Z-Score Calculator
Calculate z-scores and find probabilities using the standard normal distribution.
Result
Fill in the fields above, then press Calculate.
A z-score calculator converts between raw scores and standard deviations from the mean, essential for statistical hypothesis testing.
Examples
Test score
Score 85, mean 75, std dev 10: Z = (85-75)/10 = 1.0, meaning 84.13th percentile
Below average
Score 60, mean 75, std dev 10: Z = -1.5, meaning 6.68th percentile
From probability
Want 95th percentile with mean 100, std dev 15: Z = 1.645, value = 124.67
Frequently Asked Questions
What is a z-score?
A z-score tells you how many standard deviations a value is from the mean. A z-score of 1 means the value is one standard deviation above the mean.
What is the 68-95-99.7 rule?
In a normal distribution, about 68% of data falls within 1 std dev of the mean, 95% within 2, and 99.7% within 3 standard deviations.
What does a negative z-score mean?
A negative z-score means the value is below the mean. For example, Z = -2 means the value is 2 standard deviations below the mean.
Result
Your result appears here and follows you as you scroll.
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Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Use the 68-95-99.7 rule as a quick sanity check for your z-score.
- •Remember that a z-score of 0 means the value equals the mean.