How unusual is one value?
A z-score says how many standard deviations a value sits above or below the mean. A z of 0 is exactly average, +1 is one deviation above, -2 is two below. This calculator returns the z-score and, assuming a normal distribution, the percentile and the probabilities to either side.
The formula
z = (x minus the mean) divided by the standard deviation. Subtracting the mean recenters the value at zero; dividing by the standard deviation rescales it into deviation units, so scores from different distributions become directly comparable.
Reading the percentile
The percentile is the share of a normal population falling below your value. A z of 1.5 lands near the 93rd percentile, meaning about 93 percent score lower and roughly 7 percent score higher. The two-tailed figure counts both tails -- values at least that far from the mean in either direction.
Related tools
To find the standard deviation first, use the standard deviation calculator; for general event odds, the probability calculator.
Worked example
A score of 85 in a distribution with mean 70 and standard deviation 10 gives z = 15 / 10 = 1.5, about the 93rd percentile, with roughly 6.7 percent scoring higher.
FAQ
Do the probabilities assume a normal curve?
Yes. The z-score itself needs no assumption, but the percentile and tail probabilities here use the standard normal distribution.
What does a negative z mean?
The value is below the mean. The size still tells you how far -- a z of -2 is as extreme as +2, just on the low side.