Vaccine Efficacy / Effectiveness Calculator
Calculate vaccine efficacy from cases in vaccinated and unvaccinated groups (1 − relative risk) with a 95% confidence interval, absolute risk reduction and number needed to vaccinate, the test-negative/case-control form (1 − odds ratio), the screening method from the proportion of cases vaccinated, and what the numbers mean for the individual.
How it works
VE = 1 − (AR_vaccinated ÷ AR_unvaccinated) = 1 − RR; case-control: VE = 1 − OR; CI from ln(RR) ± 1.96 SE; ARR = AR_u − AR_v; NNV = 1 ÷ ARR; screening: VE = 1 − [PCV/(1−PCV)]·[(1−PPV)/PPV]
Vaccine efficacy is the proportional reduction in disease among vaccinated people compared with unvaccinated people under the same exposure — one minus the risk ratio in a trial, one minus the odds ratio in the case-control and test-negative designs used once a vaccine is deployed. Ninety-five percent efficacy therefore means that of the cases that would have occurred, 95% were prevented, not that five in a hundred recipients fall ill. The absolute risk reduction and number needed to vaccinate translate that into cases prevented, which depends on how much disease is circulating, and the screening method gives a rough field estimate from just two percentages: how many people, and how many cases, were vaccinated — when 60% of a population is vaccinated but only 20% of cases are, the vaccine is working.
Worked example
A trial with 11 cases among 18,000 vaccinated and 185 among 18,000 placebo recipients has attack rates of 0.061% and 1.028%: a risk ratio of 0.059 and efficacy of 94.1% (95% CI 89.1–96.8%). The absolute risk reduction over the trial was 0.97 percentage points, so about 103 people had to be vaccinated to prevent one case in that period.
Frequently asked questions
Efficacy or effectiveness?
Efficacy is measured under controlled trial conditions; effectiveness in real-world use with imperfect storage, dosing intervals, waning and varied populations. The arithmetic is the same; effectiveness is usually a bit lower.
Why does the confidence interval matter so much for low case counts?
The uncertainty in a risk ratio is driven by the smaller case count; 3 versus 30 cases gives a wide interval even in a huge trial, which is why regulators require a lower confidence bound above 30%.
Related calculators
Standard epidemiological formulas (CDC Principles of Epidemiology, Rothman) with simple large-sample confidence intervals. Results depend on case definitions, ascertainment and study design; they inform, and do not replace, formal analysis by an epidemiologist or public-health authority.