Free statistical calculators

Relative risk calculator

Exposed group


Control group


Computational notes

The relative risk (RR), its standard error and 95% confidence interval are calculated according to Altman, 1991.

The relative risk or risk ratio is given by

Relative risk

with the standard error of the log relative risk being

Relative risk - standard error

and 95% confidence interval

Relative risk - confidence interval

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

Number Needed to Treat (NNT)

The number needed to treat (NNT) is the estimated number of patients who need to be treated with the new treatment rather than the standard treatment (or no treatment) for one additional patient to benefit (Altman 1998).

A negative number for the number needed to treat has been called the number needed to harm.

MedCalc uses the terminology suggested by Altman (1998) with NNT(Benefit) and NNT(Harm) being the number of patients needed to be treated for one additional patient to benefit or to be harmed respectively.

The 95% confidence interval is calculated according to Daly (1998) and is reported as suggested by Altman (1998).

Test of significance: the P-value is calculated according to Sheskin, 2004 (p. 542). A standard normal deviate (z-value) is calculated as ln(RR)/SE{ln(RR)}, 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. Buy from Amazon
  • Altman DG (1998) Confidence intervals for the number needed to treat. British Medical Journal 317: 1309-1312. PubMed
  • Daly LE (1998) Confidence limits made easy: interval estimation using a substitution method. American Journal of Epidemiology 147: 783-790. PubMed
  • 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. Buy from Amazon
  • Pagano M, Gauvreau K (2000) Principles of biostatistics. 2nd ed. Belmont, CA: Brooks/Cole. Buy from Amazon
  • 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. Buy from Amazon


Recommended book

Principles of Biostatistics
M Pagano, K Gauvreau

Buy from Amazon US - CA - UK - DE - FR - ES - IT

Principles of Biostatistics is aimed at students in the biological and health sciences who wish to learn modern research methods.

The book is divided into three parts. The first five chapters deal with collections of numbers and ways in which to summarize, explore, and explain them. The next two chapters focus on probability and introduce the tools needed for the subsequent investigation of uncertainty. It is only in the eighth chapter and thereafter that the authors distinguish between populations and samples and begin to investigate the inherent variability introduced by sampling, thus progressing to inference. Postponing the slightly more difficult concepts until a solid foundation has been established makes it easier for the reader to comprehend them.

Share on Facebook Share on Twitter

This site uses cookies to store information on your computer. More info...