Gaussian Distribution · Standard Score · Z Star

Normal Distribution Calculator

All-in-one normal distribution calculator and standard score calculator. Compute z score cal, z score into percentile, p from z score, z star calculator, standard normal cdf calculator, and normal distribution and standard deviation calculator models.

Standard Distribution Calculator & Probability Distribution

Versatile standard distribution calculator and standard deviation probability distribution calculator for any mean (μ) and standard deviation (σ).

Calculation Type:

Mean (μ): Center of distribution

Standard Deviation (σ): standard deviation distribution calculator

Value (x or x₁): Raw observed score

Standard Normal Distribution Curve Calculator P(X < 115) = 0.8413

Standard Score (z score cal)

+1.000

standard normal variable calculator

Probability (p from z score)

0.8413

standard normal cdf calculator

Percentile (z score into percentile)

84.13%

standard score calculator percentile

Standard Deviation %

15.00%

standard deviation percentage calculator

Calculate Percentile from Mean and Standard Deviation Calculator (Z Value Converter)

Target Percentile (0 to 100):

Derived Score x (Given μ & σ):

x = 124.67 (z = 1.645)

Answers how to find z score without x: from percentile P, z = Φ⁻¹(P/100). Serves as a versatile z value converter.

Z Score to Percentile Chart & Standard Normal Curve Table Calculator

Comprehensive z score to percentile chart, standard normal curve table calculator, and standard deviation to percentile calculator reference.

Z Score (Standard Score)	Cumulative Probability	Percentile Rank	Description
-3.00	0.0013	0.13%	Extremely Low (bottom 0.1%)
-2.50	0.0062	0.62%	Very Low Outlier
-2.00	0.0228	2.28%	Lower 2.5% Cutoff (2σ)
-1.645	0.0500	5.00%	Bottom 5% Threshold
-1.00	0.1587	15.87%	1 Standard Deviation Below Mean
-0.50	0.3085	30.85%	Moderately Below Average
0.00	0.5000	50.00%	Exact Mean / Median (Average)
+0.50	0.6915	69.15%	Moderately Above Average
+1.00	0.8413	84.13%	1 Standard Deviation Above Mean
+1.645	0.9500	95.00%	Top 5% Threshold (90% Conf)
+1.960	0.9750	97.50%	Top 2.5% Threshold (95% Conf)
+2.00	0.9772	97.72%	Upper 2.5% Cutoff (2σ)
+2.50	0.9938	99.38%	Very High Outlier
+3.00	0.9987	99.87%	Extremely High (top 0.1%)

Normal Distribution Guide & Frequently Asked Questions

How to convert z score to percentile?

When asking how to convert z score to percentile, calculate the cumulative probability Φ(z) using the standard normal cumulative distribution function (CDF) and multiply by 100%. Our standard score calculator percentile and standard deviation to percentile calculator automate this instantly.

What is a z star calculator and critical value?

A z star calculator determines the critical value z* used in confidence intervals for means and proportions. For a two-tailed test with confidence level C, z* satisfies P(−z* < Z < z*) = C. Common values: 90% → 1.645, 95% → 1.960, and 99% → 2.576.

How does normal distribution and standard deviation calculator work?

Our normal distribution and standard deviation calculator computes the probability of any continuous metric by standardizing raw values: z = (x − μ) / σ. It serves as a mean probability distribution calculator and standard deviation distribution calculator in one.

How to find z score without x?

Knowing how to find z score without x: if you know the percentile rank, probability, or shaded area under the curve, take the inverse cumulative distribution function z = Φ⁻¹(Percentile / 100). Use the calculate percentile from mean and standard deviation calculator tab above to execute this calculation.