Z Score Calculator – Find Standard Scores Easily

A z-score tells you how far a value is from the mean of a dataset, measured in standard deviations. This calculator uses the formula z = (x − μ) / σ to return that number directly.

When to use this calculator

You're comparing a single observation to a normal distribution.
You need to standardise exam scores or test results across different scales.
You're checking whether a data point is unusual or an outlier.

How it works

The formula is z = (x − μ) / σ, where x is your value, μ is the population mean, and σ is the standard deviation. A z of 0 means the value equals the mean; positive z is above the mean, negative z is below. In a normal distribution, about 68% of values fall within ±1, 95% within ±2, and 99.7% within ±3.

Real-world examples

Exam scoring: a student scores 78 when the class mean is 70 with σ = 5 → z = 1.6, putting the score in the top ~5%.
Quality control: a product weighs 502 g when the production mean is 500 g with σ = 1 → z = 2.0, just inside tolerance.
Heights: a person at 190 cm in a population with μ = 175 and σ = 7 → z ≈ 2.14, taller than ~98% of people.

Limitations

Assumes the data follows (or approximates) a normal distribution.
Requires the true population mean and standard deviation, not a small sample.
For small samples, use a t-score instead of a z-score.
A z-score alone does not tell you why a value is high or low.

Frequently asked questions

What is a z-score?

It is the number of standard deviations a value sits above or below the mean of a distribution. It standardises raw scores so they can be compared across different scales.

What does a negative z-score mean?

It means the value is below the mean. A z-score of −1.5 sits one and a half standard deviations below average.

What is considered a 'high' z-score?

By convention, |z| greater than 2 is uncommon and |z| greater than 3 is rare in a normal distribution. Outlier cut-offs are usually set around ±2 or ±3.

When should I use a z-score vs a t-score?

Use a z-score when you know the true population mean and standard deviation, or your sample is large. Use a t-score for small samples where you only have sample statistics.

Can I use this for non-normal data?

You can compute z, but its interpretation in terms of percentiles only holds when the data is approximately normal. For skewed data, use percentile ranks instead.

Z-Score Calculator

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How to Use the Z Score Calculator