Z-Score Calculator
Calculate z-scores from raw values and convert z-scores to p-values and percentiles using the standard normal distribution.
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Z-score
1.5
Above the mean by 1.5 standard deviations.
P-value (one-tailed)
0.066807
P-value (two-tailed)
0.133614
Percentile
93.32%
Frequently Asked Questions about the Z-Score Calculator
What is a z-score?
A z-score (standard score) tells you how many standard deviations a value sits above or below the mean. Z = (x - mean) / stdDev. A z of 0 equals the mean; +1 is one standard deviation above.
What is the standard normal distribution?
A normal distribution with mean 0 and standard deviation 1. Any normally distributed variable can be converted to z-scores to compare across different scales.
What is the difference between a one-tailed and two-tailed p-value?
One-tailed tests whether the value is significantly larger (or smaller) than expected in one direction. Two-tailed tests for deviation in either direction and is roughly double the one-tailed value.
Why is z = 1.96 important?
A two-tailed z of 1.96 gives p = 0.05, the classic 95 percent significance threshold. About 95 percent of values in a normal distribution fall within plus or minus 1.96 standard deviations of the mean.
How accurate is the p-value?
The calculator uses the Abramowitz and Stegun 7.1.26 erf approximation, accurate to about 1.5e-7, more than enough for typical statistics work.