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Z-Score Calculator

Calculate a Z-score from a raw score, convert Z and normal probabilities, or find the probability between two Z-scores.

Calculate Z-score

ExampleSample values — edit any field to see your result.

Results update as you type.

Z-score

1

Estimated result

P(X < x)
0.84134
Calculation
z = (5 − 3) / 2 = 1
Z-score1

Standardize a raw score, convert between a Z-score and normal-curve probability, or find the probability between two Z-scores. The three modes reproduce the full set of forms offered by calculator.net's Z-Score Calculator.

Formula

A raw score x is standardized by subtracting the population mean μ and dividing by the population standard deviation σ:

z = (x − μ) / σ

Converter and range modes use the standard normal CDF Φ. The probability between Z1 and Z2 is Φ(Z2) − Φ(Z1).

Examples

Default raw score

For x = 5, μ = 3, and σ = 2, the Z-score is 1. The probability to the left is 0.84134.

Between Z = −1 and Z = 0

The standard-normal area is Φ(0) − Φ(−1) = 0.34134.

Frequently asked questions

What does a Z-score mean?
It measures how many population standard deviations a raw score lies above or below the population mean. Positive values are above the mean and negative values are below it.
What are the three calculator modes?
Z-score mode standardizes a raw score, Converter mode converts any one Z or normal probability area, and Range mode finds the area between two Z-scores.
What percentile corresponds to Z equals 1?
The cumulative probability to the left is approximately 0.84134, so Z equals 1 is around the 84th percentile.
Can the standard deviation be zero?
No. A Z-score divides by standard deviation, so the standard deviation must be greater than zero.

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