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Z-Score Calculator

Convert a raw score to a z-score, a z-score back to a raw score, or a percentile to a z-score, and read off the matching normal-distribution probabilities.

Formulas last reviewed: September 2026

Disclaimer: Results are calculated with standard formulas and are meant for learning and quick checks. Please double-check important work, especially anything used for exams, engineering, finance or safety.

How many standard deviations from the mean?

A z-score tells you how many standard deviations a value lies above or below the mean. A z-score of 0 is exactly average, +1 is one standard deviation above, and −2 is two below. Because it is unit-free, you can compare scores from different tests or scales.

This calculator converts a raw score to a z-score, a z-score back to a raw score, or a percentile to a z-score. It also shows the matching probabilities from the normal curve.

How it is calculated

z = (x − μ) ÷ σ
x = μ + z × σ

Worked example

Score 85, mean 70, standard deviation 10

z-score
1.5
Percentile
93.32%
Share above
6.68%

This student scored better than about 93% of the group.

The 68-95-99.7 rule

z betweenShare of data
−1 and +1about 68%
−2 and +2about 95%
−3 and +3about 99.7%

Frequently asked questions

What is a good z-score?

It depends on context. Above +1 is above average, above +2 is unusually high, and values beyond ±3 are rare.

Does a z-score need a normal distribution?

It can be calculated for any data, but the percentile and probability figures assume the data is roughly bell-shaped.

How do I convert a z-score to a percentile?

Look up the area under the normal curve to the left of z. This calculator does it automatically.

What is a two-tailed probability?

It is the chance of being at least this far from the mean in either direction, used in hypothesis tests.