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Odds Ratio Calculator

Compute the odds ratio from a 2×2 table of exposure and outcome — with the exposed and unexposed odds and a plain-language interpretation.

Exposed — cases (a)

Exposed — controls (b)

Unexposed — cases (c)

Unexposed — controls (d)

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How it works

OR = (a × d) ÷ (b × c), from the 2×2 table [a b; c d] of exposed/unexposed × cases/controls

The odds ratio compares the odds of an outcome between an exposed and an unexposed group, using the cross-product of a 2×2 table: (a·d) ÷ (b·c). An OR of 1 means exposure makes no difference, above 1 means the exposed group has higher odds of the outcome, and below 1 means exposure is protective. It is the natural measure for case-control studies, where you sample by outcome and cannot compute absolute risks directly.

Worked example

For a table with a = 30, b = 70, c = 10, d = 90, the odds ratio is (30 × 90) ÷ (70 × 10) = 2700 ÷ 700 ≈ 3.857. The exposed group has about 3.86 times the odds of the outcome — a strong positive association between exposure and the outcome.

Sources: Odds ratio — Wikipedia

Frequently asked questions

What is the difference between an odds ratio and relative risk?

Relative risk compares probabilities and is intuitive in cohort studies where you can measure risk directly. The odds ratio compares odds and is used in case-control studies; for rare outcomes the two are close, but as the outcome becomes common the odds ratio grows further from the risk ratio.

What does an odds ratio of 1 mean?

It means the odds of the outcome are identical in the exposed and unexposed groups, so exposure shows no association with the outcome. Values above 1 indicate higher odds with exposure and below 1 indicate lower (protective) odds.

Why can’t any cell of the table be part of a zero product?

The formula divides by b·c, so if either b or c is zero the odds ratio is undefined (division by zero). A common fix is a continuity correction — adding 0.5 to every cell — which lets you estimate an OR when a cell is empty.

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For education only — not medical advice. Clinical measures depend on study design and prevalence; consult a professional before acting on them.