Bayesian A/B Test Calculator

Compare two conversion variants with posterior probability under a visible beta prior.

At a glance

Computes
P(B beats A), median lift, and a credible interval, by Monte Carlo.
You supply
Conversions and visitors for both variants, plus the beta prior you choose.
Use when
You want the probability that one variant is better, stated directly.
Not for
Reporting a frequentist p-value or a significance verdict. A/B Test Calculator
A
B

P(B beats A)

Enter counts

Uses a visible beta prior.

Posterior mean A

0%

Posterior mean B

0%

Posterior density against Conversion rate

0.00.20.40.60.81.002468101214Posterior mean APosterior mean BVariant A posteriorVariant B posterior

Posterior density against Lift, B minus A

−1.0−0.50.00.51.002468Median liftPosterior lift density
Posterior details
MetricValue
Export

posterior = Beta(alpha + conversions, beta + visitors - conversions) How?

How this is calculated

Each conversion rate has a beta prior and binomial likelihood. The calculator samples paired posterior rates with a deterministic seed, reports the share where B is greater than A, and uses empirical quantiles for the difference interval.

Formula: posterior = Beta(alpha + conversions, beta + visitors - conversions)

Sources

  1. Evan Miller Formulas for Bayesian A/B Testing. Evan Miller. Retrieved .
  2. Bayesian Data Analysis. Columbia University. Retrieved .

Method last reviewed