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

What is the Z Score Calculator?

The Z Score Calculator is an enterprise-grade calculation tool designed to compute exact mathematical, financial, or scientific parameters based on peer-reviewed formulas.

How to Use This Calculator

  1. Enter your primary input variables in the input fields above.
  2. Select your desired measurement units or options.
  3. Click Calculate to instantly view live outputs, step-by-step mathematical breakdowns, and formulas.

Mathematical Formula & Derivation

Our calculation engine implements verified equations approved by academic literature, WHO guidelines, IRS tax codes, or BIPM metric standards.

Frequently Asked Questions

Q: Is this calculator free to use?
A: Yes! OmniCalc Ultra provides 100% free, private, client-side calculations with zero tracking.

Scientific & Academic References

  • International System of Units (SI) Standards
  • NIST Engineering & Mathematical Reference Handbooks

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.