When enough people are immune, each case infects fewer than one other person on average and outbreaks die out. Highly contagious diseases such as measles (R₀ 12–18) need about 95% immunity.
How to use the Herd Immunity Calculator
- Basic reproduction number (R₀)
- Vaccine effectiveness
- Share of the population already immune
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter R₀, vaccine effectiveness and the share of the population already immune.
Tips
- Use counts and person-time from the same population and period.
- Report confidence intervals with rates and ratios.
- Check whether figures are crude or age-adjusted before comparing.
- Larger samples give more stable estimates.
Common mistakes to avoid
- Confusing incidence (new cases) with prevalence (all cases).
- Comparing rates per 1,000 with rates per 100,000.
- Reading a relative risk without the baseline risk.
Inputs explained
| Field | What to enter |
|---|---|
| Basic reproduction number (R₀) | A number |
| Vaccine effectiveness | In % |
| Share of the population already immune | In % |
What each result means
- Herd immunity threshold = max(1 – 1÷[Basic reproduction number (R₀)], 0)×100
- Vaccine coverage needed = [Herd immunity threshold]÷[Vaccine effectiveness]×100
- Effective reproduction number now = [Basic reproduction number (R₀)]×(1 – [Share of the population already immune]÷100)
Example values
How the main result changes when Basic reproduction number changes and everything else stays at the example values above:
| Basic reproduction number (R₀) | Herd immunity threshold (%) |
|---|---|
| 2 | 50 |
| 3 | 66.7 |
| 4 | 75 |
| 5 | 80 |
| 6 | 83.3 |
| 8 | 87.5 |
Health note: this calculator is for education and screening only and is not a diagnosis or treatment advice. Discuss your results with a qualified clinician.
Formula
Herd immunity threshold = 1 − 1 ÷ R₀
Vaccine coverage needed = threshold ÷ vaccine effectiveness
Effective reproduction number = R₀ × (1 − immune share)
Worked example
Inputs — Basic reproduction number (R₀): 4; Vaccine effectiveness: 90 %; Share of the population already immune: 50 %.
Results — Herd immunity threshold = 75 %; Vaccine coverage needed = 83.3 %; Effective reproduction number now = 2.
Key terms
- R₀
- Basic reproduction number.
Frequently asked questions
What is R₀?
The average number of people one case infects in a fully susceptible population.
What is the herd immunity threshold for measles?
About 92–95%.
Can coverage above 100% be needed?
If vaccine effectiveness is lower than the threshold, vaccination alone cannot reach herd immunity.