Skip to main content
Mail a PDF copy of this page to:
(Your email address will not be added to a mailing list)
Download our user-friendly MedCalc statistical software for your Windows desktop. Download

Other calculators ...

Free statistical calculators

Odds ratio calculator

Subjects with positive (bad) outcome


Subjects with negative (good) outcome


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

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

with the standard error of the log odds ratio being

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

and 95% confidence interval

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

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).


  • 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
  • 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 nonparametric statistical procedures. 3rd ed. Boca Raton: Chapman & Hall /CRC.

How to cite this page

  • MedCalc Software Ltd. Odds ratio calculator. (Version 22.026; accessed June 17, 2024)

See also