What this calculator does
Vaccine efficacy is the proportional reduction in disease risk among the vaccinated, compared against the unvaccinated. It is a relative measure, which is why a headline efficacy figure says nothing about how many cases were actually prevented.
The arithmetic is straightforward. An unvaccinated attack rate of 5 per cent against a vaccinated rate of 1 per cent gives 80.0 per cent efficacy, because the vaccinated group had a fifth of the risk.
The formula
Subtract the vaccinated attack rate from the unvaccinated rate and divide by the unvaccinated rate. Equivalently, efficacy is one minus the relative risk.
| Term | Meaning |
|---|---|
| Attack rate | The proportion of a group who developed the disease. |
| Efficacy | Reduction in risk measured in a controlled trial. |
| Effectiveness | The same calculation applied to real-world observational data. |
The inputs explained
| Field | What to enter |
|---|---|
| Unvaccinated attack rate (%) | Attack rate in the unvaccinated group, as a percentage. |
| Vaccinated attack rate (%) | Attack rate in the vaccinated group, as a percentage. |
When to use it
Reading a trial result
Published efficacy figures come from exactly this calculation.
Investigating an outbreak
Attack rates by vaccination status give a field estimate of effectiveness.
Understanding what efficacy means
It is a relative reduction, not a probability of protection for an individual.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What does each vaccinated attack rate give?
Three vaccinated attack rates against the same baseline.
| Vaccinated attack rate | Vaccine efficacy | Relative risk (vaccinated vs. not) |
|---|---|---|
| 0.5% | 90.0% | 0.10 |
| 1% | 80.0% | 0.20 |
| 2.5% | 50.0% | 0.50 |
Questions
Does 80 per cent efficacy mean 20 per cent of vaccinated people get sick?
No, and this is the most common misreading. It means the vaccinated group had 20 per cent of the risk the unvaccinated group faced. If the unvaccinated risk was 5 per cent, the vaccinated risk is 1 per cent, not 20.
What is the difference between efficacy and effectiveness?
Efficacy is measured in a controlled trial with defined conditions; effectiveness is measured in the real world, where adherence, storage, timing and population differ. Effectiveness is usually somewhat lower.
Why does efficacy vary between studies?
Because it depends on the population, the circulating variant, the outcome measured and the time since vaccination. Efficacy against severe disease is typically higher than against any infection.
Does high efficacy mean many cases prevented?
Not necessarily. Efficacy is relative, so a high figure against a rare disease prevents few cases in absolute terms. The number needed to vaccinate is the figure that answers that question.
For the absolute version of the same question, see the number needed to treat calculator. For a general health baseline, see the BMI calculator.