Z-Score Calculator
Standardize a value, work backward from a z-score or percentile, and see the result on a normal curve. A data set can supply the mean and standard deviation.
Choose what to calculate
Separate values with commas, spaces, semicolons or new lines. For decimal commas, use one value per line or semicolons. Invalid values are never skipped. Up to 500 values.
Your result
Where the value lies on the normal curve
The shaded probability is based on a normal distribution model, not a guarantee about the real data.
Empirical percentile uses the midrank method: (values below x + half of values equal to x) ÷ number of values × 100. It can differ from the normal-model percentile.
How the result was calculated
What is a z-score?
A z-score is the number of standard deviations between a value and the mean. Positive values are above the mean; negative values are below it.
z = (x − x̄) ÷ s
x = μ + z × σ
z = Φ⁻¹(p ÷ 100)
Normal-model probabilities assume a normal distribution. Do not apply the 68–95–99.7 rule automatically to skewed or multimodal data.
Empirical percentile uses the midrank method: (values below x + half of values equal to x) ÷ number of values × 100. It can differ from the normal-model percentile.
Z-score questions
What is a z-score?
A z-score is the number of standard deviations between a value and the mean. Positive values are above the mean; negative values are below it.
Are normal-model and empirical percentiles the same?
Not necessarily. The normal-model percentile assumes a normal distribution. The empirical percentile counts the positions of the actual values you entered.
Should I choose sample or population standard deviation?
Choose sample for a subset used to estimate a larger group; choose population when the data contain the entire group of interest.
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