OR, RR, ARR and NNT calculator (2×2)

What this computes

From a 2×2 table (events and total participants in an active arm and a control arm), it derives the four standard effect measures for a dichotomous outcome: the risk ratio (RR), the odds ratio (OR), the absolute risk reduction (ARR) or risk difference, and the number needed to treat (NNT). Ratio measures come with log-scale 95% confidence intervals. Everything updates live as you type; nothing is shown until both arms are complete.

The formulas

With cells a (active events), b (active non-events), c (control events), d (control non-events), and arm totals n1 = a + b, n2 = c + d:

r1 = a / n1            r2 = c / n2
RR  = r1 / r2
OR  = (a·d) / (b·c)
ARR = r1 − r2          NNT = ceil(1 / |ARR|)

SE(lnRR) = √(1/a − 1/n1 + 1/c − 1/n2)
SE(lnOR) = √(1/a + 1/b + 1/c + 1/d)
95% CI   = exp( ln(point) ± 1.96·SE )

The NNT is labelled NNTB when the active arm has fewer events (ARR < 0) and NNTH when it has more (ARR > 0), reading the outcome as an event you want to prevent.

When it is valid

These are the exact intervention effect measures of Cochrane Handbook chapter 6 (§6.4). The confidence intervals use the normal approximation to the sampling distribution of the log ratio, which is reliable for trial-sized cells. If a cell is zero, both the ratio and its SE are undefined, so a 0.5 continuity correction is added to all four cells before computing RR, OR and their CIs, and flagged in the output. Risks and the risk difference are always taken from the raw counts.

When it is not

The odds ratio approximates the risk ratio only when events are rare; above a ~50% event rate the two diverge sharply, and reporting an OR as if it were an RR overstates the effect. The calculator raises that warning on the inputs that trigger it. With very small cells the log-normal CI understates uncertainty. Prefer an exact method. And an NNT is only interpretable against a stated time horizon and baseline risk; it is not portable across populations with different control-arm risk. For pooling across studies, combine on the log scale (inverse-variance or Mantel–Haenszel), not by averaging these point estimates.