Proportion Z-Test Calculator
Tests whether a percentage differs from a set value, or two percentages differ from each other.
p-value
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
z statistic —
Difference — points
Reading this —
The formula
One group: z = (p − p₀) ÷ √(p₀(1 − p₀) ÷ n) Two groups: z = (p₁ − p₂) ÷ √(p(1 − p)(1/n₁ + 1/n₂))
In the two-group test, p is the pooled proportion across both groups. A two-group, two-sided z-test gives the same p-value as a chi-square test on the same 2×2 table.
What to watch out for
For the difference between two conversion rates, this is the same calculation that an A/B test uses.
Frequently Asked Questions
What is a worked example?
45 of 100 against 30 of 100 gives z = 2.191 and a two-sided p of 0.02846.
Is a difference of 15 points “15%”?
No. It is 15 percentage points. As a relative change from 30%, it is 50%.