Calculate an approximate confidence interval for the difference between two independent A/B conversion rates. Enter conversions and sample size for the control and variant, and the calculator reports the observed percentage-point difference with a two-sided normal confidence interval. The interval shows a range of effect sizes compatible with the observed data under the model. It is more informative than a single point estimate because it exposes uncertainty: a narrow interval indicates more precision, while an interval crossing zero means the data do not clearly separate a positive from a negative difference at the selected confidence level.
1. Enter control counts
Provide the number of conversions and analyzed observations for the control group.
2. Enter variant counts
Provide the matching counts for the tested variant.
3. Choose confidence
Set the two-sided confidence level you want reported.
4. Review the effect
Read the main result as variant rate minus control rate in percentage points.
5. Inspect the interval
Use the lower and upper bounds to judge the precision and plausible direction of the effect.
p1 and p2 are the observed conversion proportions, n1 and n2 are the analyzed sample sizes, and α = 1 − confidence level. The interval is displayed in percentage points.
This Wald-style normal interval is simple and useful for large samples with non-extreme rates. For very small samples or rare events, alternative interval methods or exact procedures may be more appropriate.
Use the main result together with the supporting statistics and the stated assumptions; it is a planning estimate rather than a guarantee.
Keep units and the unit of analysis consistent. Recalculate when traffic patterns, rates, priors, sample sizes, or design assumptions change.
Given
Calculation
Control rate = 10%; variant rate = 11%; difference = 1.00 percentage point. SE ≈ 0.00435, so 95% CI ≈ 0.0100 ± 1.96 × 0.00435 = [0.0015, 0.0185].
Result
Difference: +1.00 pp; 95% CI: about +0.15 to +1.85 pp
Interpretation
The interval stays above zero, so the observed uplift is statistically distinguishable from zero at the approximate 95% confidence level.
The data are compatible with both positive and negative differences at that confidence level. That corresponds to not rejecting a zero difference with the matching two-sided normal test.
No. Moving from 10% to 11% is +1 percentage point but a +10% relative lift.
No for a binary conversion metric where each observation converts at most once. The calculator rejects counts above the corresponding sample size.
In frequentist terms, the 95% refers to the long-run coverage of the interval procedure under repeated samples. It is not a direct posterior probability statement about this one fixed interval.
Different products may use pooled, unpooled, Wilson, score, Bayesian, or bootstrap methods. These can produce different bounds, especially with smaller samples or extreme rates.