Statistics · Normal Curve · Z-Table

Standard Normal Distribution Calculator

Fast, high-precision standard normal distribution calculator and standard normal distribution probability calculator. Compute z to p value, how to find p score from z score, normal distribution z score, calculator z test, and understand what does z score represent.

Standard Normal Distribution Probability Calculator

Standard normal distribution (mean μ = 0, standard deviation σ = 1). Calculates z to p value and how to get p value from z score.

Shade Area:

Z Score Normal Curve (μ = 0, σ = 1) P(Z < 1.00) = 0.8413

Z Score (Z Statistic): Or slider:

P-Value / Area

0.84134

P(Z < 1.00)

Percentile Rank

84.13%

z score to percentile formula

Complementary P(Z > z)

0.15866

Upper tail area

Inverse: Find Z Value for Given Area or Probability

Probability / Area P (0 to 1):

Calculated Z Value for P:

z = +1.6449

Knowing how to get the z value for 95% one-tailed yields z value for 95% = 1.645, or 1.96 for 97.5%.

ZTable Stats — Standard Normal Distribution Table

Quick reference for common ztable stats, normal z score cutoffs, and two-tailed confidence levels.

Z Score (z)	P(Z < z) Area Left	P(Z > z) Area Right	Percentile	Confidence Level
-3.00	0.00135	0.99865	0.14%	99.73% (3σ)
-2.58	0.00494	0.99506	0.49%	99.0% Conf
-2.00	0.02275	0.97725	2.28%	95.45% (2σ)
-1.96	0.02500	0.97500	2.50%	95.0% Conf
-1.645	0.05000	0.95000	5.00%	90.0% Conf
-1.00	0.15866	0.84134	15.87%	68.27% (1σ)
0.00	0.50000	0.50000	50.00%	Mean / Median
+1.00	0.84134	0.15866	84.13%	68.27% (1σ)
+1.645	0.95000	0.05000	95.00%	90.0% Conf
+1.96	0.97500	0.02500	97.50%	95.0% Conf
+2.00	0.97725	0.02275	97.72%	95.45% (2σ)
+2.58	0.99506	0.00494	99.51%	99.0% Conf
+3.00	0.99865	0.00135	99.86%	99.73% (3σ)

Comprehensive Guide & FAQ — Z Statistic & Normal Distribution

What is a zscore and define z score?

When students ask what is a zscore or what is az score in statistics, the textbook answer is: to define z score, it measures the exact number of standard deviations a given raw data point lies above or below the population mean. It provides the core standardized metric for bell curves.

What does z score represent and z score meaning?

What does z score represent and the true z score meaning: it indicates relative position and rarity. What does the z score tell you? A Z-score of 0 means the score equals the mean. A positive score (e.g. +2.0) means top 2.3%, whereas negative (-1.5) means below average. What does z value mean is identical across all Gaussian distributions.

Z statistic formula & how to find z in statistics?

The standard z statistic formula is z = (x − μ) / σ. How to find z in statistics and how to find az score in statistics requires three inputs: raw value x, mean μ, and standard deviation σ. For sample hypothesis testing (z statistic), the denominator becomes the standard error: σ / √n.

How do z scores work & how to interpret the z score?

Understanding how do z scores work and how to interpret the z score: because every normal distribution maps to the standard normal curve N(0,1), any score can be converted into an exact probability. Roughly 68% of data falls within ±1 Z, 95% within ±2 Z, and 99.7% within ±3 Z.

How to find p score from z score & z to p value?

To learn how to find p score from z score or how to get p value from z score, use the Cumulative Distribution Function: Φ(z) = 0.5 × [1 + erf(z / √2)]. Our standard normal distribution probability calculator automates this conversion instantly for any positive or negative Z.

Z score to percentile formula & how to use z score to find percentile?

The z score to percentile formula is simply: Percentile = Φ(z) × 100%. When learning how to use z score to find percentile, look up the cumulative area left of Z in a standard ztable stats chart and multiply by 100. For instance, z = 1.00 yields the 84.13th percentile.