Z-Score Calculator

Standardize data points, find probabilities, and interpret positions in a normal distribution — with step-by-step workings for all secondary and pre-university curricula.

Calculate Z-Score

Calculation Mode

Value → Z-Score Z-Score → Value

Data Value (x)

Population Mean (μ)

Standard Deviation (σ)

Try an example:

Enter values and click Calculate to see Z-score and probability.

Z-Score Formula

Z = (x − μ) / σ

Where x is the data value, μ is the population mean, and σ is the standard deviation.

Interpreting Z-Scores

Z = 0 — value equals the mean

Z = +1 — one SD above mean

Z = −1 — one SD below mean

|Z| > 2 — unusual (top/bottom 5%)

|Z| > 3 — very rare (top/bottom 0.3%)

Empirical Rule

±1σ — 68% of data

±2σ — 95% of data

±3σ — 99.7% of data

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Understanding Z-Scores

What is a Z-Score?

A Z-score measures how many standard deviations a data point sits above or below the mean of its distribution. It transforms raw values onto a standardized scale where the mean is 0 and the standard deviation is 1.

This makes it possible to compare values from completely different datasets — for example, comparing a student's performance on two exams with different average scores and spreads.

Z-Scores in Exams

Z-score questions appear regularly in A Level Statistics (S1/S2), IB Mathematics, and CBSE Class 12. You may be asked to standardize a value, find the probability that a randomly selected observation falls within a range, or determine the value corresponding to a given percentile.

This tool shows the full working for both directions: converting a raw value to a Z-score, and converting a Z-score back to a raw value.