interpretable. The Odds Ratio divides two odds and approximates RR only when the event is rare (below ~10%). For common outcomes in cohort studies, always prefer RR.
The log-normal CI requires at least one event and at least one non-event in each group. If the entered rates and group sizes produce a zero cell count (e.g. 100% event rate with n=10), the CI is undefined. Increase the group sizes or adjust the rates.
Number Needed to Treat (NNT) = 1 / |ARD|. It is the number of people who need to be exposed for one additional event to occur (or be prevented). A low NNT (e.g. 5) means a highly effective intervention; a high NNT (e.g. 200) means a modest effect.
Also known as
TG we-Calculate Editorial Team. (2026). Relative Risk Calculator — RR, ARD & 95% CI [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/relative-risk-calculator
TG we-Calculate Editorial Team. "Relative Risk Calculator — RR, ARD & 95% CI." TG we-Calculate. 2026. https://we-calculate.com/calculator/relative-risk-calculator.
TG we-Calculate Editorial Team, "Relative Risk Calculator — RR, ARD & 95% CI," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/relative-risk-calculator
@misc{wecalculate_relative_risk_calculator, title = {Relative Risk Calculator — RR, ARD & 95% CI}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/relative-risk-calculator}}, year = {2026}, note = {TG we-Calculate} }
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