Vaccine Efficacy Calculator
Vaccine efficacy from the cases in a vaccinated and an unvaccinated group — the attack rates, the relative risk, the efficacy percentage and the number needed to vaccinate to prevent one case.
Attack rate is cases divided by people in each group.
How the vaccine efficacy calculator works
Attack rate is cases divided by people in each group. Relative risk is the vaccinated rate over the unvaccinated rate, and efficacy is one minus that: a vaccine that cuts the rate from 1% to 0.1% is 90% effective. The absolute risk reduction — the difference between the rates — gives the number needed to vaccinate, 1 ÷ ARR, which depends on how common the disease is as much as on the vaccine.
Formula: VE = 1 − (AR_vaccinated ÷ AR_unvaccinated); NNV = 1 ÷ (AR_unvac − AR_vac)
Worked examples
| Inputs | Vaccine efficacy | Note |
|---|---|---|
| 8 vs 162 cases in 18,000 each | 95.1 % | 95.1% |
| 50 vs 100 cases in 10,000 each | 50 % | 50% |
| Unequal groups: 20 in 30,000 vs 90 in 15,000 | 88.9 % | 88.9% |
FAQFrequently asked questions
Efficacy or effectiveness?
Efficacy is measured in a randomised trial; effectiveness is the same calculation from real-world data, where the groups differ in age, exposure and behaviour. The arithmetic is identical; the interpretation is not.
Why is the number needed to vaccinate so large?
Because it depends on how common the disease is during the study: a 95% effective vaccine against a disease that infects 1% of people in a season prevents about 1 case per 105 people vaccinated. Over a longer period, or in an epidemic, it falls sharply.
What does the confidence interval tell me?
The range of efficacy consistent with the counts. With few cases it is wide; a trial with 8 versus 162 cases pins efficacy near 95% with a narrow interval, while 2 versus 10 cases could be anything from 20% to 95%.
Can efficacy be negative?
Arithmetically, if the vaccinated group has the higher attack rate. In practice that indicates confounding or chance; check the group sizes and follow-up.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- CSIRO — Australia's national science agency
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.