Z-Score (Standard Score) Calculator
Local ProcessingCalculate standard score z = (x - μ) / σ from raw value, mean, and standard deviation.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
Example: Raw Value (x) = 12, Mean (μ) = 10, Standard Deviation (σ) = 2 → 1
Tool processing runs in your browser. If you create a calculator or conversion share link, its values are included in the URL. See the privacy policy for account, analytics and advertising data.
z = (x − mean) ÷ standard deviation. Tells you how many standard deviations a value is above or below the mean.
How to Use Z-Score (Standard Score) Calculator
- 1Enter the valueType the value x you want to compare.
- 2Enter mean and SDUse the mean and standard deviation of the group it belongs to. The SD must be greater than 0.
- 3Read the resultPositive is above the mean, negative below. Beyond ±2 is usually considered unusual.
Examples
Above-average score
Input: x 85, mean 70, SD 10
Result: 1.5
Below-average score
Input: x 62, mean 70, SD 8
Result: -1
Common Use Cases
- Comparing scores from tests with different averages and difficulty
- Checking whether a measurement is outside its usual range
- A first step before looking up a probability in a z-table
Frequently Asked Questions (FAQ)
What does a z-score of 1.5 mean?
The value is 1.5 standard deviations above the mean — roughly the top 7% of a normal distribution.
What if I do not know the SD?
Paste your data into the Mean & Standard Deviation calculator first.