Odds Ratio Calculator

Work out odds ratio instantly with clear inputs, formula shown and shareable results.

About Odds Ratio Calculator

The odds ratio is the cross-product ad/bc. It is the natural measure for case-control studies, where incidence cannot be estimated directly, and its confidence interval is computed on the log scale.

Formulas

Odds ratio

OR = ad / bc

Confidence interval

exp(ln OR ± 1.96·√(1/a + 1/b + 1/c + 1/d))

Worked example

With the default values below, Odds Ratio Calculator returns Odds ratio of 6.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Exposed cases (a)minimum 0: 40
Exposed controls (b)minimum 0: 20
Unexposed cases (c)minimum 0: 15
Unexposed controls (d)minimum 0: 45

Results

Odds ratio: 6.00000000
95% lower bound: 2.713674
95% upper bound: 13.266147
Log odds ratio: 1.79175947

Step by step

1Values used
2Odds ratio
3Confidence interval
4Odds ratio= 6.00000000
595% lower bound= 2.713674
695% upper bound= 13.266147
7Log odds ratio= 1.79175947

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For a = 40, b = 20, c = 15, d = 45?

OR = 1800/300 = 6, with a 95% interval of roughly 2.72 to 13.24 — clearly above 1.

When does OR approximate relative risk?

When the outcome is rare, under about 10%; for common outcomes the odds ratio exaggerates the risk ratio.