Bayes' Theorem Calculator
Find the probability that a condition is true given a positive test, using Bayes’ theorem.
Your numbers
Your results
Bayes' Theorem Calculator by TheCalcTools
How the Bayes' Theorem Calculator works
Enter how common the condition is, how often the test is positive when it is present, and how often it is positive when it is absent.
The calculator finds the overall chance of a positive result.
Bayes’ theorem then gives the probability the condition is present given a positive result.
The formula
Worked example
Using the default values shown in the calculator:
| Prior probability P(A) (%) | 1 |
|---|---|
| P(B | A), true positive rate (%) | 90 |
| P(B | not A), false positive rate (%) | 5 |
- P(B) = 0.9 × 1% + 5% × 99% = 5.85%.
- P(A | B) = 0.9% ÷ 5.85% = 15.38%.
- Even with a positive result, the chance is about one in seven.
Result:
| P(B), overall chance of a positive | 5.85% |
|---|---|
| P(A | B), posterior | 15.38% |
| P(not A | not B) | 99.89% |
Frequently asked questions
Why is the posterior so low for rare conditions?
When a condition is rare, most positive results come from the many healthy people who get a false positive, even if the test is accurate.
What is the prior?
The probability of the condition before you see the new evidence, often the base rate in the population.
Sources and further reading
Related calculators
More in Statistics & Probability · All calculators
This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.