Z-Score Calculator
Standard score and percentile from value, mean, and SD.
z = (X − μ) / σ. The percentile assumes the data is normally distributed. The CDF uses the Abramowitz and Stegun erf approximation, accurate to about 1 part in 10⁷.
About
Enter a value, the population mean, and the standard deviation. Get the z-score (how many standard deviations from the mean) plus the percentile under a normal curve. Useful for grading on a curve, IQ scores, or quick statistics homework.
How to use
- Enter the value, mean, and standard deviation.
- Read z and the percentile under a normal curve.
FAQ
Does this assume a normal distribution?+
The percentile does. The z-score itself is just (X − μ) / σ and works on any data. The percentile is only meaningful if the underlying distribution is roughly normal.
How accurate is the percentile?+
It uses the Abramowitz and Stegun erf approximation, accurate to about 1 part in 10⁷. Plenty for any homework or back-of-envelope use.