🔔Z-Score Calculator
Convert between a z-score and a percentile with a shaded bell curve.
Free Z-Score Calculator
Trying to find how a value compares to the rest of a normal distribution? Our free z-score calculator converts between raw scores, z-scores, and percentiles instantly — with a shaded bell curve so you can see exactly what the number means.
Enter a value along with the mean and standard deviation to get its z-score, or enter a z-score directly to find its percentile and the area under the curve to the left, right, or between two points. Every result comes with the formula shown step by step, so you understand the calculation, not just the answer.
Built for statistics students, researchers, and anyone checking a z-table by hand, this tool replaces manual lookup tables with instant, accurate results. See the About page or the FAQ for more.
About the Z-Score Calculator
Features
Both calculation directions
From raw value to z-score, or from z-score to percentile.
Shaded bell curve
Visualizes the selected region — left, right, two-tailed, or between −z and +z.
Step-by-step derivation
Shows the z-score formula substitution with your actual numbers.
Accurate normal CDF
Uses the Abramowitz-Stegun erf approximation, accurate to 4+ decimal places.
Frequently Asked Questions
What is a z-score?
A z-score tells you how many standard deviations a value is from the mean of its distribution.
How do I calculate a z-score?
Enter your raw value, the mean, and the standard deviation, and the calculator applies z = (x − μ) / σ.
What does the percentile mean?
It's the percentage of the distribution that falls below your value, based on the standard normal distribution.
Can I go the other way, from z-score to percentile?
Yes, switch to the "from z-score" mode and enter the z-score directly.
What does the shaded curve show?
It visualizes the area under the standard normal curve corresponding to your selected result (left, right, or two-tailed).
What if my standard deviation is zero or negative?
Standard deviation must be greater than zero; the calculator flags invalid entries instead of producing an error or NaN.
How accurate is the percentile calculation?
It uses a high-precision normal CDF approximation, matching standard z-tables to four decimal places.
Can I find the area between two z-scores?
Yes, the "between" option shows the area between −z and +z.
Is my data stored?
No, everything is calculated client-side in your browser.
Is it free?
Yes, completely free with no sign-up or limits.