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Z-Score Calculator (Standard Score & Percentile)
Compute z-score, percentile rank, and one/two-tailed p-values under the standard normal distribution. z = (x − μ) / σ.
MATHCompute the standard score (z-score) of a value, its percentile rank, and one/two-tailed tail probabilities under the standard normal distribution. Formula: z = (x − μ) / σ.
Common benchmarks: z = ±1.96 is the 95% confidence boundary (two-tailed p = 0.05); z = ±2.58 is 99% (p = 0.01); z = ±3 means only 0.27% of values are this extreme. About 68% of values fall within ±1σ, 95% within ±2σ, 99.7% within ±3σ (empirical rule).
Disclaimer: Requires normally distributed data and known population parameters. For sample data with small n, use a t-score instead. Probabilities computed via Abramowitz-Stegun rational approximation.
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Frequently Asked Questions
What is the Z-Score Calculator (Standard Score & Percentile) for?
Compute the standard score (z-score) of a value, its percentile rank, and one/two-tailed tail probabilities under the standard normal distribution. Formula: z = (x − μ) / σ.
How do I use the Z-Score Calculator (Standard Score & Percentile)?
Common benchmarks: z = ±1.96 is the 95% confidence boundary (two-tailed p = 0.05); z = ±2.58 is 99% (p = 0.01); z = ±3 means only 0.27% of values are this extreme. About 68% of values fall within ±1σ, 95% within ±2σ, 99.7% within ±3σ (empirical rule).
How accurate are my z-score (standard score & percentile) results?
Requires normally distributed data and known population parameters. For sample data with small n, use a t-score instead. Probabilities computed via Abramowitz-Stegun rational approximation.
Is the Z-Score Calculator (Standard Score & Percentile) free to use?
Yes - every calculator on WhichCalc is completely free with no signup, no usage limits, and no tracking on the calculation itself. Results display instantly in your browser and your inputs are never sent to a server. Bookmark the page if you use this calculator regularly.
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