Calculate relative risk, odds ratio, absolute risk difference, and NNT from a 2×2 contingency table. Includes 95% confidence intervals and chi-squared test.
The Relative Risk Calculator computes the relative risk (RR), odds ratio (OR), absolute risk difference, number needed to treat (NNT), and attributable fractions from a 2×2 contingency table. It includes 95% confidence intervals for RR and OR, plus a chi-squared significance test.
Relative risk is the ratio of the probability of an outcome in the exposed group versus the unexposed group. It's the primary measure of association in cohort studies, clinical trials, and epidemiological research. An RR of 2.0 means the exposed group has twice the risk of the outcome; an RR of 0.5 means half the risk.
This calculator provides a complete epidemiological toolkit: risk comparison visualization, confidence intervals using the log method, the odds ratio for case-control comparisons, and clinical measures like NNT/NNH that translate statistical results into actionable treatment decisions. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Evaluating risk is the central task of epidemiology and evidence-based medicine. This calculator provides all the standard measures of association in one place, with confidence intervals and significance testing — saving researchers from manual computation and potential arithmetic errors.
Clinical researchers use it to evaluate treatment efficacy, public health officials assess exposure risks, and students learn epidemiological methods. The visual risk comparison and comprehensive association table make results immediately understandable.
RR = [a/(a+b)] / [c/(c+d)]. OR = (a×d) / (b×c). ARD = Risk(exposed) - Risk(unexposed). NNT = 1 / |ARD|. χ² = Σ[(O-E)²/E].
Result: RR = 1.714, OR = 3.857, ARD = 31.25%
Risk(exposed) = 30/40 = 75%. Risk(unexposed) = 70/160 = 43.75%. RR = 75/43.75 = 1.714 — exposed group has 71.4% higher risk. OR = (30×90)/(10×70) = 3.857.
In cohort studies, you follow exposed and unexposed groups forward and observe outcomes, allowing direct calculation of relative risk. In case-control studies, you start with cases (outcomes) and controls, then look back at exposure — here, only the odds ratio can be calculated directly. The rare disease assumption lets us approximate RR from OR when the outcome is rare.
A large study might find a statistically significant RR of 1.02 — the CI excludes 1.0, but the 2% increase in risk has negligible clinical impact. Conversely, a small study might find RR = 3.0 with a wide CI that includes 1.0 — clinically important but statistically uncertain. The NNT helps bridge this gap by expressing results in practical, patient-level terms.
Raw relative risk from a 2×2 table doesn't account for confounders. In practice, researchers use stratified analysis (Mantel-Haenszel method) or regression (Cox, logistic) to adjust for age, sex, and other variables. This calculator provides the unadjusted (crude) estimates, which should be interpreted alongside adjusted analyses.
Relative risk compares probabilities (risks) between groups. Odds ratio compares odds. In rare outcomes (<10%), they are approximately equal. For common outcomes, the OR overestimates the RR. RR is preferred in cohort studies; OR is used in case-control studies.
An RR of 1.0 means no association — the exposure does not affect the outcome. RR > 1 indicates increased risk with exposure. RR < 1 indicates decreased risk (protective effect). The 95% CI tells you if the result is statistically significant (CI excludes 1.0).
Number Needed to Treat (NNT) is the number of patients who must be treated for one additional patient to benefit. It equals 1/|ARD|. Lower NNT means more effective treatment. NNH (Number Needed to Harm) uses the same formula when exposure increases risk.
Relative risk tells you the strength of association. Absolute risk difference tells you the actual impact. A treatment that reduces risk from 0.02% to 0.01% has RR = 0.5 (impressive sounding) but ARD = 0.01% (tiny real impact). Always report both.
If the 95% CI for RR includes 1.0, the result is not statistically significant at p = 0.05. The narrower the CI, the more precise the estimate. Wide CIs suggest small sample sizes or high variability.
The attributable fraction among the exposed (AFe) estimates what proportion of cases in exposed individuals can be attributed to the exposure. AFe = (RR-1)/RR. It's useful for public health planning.