Z-Score Standardization Calculator (z = (x - μ) / σ)
A standard Z-score transforms a raw observation x into standard deviation units σ above or below the population mean μ: z = (x - μ) / σ.
Number of standard deviations from the mean
Observed data point
Center of the distribution
Dispersion parameter of the distribution (σ > 0)
Step-by-Step Calculation
A standard Z-score transforms a raw observation x into standard deviation units σ above or below the population mean μ: z = (x - μ) / σ.
Real-World Reference Values
One standard deviation around the mean
Standard α = 0.05 significance threshold
High-precision quality control thresholds
20-Row Comparison Table
Standard Z-Score (z) · Raw Observation Value (x)
| # | Raw Observation Value (x) | Standard Z-Score (z) | Δ % |
|---|---|---|---|
| 01 | -2,120.60 | -148.04 | -7653.06% |
| 02 | -1,857.44 | -130.4961 | -6757.97% |
| 03 | -1,594.28 | -112.9523 | -5862.87% |
| 04 | -1,331.13 | -95.4084 | -4967.78% |
| 05 | -1,067.97 | -77.8646 | -4072.68% |
| 06 | -804.8105 | -60.3207 | -3177.59% |
| 07 | -541.6526 | -42.7768 | -2282.49% |
| 08 | -278.4947 | -25.233 | -1387.40% |
| 09 | -15.3368 | -7.6891 | -492.30% |
| 10 | 129.4 Current | 1.96 | 0.00% |
| 11 | 510.9789 | 27.3986 | +1297.89% |
| 12 | 774.1368 | 44.9425 | +2192.98% |
| 13 | 1,037.29 | 62.4863 | +3088.08% |
| 14 | 1,300.45 | 80.0302 | +3983.17% |
| 15 | 1,563.61 | 97.574 | +4878.27% |
| 16 | 1,826.77 | 115.1179 | +5773.36% |
| 17 | 2,089.93 | 132.6618 | +6668.46% |
| 18 | 2,353.08 | 150.2056 | +7563.55% |
| 19 | 2,616.24 | 167.7495 | +8458.65% |
| 20 | 2,879.40 | 185.2933 | +9353.74% |
Frequently Asked Questions
How do I find the raw score x corresponding to the 97.5th percentile (z = 1.96)?+
Click SOLVE FOR on x (Raw Observation Value), set z = 1.96, and enter your mean μ and standard deviation σ to evaluate x = μ + zσ.
What does a negative Z-score mean?+
A negative Z-score indicates that the raw observation x lies below the population mean μ.
Why do data scientists standardize features using Z-scores?+
Z-score standardization gives every feature zero mean and unit variance (μ = 0, σ = 1), preventing large-scale features from dominating gradient descent or PCA.