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Z-Score Calculator

Free z-score calculator: enter a value, mean and standard deviation to get the z-score and percentile rank for test scores and growth charts.

A z-score (also called a standard score) tells you how many standard deviations a value is above or below the mean of a dataset. With x = 85, a mean of 70 and a standard deviation of 10, the z-score is 1.5 — the value sits 1.5 standard deviations above average, near the 93rd percentile.

This z-score calculator computes the z-score, the percentile rank and the distance from the mean in one step. Students use it for statistics homework, teachers check test scores, and health workers compare growth measurements to reference tables.

The percentile is calculated from the standard normal distribution, so it assumes your data follows a bell-shaped curve — a reasonable assumption for many test scores and biological measurements.

Enter the value, mean and standard deviation; the z-score, percentile and badge update instantly.

The standard deviation measures how spread out the data is around the mean. Natural data usually has a positive standard deviation below the magnitude of the mean (e.g. test scores are often 5-15). A smaller standard deviation makes the same distance produce a larger z-score: with σ = 5, a 15-point gap gives z = 3; with σ = 15, only z = 1.
Example
Example: Test Score of 85

A class has a mean score of 70 with a standard deviation of 10. A student scores 85:

z = (85 − 70) / 10 = 1.5
Percentile = Φ(1.5) ≈ 93.3%

The student outperformed about 93.3% of the class (6.7% scored higher). The score sits 15 points above the mean.

Key Insight: A z-score of 2 or more means the value is well above average — about 97.7% of the data falls below it in a normal distribution. Values with |z| above 2 are often flagged as unusual in quality control and medicine.

Frequently Asked Questions

What is a z-score?

A z-score is the number of standard deviations a value is from the mean. A z-score of 0 means the value equals the mean, positive means above average, negative means below average.

How do I interpret a z-score of 2?

A z-score of 2 means the value is 2 standard deviations above the mean. In a normal distribution this is about the 97.7th percentile — only about 2.3% of values are higher.

What is the z-score formula?

z = (x − μ) / σ, where x is the value, μ is the mean and σ is the standard deviation. The percentile is then read from the standard normal distribution.

How are z-scores used in medicine?

Pediatric growth charts (WHO) express weight, height and BMI as z-scores relative to a healthy reference population. A weight-for-age z-score below −2 indicates underweight, above +2 indicates overweight; the same formula applies with the reference mean and standard deviation.

The percentile assumes a normal distribution; the z-score itself is defined for any dataset. Medical thresholds (e.g. WHO growth standards) use their own reference means and standard deviations. For small samples, verify the distribution before interpreting percentiles.

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