Vaccine Efficacy Calculator — VE, Relative Risk and NNV
Enter the number of participants and disease cases in the vaccinated and unvaccinated groups to calculate vaccine efficacy (VE), relative risk, absolute risk reduction, and the number of people who must be vaccinated to prevent one case.
Percentage reduction in disease risk compared to unvaccinated group
- 1
Attack rate — vaccinated (ARV)
50 ÷ 10,000 = 0.005 - 2
Attack rate — unvaccinated (ARU)
400 ÷ 10,000 = 0.04 - 3
Relative risk (RR)
0.005 ÷ 0.04 = 0.125 - 4
Vaccine efficacy (VE)
(1 − 0.125) × 100 = 87.5VE is the percentage reduction in disease risk relative to the unvaccinated group.
How does this calculator work?
VE = (1 − RR) × 100%, where RR = (cases_vaccinated / n_vaccinated) ÷ (cases_unvaccinated / n_unvaccinated). Absolute risk reduction (ARR) = ARU − ARV. Number needed to vaccinate (NNV) = 1 / ARR. A 90% VE with a low ARU still implies a high NNV — check both relative and absolute measures when interpreting vaccine data.
Formula
How this is calculated
Vaccine efficacy measures how much a vaccine reduces the risk of disease relative to an unvaccinated group. The attack rate (AR) is the proportion of each group that develops the disease: ARV for vaccinated and ARU for unvaccinated. The relative risk (RR) is the ratio ARV ÷ ARU — a vaccine that cuts risk in half gives RR = 0.5. Vaccine efficacy (VE) converts this to a percentage: VE = (1 − RR) × 100%. An 80% VE means vaccinated people have 80% less risk than unvaccinated ones.
The absolute risk reduction (ARR) is ARU − ARV — the raw percentage-point difference in attack rates. This is often a more practically meaningful number than VE: a vaccine that reduces risk from 0.2% to 0.1% has a 50% VE but an ARR of only 0.1 percentage points. The number needed to vaccinate (NNV) = 1 ÷ ARR answers "how many people must be vaccinated to prevent one case." A low ARR produces a high NNV.
This calculator assumes both groups had equal exposure to the pathogen and comparable baseline risk — conditions met by randomised controlled trials but potentially violated in observational data, where confounders like healthcare-seeking behaviour or age can bias results. VE from observational studies should be interpreted with caution.
Frequently asked questions
Vaccine efficacy (VE) is measured in randomised controlled trials under controlled conditions and represents the best-case protection. Vaccine effectiveness is measured in real-world observational studies after deployment and may be lower due to differences in study populations, pathogen variants, and time since vaccination. Both use the same formula: (1 − RR) × 100%.
A negative VE means the vaccinated group had a higher attack rate than the unvaccinated group, suggesting the vaccine provided no protection or was even associated with more cases. This can result from confounding in observational studies (e.g., vaccinated people were older and higher-risk), vaccine failure, or study design issues. A negative VE from a small study may not be statistically significant.
NNV = 1 ÷ ARR. It answers "how many people must be vaccinated to prevent one additional disease case." A low ARR (small absolute benefit) gives a large NNV. For example, if the unvaccinated rate is 1% and the vaccinated rate is 0.1%, ARR = 0.9% and NNV ≈ 111 — you need to vaccinate 111 people to prevent one case. NNV is more informative than VE alone when weighing vaccination programme costs.
Also known as
TG we-Calculate Editorial Team. (2026). Vaccine Efficacy Calculator — VE, Relative Risk and NNV [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/vaccine-efficacy-calculator
TG we-Calculate Editorial Team. "Vaccine Efficacy Calculator — VE, Relative Risk and NNV." TG we-Calculate. 2026. https://we-calculate.com/calculator/vaccine-efficacy-calculator.
TG we-Calculate Editorial Team, "Vaccine Efficacy Calculator — VE, Relative Risk and NNV," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/vaccine-efficacy-calculator
@misc{wecalculate_vaccine_efficacy_calculator, title = {Vaccine Efficacy Calculator — VE, Relative Risk and NNV}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/vaccine-efficacy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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