1
Enter the distribution
Add the raw value, mean, and a standard deviation greater than zero.
Free Z Score Calculator
A z-score calculator shows how many standard deviations a raw value is above or below the mean. Enter a value, mean, and standard deviation to see the formula steps, percentile, and normal-model tail areas.
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Standard score calculator
Enter the score and distribution
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Z-score result
z = 2.00
The value is 2.00 standard deviations above the mean.
Percentile · area left
97.72%
Area to the right
2.28%
One tail beyond |z|
2.28%
Two tails beyond ±|z|
4.55%
Step-by-step work
- 1. Use z = (x - μ) / σ.
- 2. Substitute: (85.00 - 75.00) / 5.00.
- 3. Subtract: 10.00 / 5.00.
- 4. Divide: z = 2.00.
Percentile and tail values are estimates from a continuous normal distribution. A real data set may not follow that model.
How to Use the Z Score Calculator
2
Follow the formula
See subtraction and division substituted into z = (x - mean) / standard deviation.
3
Read the context
Use the labeled percentile and tail estimates only when a normal model is appropriate.
Frequently Asked Questions
What is a z-score calculator?
A z-score calculator shows how many standard deviations a value is above or below a distribution's mean using z = (x - mean) / standard deviation.
What does a positive or negative z-score mean?
A positive z-score is above the mean, a negative z-score is below the mean, and a z-score of zero is exactly at the mean.
How do I convert a z-score to a percentile?
Use the cumulative normal distribution. The resulting area to the left, multiplied by 100, is the approximate percentile under a normal model.
What is the difference between one-tailed and two-tailed probability?
A one-tailed probability measures outcomes beyond the score in one direction. A two-tailed probability includes equally extreme outcomes in both directions.
Can a z-score be greater than 3?
Yes. A z-score can have any real value, though scores beyond plus or minus 3 are uncommon in a normal distribution.
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