Enter the total proportion of the area under the curve of any data set. The calculator will convert the area of the proportion into the raw Z score.

- Z Score Calculator
- T Statistic Calculator
- Point Estimate Calculator
- Relative Standard Deviation Calculator

## Area to Z Score Formula

The following table is used to calculate the z score from an area.

Proportion of Area (P-Value) | Z |

80% | 1.282 |

85% | 1.44 |

90% | 1.645 |

95% | 1.96 |

99% | 2.576 |

99.50% | 2.807 |

99.90% | 3.291 |

The proportion of the area under the curve is also known as the P-value. This can be represented as a decimal or a percentage. For example, in the table above, 80% would be equal to a decimal amount of .80.

Often times this p-value is also considered to be the confidence interval. That's because a confidence interval is a percentage of a data set that you feel is accurate.

For the use of the calculator above, you must select the P-Value from the drop-down menu, then hit calculate. The calculator will return the corresponding z-score.

## What is a Z-Score?

A Z-score is a statistical measure that quantifies how far a particular observation or data point is from the mean of a distribution, in terms of standard deviations.

It allows for comparing different data points within a dataset, regardless of the units or scales of measurement. Z-scores are crucial in statistics and data analysis as they provide standardized values that facilitate meaningful comparisons and enable the identification of outliers or extreme observations.

By calculating the Z-score of a data point, we measure how unusual or typical that observation is within its distribution. A positive Z-score indicates that the data point is above the mean, whereas a negative Z-score suggests it is below the mean.

The magnitude of the Z-score reflects how far the data point deviates from the mean, given the standard deviation of the distribution. Consequently, Z-scores allow us to assess whether an observation is relatively high or low compared to others in the dataset.

## FAQ

**What is a z score?**

A z-score is a statistical value used to relate a single value to the overall mean of a group of data.

**What is a p value?**

A p-value is a proportion of the area or proportion of a data set used in statistical measurement.