A/B Test Calculator

Is Variant B Actually Better, or Did It Just Get Lucky?

Two variants rarely produce identical conversion rates even when they perform identically in reality — random variation in who happens to visit and convert guarantees some difference every time. An A/B test calculator exists to answer the harder question underneath the raw numbers: is the observed gap large enough, given the sample sizes involved, to trust as a real effect rather than statistical noise?

The Formula

Rate A = Conversions A / Visitors A
Rate B = Conversions B / Visitors B
Pooled Rate = (Conversions A + Conversions B) / (Visitors A + Visitors B)
Standard Error = √(Pooled Rate × (1 − Pooled Rate) × (1/Visitors A + 1/Visitors B))
Z-Score = (Rate B − Rate A) / Standard Error

This is a two-proportion z-test. The Z-score is converted into a p-value using the standard normal distribution, and the result is compared against the confidence level you set.

Worked Example

Consider a test where Variant A converts 520 of 10,000 visitors and Variant B converts 610 of 10,000 visitors:

Two-proportion z-test worked through
QuantityValue
Rate A5.2%
Rate B6.1%
Pooled rate5.65%
Standard error0.00327
Z-score2.7563
Two-tailed p-value0.0058
Confidence achieved99.42%

At a 95% confidence threshold, this result is statistically significant — the achieved confidence of 99.42% clears the bar.

Standard Z-Score Thresholds

Critical z-values for common two-tailed confidence levels
Confidence LevelCritical Z-Score
90%1.645
95%1.960
99%2.576

If the calculated |Z-Score| exceeds the critical value for your chosen confidence level, the result is statistically significant.

Note: Statistical significance confirms an effect is unlikely to be random noise — it does not by itself guarantee the effect is large enough to matter commercially. Check the magnitude with the Conversion Lift Calculator alongside this test.

How to Use This Calculator

  1. Enter Variant A Visitors and Variant A Conversions.
  2. Enter Variant B Visitors and Variant B Conversions.
  3. Set your desired confidence level (95% is the common default).
  4. Select Calculate to get the z-score, p-value, achieved confidence, and whether the result is statistically significant.

Related Calculations

Once significance is confirmed, quantify the size of the win with the Conversion Lift Calculator.