Z-Score Calculator
Convert a raw value into a z-score to see how far it sits from the mean in standard deviations.
Number of standard deviations the value lies from the mean.
- 1
Deviation from the mean
x − μ = 85 − 70 = 15The signed distance of the value from the centre of the distribution. - 2
Z-score
(x − μ) ÷ σ = 15 ÷ 10 = 1.5000
Formula
How this is calculated
The calculator takes three numbers: x, the raw value (data point) you want to evaluate; μ (mu), the mean of the distribution; and σ (sigma), the standard deviation, which measures the typical spread of the data. All three must share the same unit of measurement, and the z-score itself is unitless because the units cancel.
First it computes the deviation, x − μ, which is the signed distance of your value from the centre of the distribution. It then divides that distance by σ, rescaling it into "number of standard deviations." So z = (x − μ) / σ. A positive z means x is above the mean, a negative z means below, and z = 0 means x equals the mean exactly.
The key assumption is that σ describes the spread of the same population x and μ come from. The formula is purely arithmetic and works for any data, but interpreting z against the familiar 68-95-99.7 percentages assumes a roughly normal (bell-shaped) distribution. The standard deviation must be greater than zero; if σ = 0 the division is undefined, so the calculator flags that case instead of returning a result.
About this calculator
A z-score, or standard score, tells you how many standard deviations a particular value lies above or below the mean of its distribution. A positive z-score means the value is above the mean; a negative one means it is below. A z-score of 0 indicates the value equals the mean exactly.
Standardizing data this way lets you compare values measured on different scales — for example, a test score and a height — by expressing each in common units of standard deviation. Z-scores are central to the normal distribution: about 68% of values fall within z = ±1, 95% within ±2, and 99.7% within ±3. The standard deviation must be greater than zero, otherwise the z-score is undefined.
Frequently asked questions
It tells you how far a value is from the mean, measured in standard deviations. A z-score of 2 means the value is two standard deviations above average.
Yes. A negative z-score simply means the value is below the mean. The sign indicates direction, and the magnitude indicates distance.
Values with z-scores beyond ±2 are often considered unusual, and beyond ±3 are rare, since roughly 99.7% of a normal distribution falls within three standard deviations of the mean.
Also known as
TG we-Calculate Editorial Team. (2026). Z-Score Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/z-score-calculator
TG we-Calculate Editorial Team. "Z-Score Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/z-score-calculator.
TG we-Calculate Editorial Team, "Z-Score Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/z-score-calculator
@misc{wecalculate_z_score_calculator, title = {Z-Score Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/z-score-calculator}}, year = {2026}, note = {TG we-Calculate} }
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