Math & Science100% Free Tool

Free Z-Score & Normal Distribution Probability Calculator Online

Calculate Z-scores (standard score z = (x - μ) / σ), percentile ranks, and cumulative normal distribution probability P(Z < z). — 100% free online utility, zero sign-up, zero paywalls, and private client-side processing.

100% Client-Side0ms Latency
Algebraic & Polynomial Solverax² + bx + c = 0
Roots of Equationx₁ = 3.000, x₂ = 2.000
Discriminant (Δ)1
Parabola Vertex(2.50, -0.25)
Axis of Symmetryx = 2.50

How It Works

1

Enter Raw Score (x)

Input individual test score or measurement value.

2

Enter Population Mean (μ)

Input expected average benchmark.

3

Enter Standard Deviation (σ)

Input population or sample standard deviation.

4

Inspect Z & Percentile

Review Z-score, left-tail P(X < x), and right-tail probabilities.

Frequently Asked Questions

A Z-score indicates how many standard deviations an observation is above or below the mean. Z = 0 is average; Z = +2.0 means top ~2.5% of the distribution.

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