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Twenty percent to thirty percent
The control converts at 20 percent. You hope the new page converts at 30 percent. Use 1.96 for two-sided 95 percent significance and 0.84 for 80 percent power. Keep two variants.
Baseline conversion rate: 25% lower
Change baseline conversion rate to 15 % while keeping the other example values the same.
Baseline conversion rate: 25% higher
Change baseline conversion rate to 25 % while keeping the other example values the same.
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Quick answer
What does the A/B test sample size calculate?
How many visitors per variant detect a conversion-rate change at the power you type? This calculator uses baseline conversion rate, expected conversion rate, significance z (two-sided 95% is 1.96), power z (80% power is 0.84), and variants including control to estimate visitors each variant needs immediately in your browser.
With the values currently entered, the result is 291 — visitors per variant. It also shows total visitors, absolute lift, and variants.
How to use the A/B test sample size
- Replace the example values with your own numbers.
- Review the result and supporting figures as they update automatically.
- Check the formula and assumptions before using the estimate for a decision.
Inputs used
- Baseline conversion rate — entered in %
- Expected conversion rate — entered in %
- Significance z (two-sided 95% is 1.96) — entered in z
- Power z (80% power is 0.84) — entered in z
- Variants including control — entered in variants
A/B test sample size formula
n = (zα + zβ)² × (p1(1−p1) + p2(1−p2)) ÷ (p1−p2)² per variant. p1 and p2 are the two conversion rates. Equal traffic is assumed.
Assumptions
- NIST publishes the normal-approximation sample-size method for a change in a proportion. The two-variant form uses both conversion variances.
- Traffic splits evenly. Stopping early, extra variants beyond the count you type, and a later holdout sit outside this figure.
Verify the inputs
Authoritative sources
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Sources do not endorse Calculum. Check the source date, scope, and your own documents before making a financial, tax, insurance, or reporting decision.
Practical guide
A/B test sample size example and edge cases
Sample size tells you how many visitors each variant needs before a conversion change is likely to show up. NIST publishes the normal-approximation method for a change in a proportion. The two-variant form uses both conversion rates, plus a z for confidence and a z for power.
Example: Twenty percent to thirty percent
The control converts at 20 percent. You hope the new page converts at 30 percent. Use 1.96 for two-sided 95 percent significance and 0.84 for 80 percent power. Keep two variants.
- Baseline conversion rate
- 20 %
- Expected conversion rate
- 30 %
- Significance z (two-sided 95% is 1.96)
- 1.96 z
- Power z (80% power is 0.84)
- 0.84 z
- Variants including control
- 2 variants
Calculated result291visitors per variant
Each variant needs 291 visitors. The pair needs 582. If you want revenue from a visitor count you already have, open the conversion funnel calculator.
Example results use the default display profile. The calculator above follows your selected country and units.
How to read the result
- Read visitors per variant first. Then check the total. A third variant multiplies the same per-variant count again.
- A smaller lift needs more visitors. The gap sits in the denominator, so 20 percent to 22 percent needs a much larger sample than 20 percent to 30 percent.
Edge cases worth checking
You keep peeking at the dashboard
The formula assumes you stop once. Early looks raise false wins. Recalculate with a higher significance z if you will peek, or wait for the count.
Traffic will not split evenly
This page assumes equal traffic. If 70 percent stays on control, the smaller variant still needs its 291 visitors, and the test takes longer.
What changes the result most
Baseline conversion rate
Test a lower and higher baseline conversion rate. A small percentage change can move the final result more than expected.
Expected conversion rate
Test a lower and higher expected conversion rate. A small percentage change can move the final result more than expected.
Significance z (two-sided 95% is 1.96)
Change significance z (two-sided 95% is 1.96) on its own first. This shows how strongly it affects the answer.
Try a different scenario
Small changes show whether the answer is stable or sensitive.
Baseline conversion rate: 25% lower
15 %118visitors per variant
Baseline conversion rate: 25% higher
25 %1,247visitors per variant
Expected conversion rate: 25% higher
38 %96visitors per variant
Common mistakes
Check baseline conversion rate
NIST publishes the normal-approximation sample-size method for a change in a proportion. The two-variant form uses both conversion variances. Make sure this matches the number you enter.
Keep variants including control consistent
Traffic splits evenly. Stopping early, extra variants beyond the count you type, and a later holdout sit outside this figure. Use the same units and time period throughout the calculation.
Do not rely on one a/b test sample size scenario
Run a cautious case and an optimistic case. The range is often more useful than one exact-looking number.
Use this result well
How many visitors per variant detect a conversion-rate change at the power you type?
It does not replace a quote, contract, accountant, or local employment guidance.