Z-Score Calculator

Find a z-score from a raw value, or convert a z-score back into a raw value.

Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026

Result

z = (x − μ) / σ

z = 1.5

What is a z-score?

A z-score (or standard score) tells you how many standard deviations a value sits above or below the mean. A positive z-score is above average, a negative one is below, and zero is exactly average. It lets you compare values from different data sets on the same scale.

How it's calculated

Subtract the mean from your value, then divide by the standard deviation: z = (x − mean) / standard deviation. To go the other way and find the raw value for a given z-score, rearrange to x = mean + z × standard deviation. The standard deviation must be greater than zero.

Example

A test score of 85 in a class with mean 70 and standard deviation 10: z = (85 − 70) / 10 = 1.5, so the score is 1.5 standard deviations above average. Going back: a z-score of 2 with the same mean and standard deviation gives x = 70 + 2 × 10 = 90.

All calculations happen in your browser. Nothing is sent, stored, or tracked.

Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer

How to use

Choose Find z and enter your value, the mean and the standard deviation, or choose Find x and enter a z-score, mean and standard deviation to recover the raw value.

The standard deviation must be greater than zero.

Frequently asked questions

What is a z-score?+

It is the number of standard deviations a value is from the mean: z = (x − mean) / standard deviation.

What does a negative z-score mean?+

The value is below the mean. A z-score of −1 is one standard deviation below average.

What is a "good" z-score?+

It depends on context, but in a normal distribution about 95% of values fall between −2 and +2, and beyond ±3 is rare (about 0.3%).

How do I convert a z-score back to a value?+

Rearrange the formula: x = mean + z × standard deviation.

Why must the standard deviation be positive?+

Standard deviation measures spread and cannot be zero or negative; dividing by zero is undefined, so the calculator requires it to be greater than 0.