Quick Bayes Theorem Calculator

This simple calculator uses Bayes' Theorem to make probability calculations of the form:

What is the probability of A given that B is true.

For example, what is the probability that a person has Covid-19 given that they have lost their sense of smell?

This is normally expressed as follows: P(A|B), where P means probability, and | means given that.

If you already understand how Bayes' Theorem works, click the button to start your calculation. Otherwise, read on.

Further Information

The formula for Bayes' Theorem is as follows:

Let's unpick the formula using our Covid-19 example.

P(A|B) is the probability that a person has Covid-19 given that they have lost their sense of smell.
P(A) is the (prior) probability (in a given population) that a person has Covid-19.
P(B|A) is the probability that a person has lost their sense of smell given that they have Covid-19.
P(B) is the probability (in a given population) that a person has lost their sense of smell.

Our example makes it easy to understand why Bayes' Theorem can be useful for probability calculations where you know something about the conditions related to the event or phenomenon under consideration.

Consider, for instance, that the likelihood that somebody has Covid-19 if they have lost their sense of smell is clearly much higher in a population where everybody with Covid loses their sense of smell, but nobody without Covid does so, than it is in a population where only very few people with Covid lose their sense of smell, but lots of people without Covid lose their sense of smell (assuming the same overall rate of Covid in both populations).

The Calculation

Okay, so let's begin your calculation. We'll use a wizard to take you through the calculation stage by stage. Click the button to start.