Relative Risk Calculator
Calculate relative risk (RR) from a 2×2 contingency table. Get confidence intervals, absolute risk reduction (ARR), number needed to treat (NNT), attributable risk, and step-by-step solutions with interactive visualizations for clinical and epidemiological studies.
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About Relative Risk Calculator
The Relative Risk Calculator computes the relative risk (risk ratio, RR) from a 2×2 contingency table used in cohort studies, randomized controlled trials, and epidemiological research. Enter the counts for exposed and unexposed groups with and without the outcome to get the RR, confidence interval, absolute risk reduction (ARR), number needed to treat (NNT), odds ratio, attributable fraction, and a complete step-by-step solution with interactive visualizations.
What Is Relative Risk?
Relative risk (also called the risk ratio, RR) measures the strength of association between an exposure (or treatment) and an outcome. It is the ratio of the incidence rate in the exposed group to the incidence rate in the unexposed (control) group:
$$RR = \frac{p_{\text{exposed}}}{p_{\text{unexposed}}} = \frac{a/(a+b)}{c/(c+d)}$$
Key Measures Explained
| Measure | Formula | Interpretation |
|---|---|---|
| Relative Risk (RR) | \(p_1 / p_0\) | How many times more likely the outcome is in the exposed group |
| Absolute Risk Reduction (ARR) | \(p_1 - p_0\) | The actual difference in risk between groups |
| Number Needed to Treat (NNT) | \(1 / |ARR|\) | Patients to treat to prevent (or cause) one event |
| Odds Ratio (OR) | \(ad / bc\) | Ratio of odds; approximates RR when outcome is rare |
| Attributable Fraction | \((RR-1)/RR\) | Proportion of exposed cases attributable to exposure |
| Confidence Interval | \(e^{\ln(RR) \pm z \cdot SE}\) | Range likely containing the true RR |
Relative Risk vs. Odds Ratio
| Feature | Relative Risk (RR) | Odds Ratio (OR) |
|---|---|---|
| Measures | Ratio of probabilities | Ratio of odds |
| Study Design | Cohort, RCT | Case-control, cohort, RCT |
| Range | 0 to ∞ | 0 to ∞ |
| Null Value | 1 | 1 |
| Interpretation | Direct and intuitive | Less intuitive |
| Rare Disease | OR ≈ RR when outcome < 10% | Overestimates when common |
Real-World Examples
| Study | Exposure | Outcome | Typical RR |
|---|---|---|---|
| Framingham Heart Study | Smoking | Heart disease | 1.5 – 3.0 |
| Vaccine trials | mRNA vaccine | COVID-19 infection | 0.04 – 0.10 |
| Aspirin trial | Daily aspirin | MI recurrence | 0.70 – 0.85 |
| Nurses' Health Study | HRT use | Breast cancer | 1.2 – 1.4 |
| Statin trials | Statin therapy | Major cardiac event | 0.65 – 0.80 |
How to Use the Relative Risk Calculator
- Enter exposed group data: In the 2×2 table, enter the number of exposed subjects with the outcome (cell a) and without the outcome (cell b). For example, in a smoking study, a = smokers who developed lung cancer, b = smokers who did not.
- Enter unexposed group data: Enter the number of unexposed (control) subjects with the outcome (cell c) and without the outcome (cell d). For example, c = non-smokers who developed lung cancer, d = non-smokers who did not.
- Select confidence level: Choose 90%, 95%, or 99% for the confidence interval. The standard in most medical research is 95%.
- Click Calculate: The calculator computes RR, confidence interval, ARR, NNT, odds ratio, attributable fraction, p-value, and shows a step-by-step solution with risk comparison bars and a forest plot.
- Interpret the results: If the CI does not include 1.0, the result is statistically significant. The NNT visualization shows how many patients need to be treated to prevent one event.
FAQ
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"Relative Risk Calculator" at https://MiniWebtool.com// from MiniWebtool, https://MiniWebtool.com/
by miniwebtool team. Updated: 2026-04-15