Bayes Theorem Calculator

Posterior probability, medical screening

Quick Answer

Bayes Theorem Calculator: Posterior probability, medical screening. Bayes Theorem Calculator uses standard math formulas to compute accurate results instantly.

Prior P(B) %

e.g. disease prevalence

Sensitivity %

P(+|sick)

Specificity %

P(−|healthy)

P(sick | positive test)

1.94%

Negative test → 100.00% truly healthy (NPV)

Per 10,000 people

	Test +	Test −	Total
Sick	10（true +）	0（false −）	10
Healthy	499（false +）	9491（true −）	9990

Bayes' theorem

1P(B) = 0.10%；P(+|B) = 99.0%；P(+|¬B) = 5.0%
2Joint true+ = 99.0% × 0.10% = 0.099%
3False+ = 5.0% × 99.90% = 4.995%
4PPV = 0.099 ÷ 5.094 = 1.94%

💡 The base-rate fallacy: a 99%-accurate test for a 0.1% disease still yields mostly false positives — because the healthy crowd is huge, its small false-positive slice outnumbers the true positives. This is why screening low-risk groups creates overdiagnosis, and why a positive screening result always needs a confirmatory test.

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How to Use

Enter values or expressions: type directly into the Bayes Theorem Calculator — keyboard friendly.
Instant results: everything computes live as you type, no button needed.
Follow the steps: the result panel shows full working and formula substitution.
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Key Points

Bayes Theorem Calculator is a free online math tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Posterior probability, medical screening.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Bayes Theorem Calculator formula

Bayes Theorem Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Bayes Theorem Calculator?

Open the page and fill in the input fields — results update automatically. Posterior probability, medical screening.

Are the results accurate?

Yes. All calculations use standard mathematical formulas and are verified for accuracy.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required — just open and use.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. All calculations run locally in your browser. Nothing is uploaded or stored.

Related Guides

Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated: 2026-08-04

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Bayes Theorem Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/bayes

Results provided by this tool are for reference only and do not constitute professional advice.