Calculate Bayes' Theorem

Bayes' Theorem Calculator

Calculate posterior probabilities with an intuitive, purpose-built calculator. Whether you're a student learning Bayesian reasoning, a clinician interpreting test results, or anyone who wants to update beliefs with evidence, this app makes it straightforward.

Three Calculator Modes

• Basic — Enter P(A), P(B), and P(B|A) to compute P(A|B) directly from Bayes' Theorem.
• Medical Test — Input prevalence, sensitivity, and specificity to find the probability of disease given a positive or negative result. Supports both prevalence-based and positive-rate-based calculations.
• Odds Form — Work with prior probability and likelihood ratios to update beliefs, ideal for sequential reasoning.

Step-by-Step Breakdowns

Every result includes a detailed breakdown showing exactly how each value was calculated — no black boxes.

Chain Multiple Tests

Use the result of one calculation as the prior for the next with a single tap. Perfect for interpreting sequential medical tests or compounding evidence.

Built-In Reference Guide

A comprehensive info section covers:
• Key terms and definitions
• Sensitivity and specificity explained
• A worked medical test example with full notation
• The odds form of Bayes' Theorem
• How to chain tests using likelihood ratios
• Key takeaways for Bayesian thinking