Enter the total population, probability of transmission per contact, and duration of infectiousness into the calculator to determine the Rn number. This calculator can also evaluate any of the variables given the others are known.

## Rn Number Formula

The following formula is used to calculate the Rn number.

Rn = (N * p * (1 + p)^t) / ((1 + p)^t - 1)

Variables:

- Rn is the Rn number N is the total population p is the probability of transmission per contact (decimal) t is the duration of infectiousness (days)

To calculate the Rn number, multiply the total population by the probability of transmission per contact, then raise the result to the power of the duration of infectiousness. Add 1 to the probability of transmission per contact and raise it to the power of the duration of infectiousness. Divide the first result by the second result, and subtract 1 from the quotient.

## What is an Rn Number?

An Rn number, or Reproduction number, is a key parameter in epidemiology that represents the average number of people that one infected person can spread a disease to. It is used to measure the transmission potential of a disease. If the Rn is greater than 1, the number of cases increases exponentially, indicating an outbreak or epidemic. If it’s less than 1, the disease will eventually die out.

## How to Calculate Rn Number?

The following steps outline how to calculate the Rn Number.

- First, determine the total population (N).
- Next, determine the probability of transmission per contact (p) as a decimal.
- Next, determine the duration of infectiousness (t) in days.
- Next, gather the formula from above = Rn = (N * p * (1 + p)^t) / ((1 + p)^t – 1).
- Finally, calculate the Rn Number.
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Total population (N) = 1000

Probability of transmission per contact (p) = 0.05

Duration of infectiousness (t) = 7 days