Vaccine Efficacy Calculator

Calculate vaccine efficacy as (ARU - ARV) / ARU from vaccinated and unvaccinated case counts, plus risk ratio, risk reduction and a 95% interval.

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Quick Facts

Formula
VE = (ARU − ARV) / ARU
Equivalent to 1 minus the risk ratio.
Needs
Two groups
Same follow-up period and case definition in each.

Your Results

Calculated
Vaccine efficacy
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(ARU − ARV) / ARU
Attack rates
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Vaccinated (ARV) vs unvaccinated (ARU)
Risk ratio and 95% CI
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Efficacy interval shown in the note below
Number needed to vaccinate
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People vaccinated to prevent one case in this study period

Ready

Enter case counts for both groups, then calculate.

What vaccine efficacy measures

Vaccine efficacy is the proportional reduction in disease among vaccinated people compared with unvaccinated people under the conditions of a study, usually a randomized trial. It is calculated from two attack rates: the attack rate in the unvaccinated group (ARU) and the attack rate in the vaccinated group (ARV). Efficacy is the share of the unvaccinated attack rate that vaccination removes: VE = (ARU − ARV) / ARU, which equals 1 − ARV/ARU, or 1 minus the risk ratio.

The calculator takes the group sizes and the case counts, works out both attack rates, and reports efficacy, the risk ratio, the absolute risk reduction (ARU − ARV), the number needed to vaccinate, and an approximate 95% confidence interval for efficacy. If you only have attack rates, enter 100 as each group size and the rate per 100 people as the case count (decimals are accepted for cases).

The equations

  • ARV = vaccinated cases / vaccinated group size. ARU = unvaccinated cases / unvaccinated group size.
  • Risk ratio RR = ARV / ARU. VE = 1 − RR.
  • Absolute risk reduction = ARU − ARV. Number needed to vaccinate = 1 / (ARU − ARV).
  • 95% interval: the standard error of ln(RR) is √(1/a − 1/nV + 1/c − 1/nU), where a and c are the vaccinated and unvaccinated case counts. The interval for RR is RR × e±1.96 × SE, and the efficacy interval is 1 minus each end. If the vaccinated group has zero cases, 0.5 is added to the cases in the interval calculation only.

Worked example

Suppose 20,000 vaccinated people had 8 cases and 20,000 unvaccinated people had 160 cases, which are the default inputs. ARV = 8 / 20,000 = 0.04% and ARU = 160 / 20,000 = 0.80%.

VE = (0.0080 − 0.0004) / 0.0080 = 0.95, or 95.0%. The risk ratio is 0.05. The absolute risk reduction is 0.76 percentage points, so the number needed to vaccinate is 1 / 0.0076 ≈ 131.6 people. The standard error of ln(RR) is √(1/8 − 1/20,000 + 1/160 − 1/20,000) ≈ 0.362, so RR ranges from 0.05 × e−0.710 ≈ 0.025 to 0.05 × e0.710 ≈ 0.102, giving an efficacy interval of about 89.8% to 97.5%.

Efficacy versus effectiveness, and common mistakes

  • Efficacy is not effectiveness. Efficacy comes from controlled trials. Effectiveness is the protection observed in routine use, which can differ because of the population, variants, timing and how the outcome is measured.
  • Efficacy is a relative figure. 95% efficacy does not mean 5% of vaccinated people get the disease. It means the vaccinated attack rate is 5% of the unvaccinated attack rate. Use the absolute risk reduction alongside it.
  • Comparing groups that differ. Observational comparisons of vaccinated and unvaccinated people can be confounded by age, exposure and health behaviour. Randomized trials avoid most of this.
  • Different follow-up or case definitions. Both groups must be followed for the same time and counted with the same rules, otherwise the attack rates are not comparable.
  • Small counts. With few cases the interval is wide, so a high point estimate can still be uncertain. This tool uses a simple large-sample approximation, not the exact methods used in formal trial analyses.

This is an educational calculator. It does not replace the analysis of a trial statistician or public health guidance from your health authority.

Frequently Asked Questions

What is the formula for vaccine efficacy?
Vaccine efficacy equals (ARU − ARV) / ARU, where ARU is the attack rate in the unvaccinated group and ARV is the attack rate in the vaccinated group. It is the same as 1 minus the risk ratio.
Can vaccine efficacy be negative?
Yes. If the vaccinated group has a higher attack rate than the unvaccinated group, the risk ratio is above 1 and the efficacy is negative, which suggests no benefit or possible harm. With small counts this can also just be chance, so check the interval.
Does 90% efficacy mean 10% of vaccinated people get sick?
No. It means the attack rate among vaccinated people was 90% lower than among unvaccinated people. If 1% of unvaccinated people got sick, about 0.1% of vaccinated people would, all else equal.
Can I use attack rates instead of counts?
Yes. Enter 100 as both group sizes and each rate per 100 people as the case count. For example, 0.04% and 0.80% become 0.04 and 0.8 cases per 100. The interval will not be meaningful in that case because it depends on real counts.

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