Z-Table (Standard Normal)

Find the area under the standard normal curve for any Z-score, representing cumulative probability.

Probability lookup

Enter Z-Score

Interactive Z-Table Slice

Z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9699	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.9750	0.9756	0.9761	0.9767
2.0	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.9830	0.9834	0.9838	0.9842	0.9846	0.9850	0.9854	0.9857

Area Analysis

Left-Tail P(X < Z)0.97500

Standard Normal Curve

Right-Tail P(X > Z)0.02500

Two-Tail Alpha0.05000

Curve Density0.05844

Z-Score1.96

A Z-score of 1.96 means this value is 1.96 standard deviations above the average.

Overview

A Z-table, also known as the standard normal table, is a mathematical table that allows us to find the percentage of values that fall below a specific Z-score in a normal distribution. Since the standard normal distribution has a mean of 0 and a standard deviation of 1, any value from any normal distribution can be 'standardized' into a Z-score.

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Pro Tips

Z-scores tell you how many standard deviations a value is from the mean.
A positive Z-score indicates a value above the mean, while a negative one is below the mean.
The empirical rule (68-95-99.7) is a shorthand for Z-scores of 1, 2, and 3 respectively.

Fun Facts

"In industrial quality control, 'Six Sigma' represents a Z-score of 4.5 or higher, implying only 3.4 defects per million opportunities."
"The area under the entire normal curve is exactly 1.0, representing 100% probability."
"A Z-score of 0 splits the distribution perfectly in half, with 0.5 area on each side."

Formula: Φ(z) = ∫[-∞, z] 1/√(2π) e^(-t²/2) dt

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.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

1.7

0.9554

0.9564

0.9573

0.9582

0.9591

0.9599

0.9608

0.9616

0.9625

0.9633

1.8

0.9641

0.9649

0.9656

0.9664

0.9671

0.9678

0.9686

0.9693

0.9699

0.9706

1.9

0.9713

0.9719

0.9726

0.9732

0.9738

0.9744

0.9750

0.9756

0.9761

0.9767

2.0

0.9772

0.9778

0.9783

0.9788

0.9793

0.9798

0.9803

0.9808

0.9812

0.9817

2.1

0.9821

0.9826

0.9830

0.9834

0.9838

0.9842

0.9846

0.9850

0.9854

0.9857