How this instrument works
Vaccine efficacy measures how much a vaccine cuts the risk of disease among people who got it, compared with people who didn't, inside a controlled trial. The calculation runs in two short steps: first the attack rate in each arm — cases divided by the number of people in that arm — then a relative risk (vaccinated attack rate over unvaccinated attack rate) that gets converted to a percentage risk reduction. A relative risk of 0.05 means the vaccinated group's risk was 5% of the unvaccinated group's, which converts to 95% efficacy.
This is the same relative-risk formula taught in CDC epidemiology training and used in Orenstein and colleagues' 1985 field-methods paper for measuring vaccine efficacy from case counts. It isn't specific to any one disease or brand — the identical arithmetic applies to a measles vaccine trial, a flu vaccine trial, or a COVID-19 vaccine trial, because it only needs case counts and group sizes, not anything about the pathogen itself.
What it doesn't give you is a confidence interval. Published trial results report efficacy alongside a range (the BNT162b2 trial's 95.0% came with a 90.3–97.6% credible interval) computed with additional statistical methods this instrument doesn't attempt — it produces the same point estimate, not the uncertainty around it. Treat a result from a small trial with the same caution the original authors would: a big efficacy number from a handful of cases carries a wide margin of error even though the formula itself is exact.
- Enter Cases among vaccinated group and Total people in vaccinated group from the trial or study you're checking.
- Enter Cases among unvaccinated group and Total people in unvaccinated group for the comparison arm.
- Read Attack rate, vaccinated and Attack rate, unvaccinated — each group's case share as a percentage.
- Read Relative risk — the vaccinated arm's risk divided by the unvaccinated arm's.
- Read Vaccine efficacy (%) — the final percentage risk reduction, this instrument's headline figure.
Worked example — the Pfizer-BioNTech BNT162b2 phase 3 trial
Enter 8 cases among 17,411 vaccinated participants and 162 cases among 17,511 who received placebo — the exact case counts published for the BNT162b2 phase 3 trial. The vaccinated arm's attack rate works out to 0.0459%, the placebo arm's to 0.9251%, for a relative risk of 0.0497. Vaccine efficacy is (1 − 0.0497) × 100 = 95.03%, matching the trial's published topline figure of 95.0% once rounded to one decimal place.
The same formula scales to tidier numbers just as cleanly. Ten cases among 1,000 vaccinated versus 100 cases among 1,000 unvaccinated gives attack rates of exactly 1% and 10%, a relative risk of exactly 0.1, and a vaccine efficacy of exactly 90% — useful for sanity-checking that the instrument is doing what the formula says before trusting it on real trial data.
Questions
What's the difference between vaccine efficacy and effectiveness?
Efficacy is measured inside a controlled trial, where randomization balances the vaccinated and unvaccinated groups on everything except the vaccine itself. Effectiveness is measured afterward, in the general population, where age, prior infection, behavior and other factors all vary between people who chose to get vaccinated and those who didn't. This calculator's formula works for either kind of study — the difference is in how the case counts were collected, not in the arithmetic.
Does this only work for COVID-19 vaccines?
No. The relative-risk formula behind vaccine efficacy has nothing COVID-specific in it — it only needs case counts and group sizes from any two-arm comparison. The same calculation is standard for measles, influenza, rotavirus, or any other vaccine trial. The Pfizer-BioNTech example here is used because its numbers are public and independently checkable, not because the formula is limited to that vaccine.
What does a negative vaccine efficacy mean?
It means the vaccinated group's attack rate was higher than the unvaccinated group's, so relative risk exceeds 1 and (1 − RR) goes negative. In a well-run large trial that's a signal worth investigating; in a small study it can also just be statistical noise from a handful of cases. The formula reports whatever the numbers say — it doesn't judge whether the result is meaningful.
Why doesn't this calculator show a confidence interval?
Because a confidence interval needs a separate statistical step beyond the point-estimate formula this instrument runs — typically a Poisson or exact binomial method applied to the same case counts. Published trial papers report both; this tool reproduces only the efficacy percentage itself, which is why a small-sample result here should be read as a starting estimate, not a precise figure.
Can I use this for a real-world effectiveness study instead of a trial?
Yes — the arithmetic is identical whether the case counts come from a randomized trial or an observational cohort or case-control study. What changes is how much you should trust the result: a trial's randomization controls for confounding factors automatically, while an observational study needs separate statistical adjustment for things like age and prior exposure that this formula doesn't account for.
What happens if I enter zero cases for the unvaccinated group?
The calculator blocks it and explains why, rather than dividing by zero — an unvaccinated attack rate of zero would make relative risk undefined. In real trial data this is rare but not impossible with very small or very short studies; it means there isn't yet enough data in the comparison group to compute a stable efficacy figure.
References
- Polack et al. 2020, N Engl J Med — BNT162b2 phase 3 trial (PubMed)
- WHO — Vaccine efficacy, effectiveness and protection
- Orenstein et al. 1985, Bull World Health Organ — field evaluation of vaccine efficacy (PubMed)
Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.