Z-Score Calculator - calculatorsee.com


Z-Score Calculator

Calculate standard score (Z-score) from raw score, mean, and standard deviation, and find corresponding tail probabilities.

Calculator Inputs

Observed data point.
Average of distribution.
Spread.

Calculated Results

Z-Score
1.500 (Standard Deviations)
Percentile Rank 93.32 percentile
P-Value P(X <= x) 0.9332
Right Tail Area P(X >= x) 0.0668
Values calculate live as you adjust inputs.

About Z-Score Calculator

Measures how many standard deviations an observation x is above or below the mean of a normal distribution.

What is Z-Score Calculator?

Measures how many standard deviations an observation x is above or below the mean of a normal distribution.

How to Use This Calculator

  1. Enter raw score, mean, and standard deviation.
  2. Review Z-score and normal curve percentile rank.

The Mathematical Formula & Variables

Z = (Raw Score - Mean) / Standard Deviation

Step-by-Step Worked Example

Scenario: x = 115, mean = 100, standard deviation = 10.

  1. Z = (115 - 100) / 10 = 15 / 10 = 1.5.
  2. A Z-score of 1.5 corresponds to the 93.32nd percentile.

Result: Z = 1.500

Frequently Asked Questions

What does a negative Z-score indicate?

A negative Z-score indicates that the data point is below the population mean.