Z-Table Calculator with Normal Distribution Curve

Calculate Z-scores, cumulative probabilities, percentiles, tail areas, and critical values with a visual standard normal distribution curve.

✓ Instant results ✓ Step-by-step solution ✓ Interactive curve ✓ Mobile friendly

Visual probability

Standard Normal Distribution

Selected region P(Z ≤ 1.96)

Probability 0.9750

The standard normal curve displays the selected probability.

Calculator

Choose a Calculation

Enter Z-score Example: 1.96, −1.28, or 0

Probability region

Left tail P(Z ≤ z) Right tail P(Z ≥ z) Central area P(−|z| ≤ Z ≤ |z|) Two tails P(|Z| ≥ |z|)

Display precision

Calculated answer

Results

What this result means

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Formula

What Is a Z-Score?

A Z-score measures how many standard deviations a value is above or below the mean.

z = x − μσ

x = observed or raw value
μ = population mean
σ = population standard deviation

Quick reference

Common Critical Z-Values

Confidence	Two-sided critical Z
80%	±1.282
90%	±1.645
95%	±1.960
98%	±2.326
99%	±2.576
99.9%	±3.291

Standard normal table

Cumulative Z-Table

This table shows the cumulative area to the left of a positive Z-score: Φ(z) = P(Z ≤ z). For negative values, use Φ(−z) = 1 − Φ(z).

How to read: For Z = 1.96, use row 1.9 and column 0.06.

Calculation Method

Probabilities are calculated using a numerical approximation of the standard normal cumulative distribution function. Results may differ slightly from printed Z-tables because of rounding.

Educational purpose: This calculator supports learning and statistical problem-solving. Verify critical decisions using an appropriate statistical method and qualified professional review.

Created by Digital E-Learning

Published: August 27, 2026
Last Updated: August 27, 2026

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