--- title: "Bayes' Theorem Calculator | Posterior Probability Tool | XTRAW Tools" description: "Apply Bayes' theorem to update a prior probability with new evidence. Use this free browser-based Bayes theorem calculator from XTRAW Tools." url: "https://xtraw.com/tools/calculators/science-calculators/bayes-theorem-calculator" date: "2026-07-06T06:02:08+00:00" language: "en-GB" --- [Sensitivity & Specificity Calculator](https://xtraw.com/tools/calculators/science-calculators/sensitivity-specificity-calculator)[Negative Predictive Value Calculator](https://xtraw.com/tools/calculators/science-calculators/negative-predictive-value-calculator) [![Bayes' Theorem Calculator from XTRAW Tools](https://xtraw.com/images/virtuemart/product/xtraw-bayes-theorem-calculator-360x360.jpg)](https://xtraw.com/images/virtuemart/product/xtraw-bayes-theorem-calculator-360x360.jpg "Bayes' Theorem Calculator from XTRAW Tools") new [Back to: Science Calculators](https://xtraw.com/tools/calculators/science-calculators "Science Calculators") # Bayes' Theorem Calculator Apply Bayes' theorem to update a prior probability with new evidence. Use this free browser-based bayes' theorem calculator from XTRAW Tools. **Bayes' Theorem Calculator** helps you apply Bayes' theorem to update a prior probability with new evidence. Use this free browser-based calculator from XTRAW Tools to compare inputs, estimate results, and plan your next step. ## How to Use the Bayes' Theorem Calculator 1. Enter the required calculator inputs shown in the form. 2. Review the probability, distribution, dataset, contingency table, correlation, regression, or diagnostic assumptions. 3. Run the calculator, then adjust one input at a time to compare scenarios or check your estimate. ## What This Calculator Helps With Apply Bayes' theorem to update a prior probability with new evidence. It is designed for students, teachers, researchers, analysts, gamers, probability learners, science users, and anyone working with statistics who want a fast, browser-based estimate before relying on a spreadsheet, textbook, analytics platform, research software, professional source, or specialist. - Prior Probability P(A) (0–1): 0.3 - Likelihood P(B|A) (0–1): 0.8 - Marginal Probability P(B) (0–1): 0.5 ## Common Uses People use this calculator when they need a quick way to estimate probability, compare statistical assumptions, review distribution values, or check a statistics formula. - **Math Solving:** Solve probability, statistics, distribution, regression, diagnostic, or classroom problems from entered values. - **Measurement:** Measure sensitivity, specificity, predictive values, correlation, probabilities, distribution values, or model estimates. - **Project Planning:** Plan research, surveys, lessons, experiments, dashboards, probability scenarios, or analysis workflows using transparent formulas. ## Formula or Method P(A|B) = P(B|A) × P(A) / P(B) ## Example **Example inputs:** Prior Probability P(A) (0–1): 0.3; Likelihood P(B|A) (0–1): 0.8; Marginal Probability P(B) (0–1): 0.5 **Example result:** Using the default inputs, posterior probability is 48.00%. ## Related Tools - [Normal Distribution Calculator](https://xtraw.com/tools/normal-distribution-calculator) - [Binomial Distribution Calculator](https://xtraw.com/tools/binomial-distribution-calculator) - [Dice Probability Calculator](https://xtraw.com/tools/dice-probability-calculator) - [Coin Flip Probability Calculator](https://xtraw.com/tools/coin-flip-probability-calculator) - [Odds Ratio Calculator](https://xtraw.com/tools/odds-ratio-calculator) - [Relative Risk Calculator](https://xtraw.com/tools/relative-risk-calculator) ## Bayes' Theorem Calculator FAQ ### Is the Bayes' Theorem Calculator free? Yes. This calculator is free to use on XTRAW Tools. ### Do I need to create an account? No. XTRAW tools are designed for browser-based use without requiring an account. ### Are the results exact? Results may be estimates depending on the inputs, formula, rounding, statistical method, probability model, and purpose of the calculator. Always verify important results before relying on them. **Disclaimer:** This calculator is provided for general informational, educational, and convenience purposes only. It is not legal, financial, medical, gambling, academic, research, statistical consulting, safety, or professional advice. 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