A/B Testing Screen Resolution Per-User Formula
Learn how to estimate the number of users required in each A/B test variation for a conversion-rate experiment.
This calculation estimates the per-variation sample size needed to detect a chosen absolute conversion-rate change. It combines the baseline conversion rate, minimum detectable effect, confidence level, and statistical power to help plan an evenly split A/B test.
- 100% Free
- No Sign-Up Required
- Private & Secure
- Mobile Friendly
Users Needed Per Variation
Where:
The formula estimates how many eligible users each group needs to reliably distinguish the baseline conversion rate from the target conversion rate. Smaller changes and stricter confidence or power settings increase the required number.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| n - Users per variation | Estimated minimum number of eligible users required in the control group and separately in the treatment group. | users |
| p₁ - Baseline proportion | The control conversion rate expressed as a decimal proportion. | number |
| p₂ - Treatment proportion | The expected treatment conversion rate after adding the selected absolute change. | number |
| p̄ - Pooled proportion | The average of the baseline and treatment proportions. | number |
| effectSize - Conversion-rate difference | The absolute difference between treatment and baseline proportions. | number |
| significanceZ - Significance z-value | The z-value representing the selected two-sided confidence level. | N/A |
| powerZ - Power z-value | The z-value representing the selected statistical power. | N/A |
Step-by-Step Calculation
Convert the baseline rate to a proportion
A conversion rate entered as a percentage is converted to a decimal for the sample-size calculation.
baselineProportion = baselineConversionRate / 100
Set the target treatment rate
The calculator adds the absolute percentage-point change to the baseline rate.
treatmentProportion = (baselineConversionRate + minimumDetectableEffect) / 100
Find the pooled proportion
This average is used in the normal approximation for two conversion proportions.
pooledProportion = (baselineProportion + treatmentProportion) / 2
Calculate the detectable difference
This is the decimal version of the minimum detectable effect.
effectSize = treatmentProportion - baselineProportion
Estimate the unrounded group size
The calculation combines sampling variation, the chosen confidence threshold, and desired power.
usersPerVariationRaw = pow((significanceZ * sqrt(2 * pooledProportion * (1 - pooledProportion)) + powerZ * sqrt(baselineProportion * (1 - baselineProportion) + treatmentProportion * (1 - treatmentProportion))) / effectSize, 2)
Round up and find total traffic
Each group is rounded up to a whole user, then doubled for an equal 50/50 A/B allocation.
usersPerVariation = ceil(usersPerVariationRaw); totalUsersNeeded = usersPerVariation * 2
Example: Detecting a 1 percentage-point signup increase
Convert baseline
10 / 100
0.10
Calculate treatment proportion
(10 + 1) / 100
0.11
Calculate pooled proportion
(0.10 + 0.11) / 2
0.105
Calculate effect size
0.11 - 0.10
0.01
Estimate and round group size
ceil(pow((1.96 * sqrt(2 * 0.105 * 0.895) + 0.84 * sqrt(0.10 * 0.90 + 0.11 * 0.89)) / 0.01, 2))
14,739 users per variation
Calculate total users
14,739 * 2
29,478 users
Final Result
Plan for approximately 14,739 eligible users in each variation, or 29,478 users in total.
Assumptions
- ✓The experiment compares two independent variations with an equal 50/50 split of eligible users.
- ✓The primary metric is binary, such as a signup, purchase, or completed form.
- ✓The selected change is an absolute conversion-rate difference in percentage points.
- ✓The calculation uses a two-sided normal approximation.
- ✓Each counted user has one independent conversion opportunity.
Limitations
- !Actual traffic requirements may change when allocation is uneven, users are excluded, or the analysis method differs.
- !Very low conversion rates or sparse expected conversions can make a normal approximation less suitable.
- !The estimate does not account for repeated interim checks, multiple metrics, or multiple comparisons.
- !A sufficient sample size does not guarantee that the observed result will be practically useful or free from implementation issues.
Common Mistakes to Avoid
Entering a relative lift as though it were an absolute percentage-point change.
Using total users as the requirement for each variation instead of dividing traffic between control and treatment.
Confusing 95% confidence with 95% statistical power.
Changing the primary metric or eligibility rules after the test begins.
Stopping a test early solely because an interim result appears favorable.
Related Formulas
Frequently Asked Questions
What does per user or per variation mean in this calculator?
It means the estimated number of eligible users needed in the control group and the same number needed in the treatment group.
Is a 1% minimum detectable effect the same as a 1% relative lift?
No. Here, 1 means one absolute percentage point, such as a change from 10% to 11%. A 1% relative lift from 10% would be 10.1%.
Why does the sample size rise sharply for smaller effects?
Small conversion differences are harder to separate from ordinary random variation, so more users are needed.
How do confidence and power affect the formula?
Higher confidence or higher power uses larger z-values, which increases the estimated users per variation.
Can this formula be used for more than two variations?
It is designed for one control and one treatment. Tests with more variations need additional planning for allocation and multiple comparisons.
Ready to calculate your result?
Use the calculator to get instant results with your own inputs.