Z-Score Calculator
Turn a raw value into a z-score: how many standard deviations it sits above or below the mean. Enter the value, mean, and standard deviation to get the z-score, its percentile on the normal curve, and a two-tailed p-value, updated as you type.
How to calculate a z-score
- Enter the raw value (the data point you want to score).
- Enter the mean and the standard deviation of the distribution.
- Read the z-score, percentile, and p-value, plus the sentence explaining what they mean.
Examples
A test score of 85
value = 85, mean = 70, sd = 10
z = 1.5, percentile ≈ 93rd, two-tailed p ≈ 0.1336
A value at the mean
value = 70, mean = 70, sd = 10
z = 0, percentile = 50th (right in the middle)
Frequently asked questions
What is a z-score?
A z-score, or standard score, tells you how many standard deviations a value lies from the mean. It is calculated as (value minus mean) divided by the standard deviation. A z-score of 0 sits exactly at the mean, a positive score is above it, and a negative score is below it.
How do I turn a z-score into a percentile?
The percentile is the percentage of a normal distribution that falls at or below the z-score. This calculator uses the standard normal cumulative distribution function, so a z of 0 maps to the 50th percentile, 1.0 to about the 84th, and 1.96 to roughly the 97.5th.
What is the two-tailed p-value?
The two-tailed p-value is the probability of observing a value at least as far from the mean as yours, in either direction, if the data really followed the normal distribution. A z of 1.96 gives a p-value near 0.05, the common threshold for statistical significance.
What counts as a high or unusual z-score?
There is no fixed cutoff, but roughly 68% of values fall within one standard deviation of the mean, 95% within about two, and 99.7% within three. So a z-score beyond plus or minus 2 is fairly uncommon, and beyond plus or minus 3 is rare.
Can the z-score be negative?
Yes. A negative z-score simply means the value is below the mean. The size of the number, ignoring the sign, tells you how far it is from the mean, so a z of -2 is just as far out as a z of +2, only on the lower side.
Is my data sent anywhere?
No. Every calculation runs entirely in your browser, so the numbers you enter never leave your device.
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