Z Score Probability Calculator
Calculate the probability (area under the normal distribution curve) for any Z-score
Standard Normal Distribution (μ = 0, σ = 1)
Z Score Probability Calculator
Our Z Score Probability Calculator is a powerful tool designed to convert Z-scores into probabilities under the standard normal distribution. Whether you are a student, researcher, or data analyst, this z-score probability calculator helps you understand how far a value lies from the mean and what probability is associated with it. You may also see this tool referred to as a z score to probability calculator or probability z score calculator.
What is a Z Score?
A Z score (or standard score) measures how many standard deviations a data point is from the mean of a distribution. For example, a Z score of 0 means the value is exactly at the mean, while a Z score of +2 means the value is two standard deviations above the mean. This standardization allows comparison across different datasets. If you are searching for a z score calculator probability, you are essentially looking for the probability associated with a specific Z value.
How to Calculate Z Score
The formula for calculating a Z score is:
Z = (X - μ) / σ
Where:
- X = the raw data point
- μ = the population mean
- σ = the standard deviation
How Does the Z Score Probability Calculator Work?
The probability of z score calculator uses the cumulative distribution function (CDF) of the standard normal distribution. It applies the mathematical error function to determine the area under the curve to the left of the entered Z value. In simpler terms, the calculator answers: “What percentage of the data lies below this Z score?”. This is why the tool is also called a probability z-score calculator.
Features of the Z Score Probability Calculator
- Converts Z scores into probabilities instantly.
- Supports both positive and negative Z values.
- Uses accurate statistical formulas for standard normal distribution.
- Mobile-friendly and easy-to-use design.
- Free, reliable, and educational for statistics learners.
Z Score to Probability Reference Table
| Z Score | Probability (%) | Interpretation |
|---|---|---|
| 0.0 | 50% | Exactly at the mean |
| +1.0 | 84.13% | Above mean by 1 standard deviation |
| +2.0 | 97.72% | Above mean by 2 standard deviations |
| -1.0 | 15.87% | Below mean by 1 standard deviation |
| -2.0 | 2.28% | Below mean by 2 standard deviations |
To learn more about Z scores and probabilities, visit this resource: StatisticsHowTo: Understanding Z-Scores .