CALCULATE WITH CONFIDENCE

Statistics · Probability

Bayes’ Theorem Calculator

Update a prior probability using evidence sensitivity and its false-positive probability.

Statistics · Probability

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
Follow each branch by multiplying conditional probabilities; add mutually exclusive terminal paths when the question combines them.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Feedback

Understand the probability

What the bayes’ theorem calculator is calculating

Following conditional branches. Conditional probability changes the reference group. A branch probability must be read inside the branch condition, while Bayes’ theorem reverses the conditioning direction using prior probabilities.

Probability rule

P(A|B)=P(B|A)P(A)/[P(B|A)P(A)+P(B|not A)P(not A)].

Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.

How to interpret it

A strong test result can still imply a modest posterior when the prior event is rare.

Model boundary: Inputs must describe the same population and evidence definition; this arithmetic is not a medical diagnosis.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the bayes’ theorem calculator works

P(A|B)=P(B|A)P(A)/[P(B|A)P(A)+P(B|not A)P(not A)].

A strong test result can still imply a modest posterior when the prior event is rare.

Worked example

Bayes’ Theorem example

A 1% prior, 90% sensitivity, and 5% false-positive probability give a posterior of about 15.38%.

P(A|B)=P(B|A)P(A)/[P(B|A)P(A)+P(B|not A)P(not A)].

Supported inputs

Precision and limits

Model and design

Inputs must describe the same population and evidence definition; this arithmetic is not a medical diagnosis.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

A strong test result can still imply a modest posterior when the prior event is rare.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

Continue calculating

Related calculators