📉 Standard Normal Z-Score & Percentile Calculator
Calculate standard normal distribution Z-scores, percentiles, left-tail and right-tail p-value probabilities from raw scores, mean, and standard deviation.
Free No Signup Required Browser-Based
Standard Normal Z-Score
+1.5000
Your score is in the 93.32th Percentile of the distribution
Left-Tail Probability P(Z < z)
0.9332 (93.32%)Right-Tail Probability P(Z > z)
0.0668How to Use Standard Normal Z-Score & Percentile Calculator
- Enter raw score (x), population mean (μ), and standard deviation (σ)
- Review computed Z-score and exact percentile ranking
- Inspect left-tail and right-tail cumulative normal probabilities
📖 Technical Encyclopedia & Standards Reference
Calculate standard normal distribution Z-scores, percentiles, left-tail and right-tail p-value probabilities from raw scores, mean, and standard deviation. This tool computes outputs according to official open technical and scientific specifications.
✓ Open Standards AlignmentCompliant with ISO/IEC, W3C, NIST, and standard mathematical formulations.
✓ 100% Client-Side / SecureZero server logging. Computations execute entirely in your local browser sandbox.
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Frequently Asked Questions
What is a Z-Score in statistics?
A Z-score indicates how many standard deviations an individual raw score (x) lies above or below the population mean (μ): z = (x - μ) / σ.
How do you interpret a positive vs negative Z-score?
A positive Z-score indicates a value above the mean, while a negative Z-score indicates a value below the mean. A Z-score of 0 is exactly on the mean (50th percentile).