About Z-Score Calculator

Z-Score Calculator is a free toolkit of standard-normal distribution calculators — z-scores, percentiles, p-values, critical values, confidence intervals, hypothesis tests, sample size, and more. No signups, no data collection, no cookies beyond the bare minimum the ad library needs. Plug numbers in, see the math.

How the math is verified

The standard normal CDF uses the Abramowitz & Stegun rational approximation, and the inverse CDF uses Acklam's rational approximation — both standard, well-tested numerical methods with known accuracy bounds (about 1.5 × 10⁻⁷ for CDF, 1.15 × 10⁻⁹ for inverse). Every calculator routes through a single math layer with NaN-guarding parsers and finite-only validators. Worked examples on each page are computed and independently verified against textbook values and published statistical tables. Reader bug reports are welcomed — they catch real issues, especially in edge cases.

A note on appropriate use

These tools assume the underlying distribution is normal (or approximately so by the central limit theorem when sample sizes are large). For small samples drawn from non-normal populations, or when the population standard deviation is unknown, a t-distribution or non-parametric method is more appropriate. The calculators are built for coursework, quick checks, and routine analysis — not as a substitute for proper statistical methodology when the assumptions are at risk.

About the author

Hi, I'm Jimmy Raymond. I built Z-Score Calculator while working through statistics problems and wanted a fast, accurate, and uncluttered reference. The same numerical methods that ship in production scientific software ship here — Abramowitz & Stegun and Acklam aren't shortcuts, they're what professional stat packages use too.

I have a B.S. in Environmental Engineering from New Mexico Tech and a B.S. in Computer Science from the University of New Mexico. My professional work has been in safety-critical aerospace, real-time embedded software, and full-stack web — contexts where wrong numbers have consequences. That discipline is where this site's design philosophy comes from: state the formula, state the assumptions, guard against bad inputs, and be honest about what the tool can and can't do.

I'm based in Albuquerque, New Mexico.

Contact

Email me at aj@ajdesigner.com for corrections, feature requests, or general feedback. You can also find me on LinkedIn.

— Jimmy