Proportion z-test calculator

Test whether a percentage differs from a claimed value, or whether two groups' percentages differ, with the p-value, confidence interval and every step.

  • Free, no sign-up
  • Step-by-step working
  • Runs in your browser

Not sure this is the right tool? Find the right one

  1. 1 Enter your data
  2. 2 Choose an option
  3. 3 Click “Run z-test”
  4. 4 Read the result

Tip: You can paste values copied from Excel, Google Sheets or a report instead of typing them.

These are example values so you can see how the tool works. Replace them with your own, then press the button.

Choose your test

Which test?

Enter your counts

Options (the defaults suit most tests)

Your result

How to use the proportion z-test calculator

  1. Choose two proportions to compare two groups (for example an A/B test), or one proportion to compare a sample with a claimed value.
  2. Enter the number of successes and the sample size for each group, and for one proportion the value you're testing against (p₀).
  3. Keep the two-tailed test at α = 0.05 unless your hypothesis named a direction in advance, then click Run z-test.
  4. Read the p-value and decision, the confidence interval and, for two groups, the difference and relative lift.
  5. Check the conditions box: the test needs at least 10 expected successes and failures in each group.

Proportion z-test formulas

One proportion, comparing the sample proportion with p₀:

z = p − p0p0(1 − p0)n , p = xn

Two proportions, using the pooled proportion under the null hypothesis that both groups share the same rate:

z = p2 − p1pc(1 − pc)(1n1 + 1n2) , pc = x1 + x2n1 + n2

p
The sample proportion: successes divided by the sample size
p0
The proportion in the null hypothesis (one-proportion test)
p1, p2
The proportions in group 1 and group 2
pc
The pooled (combined) proportion of both groups, used for the test's standard error
x, n
The number of successes and the sample size
z
The test statistic: how many standard errors the observed difference is from the null value

Worked example

A coin lands heads 30 times in 50 flips. Is that evidence the coin favors heads (more than 50%)?

  1. Sample proportion
    p = 3050 = 0.6
  2. Check conditions: np₀ = 25 and n(1 − p₀) = 25 are both at least 10
  3. Standard error under the null, then z
    z = 0.6 − 0.50.5 × 0.550 = 0.10.0707 = 1.414
  4. One-tailed p-value (greater than)
    p = P(Z ≥ 1.414) = 0.0786

What it means: p = 0.079 is above 0.05, so 30 heads in 50 flips isn't strong evidence of a biased coin. A fair coin gives 30 or more heads about 8% of the time. With 300 heads in 500 flips (the same 60%), z would be 4.47 and the result highly significant: sample size matters.

How to interpret the result

  • p ≤ α: the difference is statistically significant: unlikely to be due to chance alone.
  • The confidence interval gives the plausible range for the true proportion (or the true difference). If the interval for a difference excludes 0, the two-tailed test is significant at the same level.
  • The relative lift (two groups) expresses the difference as a percentage of group 1's rate, which is how A/B test results are usually reported.
  • Significant isn't the same as important. With huge samples, a 0.1-point difference can be significant; judge whether the size of the difference matters in practice.

Planning a survey or test? The sample size calculator tells you how many responses you need. For a confidence interval on its own, use the confidence interval calculator.

Frequently asked questions

When do I use a proportion z-test?

When your data are yes/no outcomes and you are comparing percentages. A one-proportion test compares one sample percentage with a claimed value, such as whether 58% of 100 voters is really more than half. A two-proportion test compares two groups, such as the conversion rates of two versions of a web page (an A/B test) or the share of students passing under two teaching methods.

What are the conditions for a proportion z-test?

The data should be a random sample (or randomly assigned groups), observations independent (the sample less than 10% of the population when sampling without replacement), and the sample large enough for the normal approximation: at least 10 expected successes and 10 expected failures. For one proportion, check np₀ and n(1 − p₀); for two proportions, check each group with the pooled proportion. The calculator checks the counts for you.

Why does the two-proportion test use a pooled proportion?

The null hypothesis says both groups share the same true proportion, so the test combines them to estimate it: p̂c = (x₁ + x₂) / (n₁ + n₂). That pooled value gives the standard error under the null. The confidence interval for the difference doesn’t assume the proportions are equal, so it uses each group’s own proportion instead (unpooled).

What is the difference between a proportion z-test and a chi-square test?

For two groups and a yes/no outcome, the two-sided two-proportion z-test and the chi-square test of independence on the 2×2 table give exactly the same p-value: χ² equals z². The z-test can also be one-sided and gives a confidence interval for the difference. For more than two groups or outcomes, use the chi-square test.

Is a proportion z-test the same as an A/B test calculator?

Yes, for conversion rates. Enter the visitors (n) and conversions (x) for version A as group 1 and version B as group 2. The result gives the p-value, the confidence interval for the difference in conversion rate, and the relative lift. Decide the sample size before the test starts, and avoid stopping as soon as the result looks significant: peeking inflates false positives.

How do I run a proportion z-test on a TI-84?

Press STAT, move to TESTS, and choose 5:1-PropZTest or 6:2-PropZTest. Enter p₀ (one-proportion only), x and n for each group, pick the alternative and choose Calculate. The z and p-values match this calculator. A:1-PropZInt and B:2-PropZInt give the confidence intervals.

Last reviewed November 13, 2026