Skip to main content

Odds Ratio Calculator

Use this free calculator to compute the odds ratio (OR), 95% confidence interval, and p-value from a 2×2 contingency table. Enter the number of subjects with a positive and negative outcome in the exposed and non-exposed groups.

The odds ratio is the standard effect measure in case-control studies and is also reported in logistic regression. It expresses how much more (or less) likely an outcome is in the exposed group compared with the non-exposed group.

Example: 30 exposed vs 10 non-exposed had a positive outcome; 20 vs 40 had a negative outcome.

 

Subjects with positive (bad) outcome
:  a
:  c
Subjects with negative (good) outcome
:  b
:  d

Interpreting the odds ratio

An odds ratio of 1 indicates no association — the odds of the outcome are the same in both groups. An OR greater than 1 indicates that the exposed group has higher odds of the outcome; an OR less than 1 indicates lower odds (a protective effect). For example, OR = 3.0 means the exposed group has three times the odds of the outcome compared with the non-exposed group.

If the 95% confidence interval does not include 1, the association is statistically significant at the 5% level.

The odds ratio is most appropriate for case-control studies or when the outcome is rare (<10%). When the outcome is common in a cohort or cross-sectional study, the OR overestimates the relative risk — in those situations consider using the relative risk calculator instead.

Computational notes

The odds ratio (OR), its standard error and 95% confidence interval are calculated according to Altman, 1991.

The odds ratio is given by

$$ \begin{align} OR & = \frac {a/b} {c/d} \\ & = \frac {a \times d } { b \times c} \end{align}$$

with the standard error of the log odds ratio being

$$ \operatorname{SE} \left \{ \operatorname{ln}\left(OR\right) \right \} = \sqrt { \frac {1}{a} + \frac {1}{b} + \frac {1}{c} + \frac {1}{d} } $$

and 95% confidence interval

$$ \operatorname{95\%\text{ } CI} = \operatorname{exp} \Big( \text{ } \operatorname{ln}\left(OR\right) - 1.96 \times \operatorname{SE} \left \{ \operatorname{ln}\left(OR\right) \right \} \text{ }\Big) \quad \text{ to }\quad \operatorname{exp} \Big(\text{ } \operatorname{ln}\left(OR\right) + 1.96 \times \operatorname{SE} \left \{ \operatorname{ln}\left(OR\right) \right \} \text{ }\Big)$$

Where zeros cause problems with computation of the odds ratio or its standard error, 0.5 is added to all cells (a, b, c, d) (Pagano & Gauvreau, 2000; Deeks & Higgins, 2010).

Test of significance: the P-value is calculated according to Sheskin, 2004 (p. 542). A standard normal deviate (z-value) is calculated as ln(OR)/SE{ln(OR)}, and the P-value is the area of the normal distribution that falls outside ±z (see Values of the Normal distribution table).

Literature

  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
  • Altman DG, Deeks JJ, Sackett DL. Odds ratios should be avoided when events are common [letter]. BMJ 1998;317:1318.
  • Deeks JJ, Higgins JPT (2010) Statistical algorithms in Review Manager 5. Retrieved from https://training.cochrane.org/
  • Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2nd ed. Oxford: Blackwell Science.
  • Pagano M, Gauvreau K (2000) Principles of biostatistics. 2nd ed. Belmont, CA: Brooks/Cole.
  • Parshall MB (2013) Unpacking the 2 x 2 table. Heart & Lung 42:221-226. PubMed
  • Sheskin DJ (2004) Handbook of parametric and non-parametric statistical procedures. 3rd ed. Boca Raton: Chapman & Hall /CRC.

How to cite this page

  • MedCalc Software Ltd. Odds Ratio Calculator with 95% CI and P-value | MedCalc. https://www.medcalc.org/en/calc/odds_ratio.php (Version 23.6.2; accessed July 18, 2026)

Other free statistical calculators

See also

https://www.medcalc.org/en/calc/odds_ratio.php

© 2026 MedCalc Software Ltd