Value to z and percentile
Z-Score Calculator: z, Percentile and P-Value
Enter a value, the mean and the standard deviation to get the z-score, the percentile, the area to the right and the two-tailed p-value, shaded on a normal curve.
z = 1.5000
85 is 1.50 standard deviations above the mean of 70. About 93.32% of a normal distribution falls below it.
z = (x − μ) ÷ σ = (85 − 70) ÷ 10.
Every value is calculated in your browser from the standard normal distribution (Marsaglia’s series for Φ) and rounded to four decimals; the tables were checked cell by cell against an independent calculation. These tables give the area to the left of z. Some textbooks, including the NIST handbook, print the area from 0 to z instead, which is the left area minus 0.5 for positive z.
The z-score formula
z = (x − μ) ÷ σ. A test score of 85 in a class with a mean of 70 and a standard deviation of 10 is z = 1.5, which is above about 93.32% of a normal distribution.
- Positive z means above the mean; negative z means below it.
- Use the standard error σ ÷ √n instead of σ when x is a sample mean.
Common questions
How do I convert a z-score to a percentile?
Look up the area to the left of z and multiply by 100. z = 1.5 has a left area of 0.9332, the 93rd percentile.
What is a two-tailed p-value?
The probability of a result at least as far from the mean in either direction: twice the area beyond |z|. For z = 1.96 it is 0.05.
The studio notebook
A useful place to begin.
Clear steps, considered details, and ideas you can put to use.
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T Table vs Z Table: Which One to Use and How to Read It
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How to Read a Chi-Square Table (df, Critical Values, p-Values)
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