Enter your 2×2 contingency table values — Cases with Exposure (a), Cases without Exposure (b), Controls with Exposure (c), and Controls without Exposure (d) — along with your Confidence Level to calculate the Odds Ratio, its confidence interval bounds, Standard Error (ln OR), and Total Cases.
Odds Ratio
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95% CI Lower Bound
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95% CI Upper Bound
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Standard Error (ln OR)
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Total Cases
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Total Controls
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An odds ratio (OR) is a measure of association between exposure and disease in case-control studies. It compares the odds of exposure in cases (diseased) versus controls (healthy). An OR > 1 indicates increased risk, OR < 1 indicates decreased risk, and OR = 1 indicates no association.
The confidence interval shows the range of plausible values for the true odds ratio. If the CI includes 1.0, the association is not statistically significant. A narrower CI indicates more precise estimates, while a wider CI suggests less certainty.
When zeros occur in any cell, it causes computational problems. The standard approach is to add 0.5 to all cells (a, b, c, d) before calculating the odds ratio and confidence intervals. This continuity correction helps stabilize the estimates.
Larger sample sizes provide more reliable estimates with narrower confidence intervals. As a general rule, each cell in the 2x2 table should have at least 5 observations, though this depends on your study design and expected effect size.
Odds ratio is used in case-control studies where you start with cases and controls, while relative risk is used in cohort studies where you follow exposed and unexposed groups. When disease is rare, OR approximates RR, but they can differ substantially for common diseases.
Statistical significance is determined by whether the confidence interval includes 1.0. If the entire CI is above 1.0, there's a significant positive association. If entirely below 1.0, there's a significant negative association. If the CI includes 1.0, the association is not statistically significant.