Z-Score Calculator
Calculate a z-score (standard score) and its percentile under the normal model.
Your inputs
Results
z-score
1.5
- Percentile (normal model)
- 93.3193%
- Reading
- 1.50 standard deviations above the mean
✓Exact calculation — rounded only for display
What this calculator does
A z-score says how many standard deviations a value is from the mean, making different scales comparable.
Formula and method
z = (x − mean) ÷ standard deviation; percentile = Φ(z) × 100
Worked example
Calculated by this tool with its default inputs:
Inputs
- Value (x): 85
- Mean: 70
- Standard deviation: 10
Results
- z-score: 1.5
- Percentile (normal model): 93.3193%
- Reading: 1.50 standard deviations above the mean
How to read the results
Positive z is above the mean; |z| above 2 is unusual for normal data.
Assumptions and limitations
- The percentile assumes a normal distribution.
Questions
Can z be negative?
Yes — for values below the mean.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy