Bayes Theorem Calculator
Calculate posterior probability using Bayes' theorem. Enter a prior probability, P(B|A), and P(B|not A) to get the updated probability after observing evidence.
Formula:
P(A|B) = P(B|A) × P(A) / (P(B|A) × P(A) + P(B|not A) × (1 − P(A)))
| Metric | Value |
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Privacy: calculations run locally in your browser. No inputs are stored or transmitted.
How it works
Bayes' theorem updates an initial probability after new evidence is observed. This is often used for medical tests, spam filters, diagnostics, and risk analysis.
A low prior probability can still produce a modest posterior even if the test sensitivity is high, especially when the false positive rate is not very small.
Examples
- Prior: 1%
- P(B|A): 95%
- P(B|not A): 5%
- Posterior P(A|B) is much higher than 1%, but still far below 95%.
When to use this tool
This tool is designed for quick, practical tasks such as everyday calculations, data formatting, or simple conversions. It is best used when you need fast results without installing software or using complex tools.
When to use
- Quick checks or one-time calculations
- Validating or converting data before using it elsewhere
- Simple tasks that do not require advanced software
When not to use
- Critical financial, legal, or medical decisions
- Large-scale or automated processing
- Situations requiring guaranteed precision beyond basic validation
Always review results before using them in important contexts.
About this tool
This tool helps you perform quick utility operations directly in your browser. It runs entirely in your browser without sending data to a server.
You can use this tool when handling simple tasks without installing additional software. The results should be interpreted as a processed output based on your input data.
FAQ
- What does this Bayes theorem calculator compute?
It computes the posterior probability P(A|B) using a prior probability, true positive probability P(B|A), and false positive probability P(B|not A).
- What is the formula used?
This page uses P(A|B) = P(B|A) × P(A) / (P(B|A) × P(A) + P(B|not A) × (1 − P(A))).
- Can I enter percentages instead of decimals?
Yes. You can enter values as percentages or decimals and switch the input mode.
- What is posterior probability?
Posterior probability is the updated probability of event A after observing evidence B.
- Are calculations stored?
No. Everything runs locally in your browser.