About this calculator
The answer depends heavily on how common the condition is, which is why the calculator also shows the result as counts out of 10,000 people.
How to use it
- Enter how common A is.
- Enter the true and false positive rates.
- Read P(A | B) and the counts.
The formula
P(A | B) = P(B | A) × P(A) ÷ [P(B | A) × P(A) + P(B | not A) × P(not A)]
- P(A)
- prior probability
- P(B | A)
- true positive rate (sensitivity)
- P(B | not A)
- false positive rate
Worked example
A condition affecting 1%, a test with 95% sensitivity and 5% false positives
- Out of 10,000 people, 100 have it and 95 test positive; 9,900 do not and 495 test positive.
- So only 95 of 590 positives are real: P = 16.1%.
What the result means
When a condition is rare, even a good test produces more false positives than true ones. A second test usually follows.
Assumptions
- The rates are known and apply to the person tested.
Limitations
- This is not medical advice; doctors combine tests with symptoms and history.
Frequently asked questions
Why is the answer so low?
Because false positives from the large healthy group outnumber true positives from the small affected group.
What is the prior?
Your probability before the new evidence.
What is specificity?
100% minus the false positive rate.
Last reviewed on 6 October 2026. Found a mistake? Tell us.