Free statistics tool
Free Z Score Calculator
Enter a value, the mean and the standard deviation to get the z score, its percentile and its p-value. Already have a z score? Switch to the second tab to turn it into a percentile or a one- or two-tailed p-value.
Live calculator
Calculate a z score
Z score
1.5
93.32% of values fall below this point.
- Percentile (area to the left)
- 93.32%
- Area to the right
- 6.68%
- One-tailed p-value
- 0.0668
- Two-tailed p-value
- 0.1336
Formula
z = (x - μ) / σ
What is a z score?
A z score tells you how far a value is from the mean, counted in standard deviations. A z score of 0 is exactly the mean. A z score of 2 is two standard deviations above it, and -1 is one standard deviation below it. This lets you compare values from different scales, such as a test score and a page load time, on the same footing.
How to calculate a z score
The formula is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.
Example: a student scores 85 on a test where the mean is 70 and the standard deviation is 10. The z score is (85 - 70) / 10 = 1.5. The score is one and a half standard deviations above the average.
Z score to percentile and p-value
If the data follows a normal (bell-shaped) curve, each z score matches a fixed share of the area under the curve. The area to the left is the percentile: a z score of 1.5 is at the 93.32nd percentile, so 93.32% of values are lower. The area to the right (6.68%) is the one-tailed p-value.
The two-tailed p-value counts both tails: the chance of a result at least this far from the mean in either direction. For z = 1.5 it is 2 × 0.0668 = 0.1336. The well-known cut-off z = 1.96 gives a two-tailed p-value of 0.05. For a test statistic you already have, the p-value calculator walks through the same step.
Z scores in A/B testing
Most A/B test significance calculators run a two-proportion z test. They take the conversion rates of A and B, divide the difference by its standard error, and get a z score. That z score then becomes a p-value, the same way as on this page. If |z| is above 1.96, the result is significant at 95% confidence.
To skip the math, put your visitors and conversions into the A/B test significance calculator. To see the range the real conversion rate is likely in, use the confidence interval calculator.
FAQ
How do you calculate a z score?
Subtract the mean from the value, then divide by the standard deviation: z = (x - μ) / σ. A score of 85 on a test with a mean of 70 and a standard deviation of 10 has a z score of 1.5.
How do I turn a z score into a percentile?
Look up the area to the left of the z score under the standard normal curve. A z score of 1.5 has 93.32% of the area to its left, so it sits at about the 93rd percentile. The calculator above does this lookup for you.
What z score is statistically significant?
For a two-tailed test at 95% confidence, a z score above 1.96 or below -1.96 is significant (p < 0.05). At 99% confidence the cut-off is 2.576, and at 90% it is 1.645.
Can a z score be negative?
Yes. A negative z score means the value is below the mean. A z score of -1 is one standard deviation below the mean and sits at about the 16th percentile.
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