Free RevOps Tool
Sample Size Calculator (Survey and A/B Test)
How many responses a survey needs, and how many visitors per variant an A/B test takes. Both formulas disclosed, both verified against the standard references, neither hidden behind a signup.
Size the Study Before You Run It
Survey math and test math are different animals. This tool runs both and labels which one you are looking at.
1. Your survey
Responses you need
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- Responses needed
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- Without population correction
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- Assumed proportion
- 50% (worst case)
- Visitors per variant
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- Total visitors (two variants)
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- Variant rate you are testing for
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- Estimated duration
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Survey formula: n = z² × 0.25 ÷ e², with the finite population correction when you give a population. Verified against the standard references.
Sample size is the easy half. Knowing what to test is the hard half.
Get a free conversion auditHow This Calculator Works
For a survey, three choices set the sample: how confident you want to be (the z-score), how much error you can tolerate, and, optionally, how big the population is. At the standard 95% confidence and a ±5% margin of error, the math lands on the canonical 385 responses: n = z² × 0.25 ÷ e², using 0.25 because a 50/50 split is the worst case a survey can face. If the population is small, the finite population correction shrinks the requirement: the same survey inside a population of 1,000 needs 278. Tighten the margin or raise the confidence and the count climbs fast: 99% confidence at ±5% needs 664.
A/B tests answer a different question: not “what does the population think” but “is variant B genuinely better than variant A.” That takes the two-proportion formula, and its defining property is brutal: the required sample grows with the inverse square of the effect you want to detect. Detecting a 20% relative lift on a 5% baseline at 95% confidence and 80% power takes 8,155 visitors per variant, 16,310 in total, about 5 weeks at 4,000 weekly visitors. Halve the effect to a 10% lift and the requirement roughly quadruples. That is not a flaw in the calculator; it is the physics of statistics, and it carries a practical consequence: low-traffic sites should not test button shades. Test bold changes, offers, and page rewrites, where the detectable effect is big enough to reach inside a business quarter.
The formula
| What | The math |
|---|---|
| Survey sample | n = z² × 0.25 ÷ e² |
| Finite population correction | n = n₀ ÷ (1 + (n₀ − 1) ÷ N) |
| z-scores used | 90%: 1.645 · 95%: 1.960 · 99%: 2.576 · power 80%: 0.842 · power 90%: 1.282 |
| A/B sample per variant | n = (zα/2 + zβ)² × (p₁(1−p₁) + p₂(1−p₂)) ÷ (p₂ − p₁)² |
| The inverse-square law | halving the detectable effect ≈ 4× the sample |
Keep the Math Going
The rest of the free RevOps toolkit, and the team that runs this math for clients.
Decide what is worth testing: the click-through lever comes first.
Put a dollar value on the conversion rate you are testing.
Senior operators who design tests your traffic can actually win.
Frequently Asked Questions
How many responses does a survey need?
At the standard 95% confidence level and a ±5% margin of error, 385 responses for a large population; the formula is z-squared times 0.25 divided by the margin of error squared. Small populations need fewer: the finite population correction brings the same survey down to 278 responses in a population of 1,000.
What confidence level should I use?
95% is the working standard for business research: it means that if you repeated the survey many times, 19 in 20 of the resulting intervals would contain the true value. Use 99% when a wrong conclusion is expensive, and accept the larger sample it demands (664 versus 385 at a ±5% margin).
How is A/B test sample size calculated?
From four inputs: the baseline conversion rate, the minimum effect you want to detect, the confidence level, and the statistical power. The two-proportion formula combines them: n per variant = (z-alpha + z-beta) squared, times the summed variances of the two rates, divided by the squared difference between them. This calculator shows the variant rate it is testing against so nothing is hidden.
Why does a smaller effect need a such a bigger test?
Because the sample requirement grows with the inverse square of the effect size. Detecting a 10% lift takes roughly four times the traffic of a 20% lift, and a 5% lift takes roughly sixteen times. The practical read: if your traffic is modest, test changes bold enough to produce effects your traffic can actually detect.
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