Z-Score Calculator
Calculate z-score using your data.
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What this tool does
Calculate z-score using your data. The percentile assumes the underlying distribution is approximately normal. A z of +1 sits at about the 84.13th percentile; z = 0 is the mean and the 50th percentile.
How to use the Z-Score Calculator
- Enter or select value (x).
- Enter or select mean (μ).
- Enter or select standard deviation (σ).
- Read the calculated result; change any measurement to compare alternatives.
Formula
z = (x − μ) / σ; percentile = Φ(z) × 100 using the normal CDF (gammaQ-based, matching statistics.ts)
- x
- Value (x)
- mu
- Mean (μ)
- sigma
- Standard deviation (σ)
The percentile assumes the underlying distribution is approximately normal. A z of +1 sits at about the 84.13th percentile; z = 0 is the mean and the 50th percentile.
Worked example
For z-score calculator, the following measurements illustrate the exact method: Value (x): 85; Mean (μ): 70; Standard deviation (σ): 15.
Inputs
- Value (x)85
- Mean (μ)70
- Standard deviation (σ)15
Result
- Z-score1
- Percentile under the normal model (%)84.13
- Percentage above the value (%)15.87
Results explained
- Z-score
- Z-score from the formula above. The percentile assumes the underlying distribution is approximately normal. A z of +1 sits at about the 84.13th percentile; z = 0 is the mean and the 50th percentile.
- Percentile under the normal model (%)
- Percentile under the normal model (%) from the formula above. The percentile assumes the underlying distribution is approximately normal. A z of +1 sits at about the 84.13th percentile; z = 0 is the mean and the 50th percentile.
- Percentage above the value (%)
- Percentage above the value (%) from the formula above. The percentile assumes the underlying distribution is approximately normal. A z of +1 sits at about the 84.13th percentile; z = 0 is the mean and the 50th percentile.
Frequently asked questions
z = (x − μ) / σ; percentile = Φ(z) × 100 using the normal CDF (gammaQ-based, matching statistics.ts)
The percentile assumes the underlying distribution is approximately normal. A z of +1 sits at about the 84.13th percentile; z = 0 is the mean and the 50th percentile.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.