Z-score calculator

Z-score, percentile and p-value.

z-score

2

(130 − 100) ÷ 15

Percentile (area below)
97.7249938%
Area above
2.275006201%
Between −|z| and |z|
95.4499876%
Two-tailed p-value
0.04550012403

Assumes a normal distribution. Areas are accurate to about 7 decimal places.

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How to calculate a z-score

  1. Enter the value, the mean and the standard deviation.
  2. Read the z-score: how many standard deviations the value is above or below the mean.
  3. Read the percentile (the share of values below it), the area above and the p-value.

The 68-95-99.7 rule

In a normal distribution about 68% of values lie within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. So a z-score beyond ±3 is rare: about 3 values in 1,000.

Example

IQ scores are scaled to a mean of 100 and a standard deviation of 15. A score of 130 has z = (130 − 100) ÷ 15 = 2, which is about the 97.7th percentile: higher than roughly 97.7% of people.