Z Score Calculator

Q: What is a z-score?

The number of standard deviations a value is from the mean.

Q: What does Φ(z) mean?

The cumulative probability P(Z < z) from the standard normal.

Use our free z-score calculator to compute z-scores (standard scores) from raw values or find raw values from z-scores. Includes cumulative normal probability.

Math

Mode

Mean (μ)

Std Dev (σ)

Value (x)

Z-Score (z)

Formula

A z-score (standard score) describes how many standard deviations a value is from the mean. This calculator also returns the cumulative probability from the standard normal distribution.

z = (x - μ) / σ, x = μ + zσ, P(X < x) = Φ(z)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select whether to compute z from x or x from z.
2Enter the mean and standard deviation.
3Enter the known value (x or z).
4Click Calculate.

Examples

z-score: μ=100, σ=15, x=130

1.z=(130-100)/15=2
2.P(X<130)=Φ(2)≈0.9772

Result: 2.000000

x from z: μ=100, σ=15, z=2

1.x=100+2×15=130
2.P(X<130)=Φ(2)≈0.9772

Result: 130.000000

Frequently Asked Questions

The number of standard deviations a value is from the mean.

z = (x - μ) / σ.

The cumulative probability P(Z < z) from the standard normal.

Value is below the mean.

Value equals the mean.

Related Calculators

Normal Distribution Calculator Standard Deviation Calculator Mean Calculator Percentile Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-14

Z Score Calculator

Formula

How It Works

Examples

z-score: μ=100, σ=15, x=130

x from z: μ=100, σ=15, z=2

Frequently Asked Questions

What is a z-score?

Formula?

What does Φ(z) mean?

Negative z-score?

Z-score of 0?

Related Calculators

Z Score Calculator

Formula

How It Works

Examples

z-score: μ=100, σ=15, x=130

x from z: μ=100, σ=15, z=2

Frequently Asked Questions

What is a z-score?

Formula?

What does Φ(z) mean?

Negative z-score?

Z-score of 0?

Related Calculators