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Z-Score Calculator

Standard score and percentile from value, mean, and SD.

Z-score
+1.500
1.50 standard deviations above the mean
P(X < 85)
93.32%
P(X > 85)
6.68%
Within ±|z| of μ
86.64%

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

  1. Enter the value, mean, and standard deviation.
  2. 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.