Sample Size Calculator

How does the sample size calculator work?

Estimate the number of visitors needed per variant for a two-group conversion-rate experiment. Planning sample size helps you judge whether your available traffic can detect a practically useful change.

How to use this tool

Enter the baseline conversion rate and minimum detectable relative effect as percentages. The calculator uses a two-sided normal approximation, your selected confidence level, fixed 80% statistical power, and equal-sized variants. It returns visitors per variant, rounded up to a whole visitor.

Example

A 10% baseline and 20% relative MDE means detecting a change from 10% to 12%, not from 10% to 30%. At 95% confidence and 80% power, this implementation estimates 3,623 visitors per variant, or 7,246 across two variants.

Understanding your result

Use a baseline above 0% and below 100%, a positive MDE, and a resulting conversion rate below 100%. The approximation assumes independent binary outcomes. It does not adjust for multiple variants, repeated significance checks, or clustered observations. Eighty percent power is a design assumption, not an 80% chance that your hypothesis is true.

Formula used

Let p be the baseline as a decimal, d = p × relative MDE, α = 1 − confidence, and z(q) the standard normal quantile. The unrounded per-variant estimate is:

n = [z(1 − α/2) × √(2p(1 − p)) + z(0.80) × √(p(1 − p) + (p + d)(1 − p − d))]² / d²

This is the approximation used by this tool; calculators using different variance estimates or continuity corrections can return different sample sizes.

Further reading: NIST background on sample size, significance, and power.

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