Compute OR and RR with 95% CIs from a 2×2 table, plus risk difference and NNT, with Haldane correction. Free, for clinical research.
Both compare how often an outcome happens (relapse, illness, dropping out of treatment) in an exposed group and an unexposed group, but they are not the same thing. The risk ratio (RR), also called relative risk, divides two proportions: the risk of the outcome in the exposed by the risk in the unexposed. The odds ratio (OR) divides two odds: the ratio of those with the outcome to those without it, in one group and in the other. An RR of 2 reads as "twice the risk"; an OR of 2 does not, unless the outcome is rare.
A cohort study follows 200 people with insomnia for one year: 100 receive cognitive behavioural therapy and 100 do not. 20 relapse in the therapy group and 35 in the group without it. In the table: a = 20, b = 80 (therapy), c = 35, d = 65 (no therapy). The risk of relapse is 20% with therapy and 35% without it.
In APA 7 you would write: "Therapy was associated with a lower risk of relapse, RR = 0.57, 95% CI [0.36, 0.92]." The full template is in how to report odds ratios in APA 7. If the study is observational (cohort, case-control or cross-sectional), what the reviewer will check it against is the STROBE checklist; if it is a trial, the CONSORT 2025 checklist.
If the 95% confidence interval of the OR or RR includes 1, the data are compatible with no association (α = .05). But do not reduce it to "significant or not": an RR of 0.57 with an interval from 0.36 to 0.92 says the plausible reduction ranges from very large to small, and that is what your reader needs to judge the effect. If you are unsure which measure fits, the reasoning is laid out in odds ratio versus relative risk in clinical research.
If any cell is 0, the OR comes out as 0 or infinity and its standard error does not exist. The calculator then applies the Haldane-Anscombe correction, adding 0.5 to all four cells, and flags it below the result. If you use it, say so in your Methods section.
Methods: CI of the OR by Woolf’s (1955) log method and of the RR by the method of Katz et al. (1978).
If you use it in your thesis or in a paper, cite it so that readers of your Methods section know how the calculation was done.
Ciudad-Fernández, V. (2026). Odds ratio and risk ratio calculator [Web application]. Ciudad Science. Retrieved October 18, 2026, from https://analisisdedatospsicologia.com/en/tools/odds-ratio-calculator
For your Methods section: Odds ratios and risk ratios were computed with log-method 95% confidence intervals (Woolf, 1955; Katz et al., 1978) using the Ciudad Science odds ratio and risk ratio calculator (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026oddsratio,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Odds ratio and risk ratio calculator}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/tools/odds-ratio-calculator},
urldate = {2026-10-18},
note = {Accessed 2026-10-18},
}