Statistical Precision Suite

Z-SCORE CALCULATOR

Standardize your data and explore the normal distribution. Compute z-scores from raw values and determine precise probabilities with our professional statistical toolset.

Raw Score to Z-Score

Standardize a specific data point relative to its population.

Raw Score (x)

Population Mean (μ)

Standard Deviation (σ)

Enter parameters to see standardization

Z-Score & Probability Converter

Bidirectional conversion between z-scores and cumulative probabilities.

Unified Converter (Enter ANY value)

Z-Score, Z

Probability, P(x < Z)

Probability, P(x > Z)

Probability, P(0 to Z)

Probability, P(-Z < x < Z)

Probability, P(x < -Z or x > Z)

Fill any field to see statistical relationship

Probability Between Z-Scores

Find the area under the curve between any two z-points.

Left Z-Bound (z1)

Right Z-Bound (z2)

Enter bounds to visualize distribution area

What is a Z-Score?

A z-score, or standard score, is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean.

The Core Formula

z = (x - μ) / σ

Standard Score Calculation

• x: The raw score (data point)
• μ: The population mean
• σ: The population standard deviation

Why Use Z-Scores?

Z-scores allow statisticians to compare scores from different distributions. For example, you can compare a score on an SAT test to a score on an ACT test by standardizing both to their respective normal distributions.

A z-score of 0 indicates the score is exactly the mean, while a z-score of 1.0 indicates the score is one standard deviation above the mean.

The 68-95-99.7 Rule

68.27%

Within ±1σ

95.45%

Within ±2σ

99.73%

Within ±3σ

In a standard normal distribution, nearly all data falls within 3 standard deviations of the mean. This is often referred to as the Empirical Rule.

How the calculation works

A z-score counts how many standard deviations a value is from the mean.

z = (x − mean) ÷ standard deviation

In a standard normal model, about 68% of values fall between z = −1 and z = 1.

Worked example: score 85, mean 70, standard deviation 10

z = (85 − 70) ÷ 10 = 1.5.
The score is 1.5 standard deviations above the mean.

Z-scores when the mean is 70 and the standard deviation is 10

Score	z
60	-1.0
70	0.0
85	1.5

Frequently asked questions

What is the z-score of 85 if the mean is 70 and the standard deviation is 10?▼

1.5.

What z-score is the mean itself?▼

What does a negative z-score mean?▼

The value is below the mean.