How to use this calculator
- Enter or choose baseline conversion rate.
- Enter or choose minimum detectable effect.
- Enter or choose effect is.
- Enter or choose significance level α.
- Enter or choose power.
- The visitors per variant updates as you type. Use Copy result or Share to keep it.
Method
n = (z_α √(2p̄(1 − p̄)) + z_β √(p₁(1 − p₁) + p₂(1 − p₂)))² ÷ (p₂ − p₁)², p̄ = (p₁ + p₂) ÷ 2; round up
- p₁
- baseline rate
- p₂
- baseline plus the minimum detectable effect
- z_α
- z₁₋α/₂ (two-sided) or z₁₋α (one-sided)
- z_β
- normal quantile of the power
Worked example
- p₁ = 0.10, p₂ = 0.12, p̄ = 0.11; z_α = 1.96, z_β = 0.8416.
- Numerator: (1.96 × √(2 × 0.11 × 0.89) + 0.8416 × √(0.09 + 0.1056))² = 1.53634.
- n = 1.53634 ÷ 0.02² = 3840.85 → 3,841 per variant.
Detecting a lift from 10% to 12% needs 3,841 visitors per variant, 7,682 in total.
What the result means
Divide the total by your daily eligible traffic to estimate the test duration, and run whole weeks to average out weekday effects. If the duration is impractical, test a bolder change with a larger effect.
Assumptions and limits
- Equal traffic split and the pooled two-proportion z-test; matches R’s power.prop.test.
- Assumes you look at the result once, at the planned sample size.
- Not for revenue or other continuous metrics, which need their variance.
Questions
Relative or absolute effect?
A 20% relative lift on a 10% baseline is the same as a 2-point absolute lift: both target 12%.
Why does a low baseline need so many visitors?
Rare events carry little information each, and small absolute differences need large samples: required n grows with 1 ÷ (effect)².