# Herd Immunity Calculator

URL: https://speedycalculator.com/calculators/health/vaccine-immunity/
Last updated: 2026-10-30

> The herd immunity calculator works out the share of a population that must be immune to stop sustained spread of an infection from its basic reproduction number R₀, and the vaccination coverage needed given the vaccine's effectiveness.

## Inputs

- Basic reproduction number (R₀)
- Vaccine effectiveness (%)
- Share of the population already immune (%)

## Results

- Herd immunity threshold
- Vaccine coverage needed
- Effective reproduction number now

## Formula

```
Herd immunity threshold = 1 − 1 ÷ R₀
Vaccine coverage needed = threshold ÷ vaccine effectiveness
Effective reproduction number = R₀ × (1 − immune share)
```

## Explanation

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

FieldWhat to enterBasic reproduction number (R₀)A numberVaccine effectivenessIn %Share of the population already immuneIn %

### 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 (%)250366.7475580683.3887.5
*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.*

## 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.

## FAQ

**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.


## Sources

- [Fine P et al. "Herd immunity": a rough guide. Clin Infect Dis, 2011](https://pubmed.ncbi.nlm.nih.gov/21427399/)