Z-score calculator (standard score)
A z-score tells how many standard deviations a value is from the mean.
Result
2Z-score
- If the data follow a normal law, about 97.72% of values are lower.
- Share below (percentile)
- 97.725%
- Share above
- 2.275%
- Share between −z and +z
- 95.45%
Inputs
- Value
- 130
- Mean
- 100
- Standard deviation
- 15
How it is calculated
z = (value − mean) ÷ standard deviation.
Result
Z-score
- Share below (percentile)
- 97.725%
- Share above
- 2.275%
- Share between −z and +z
- 95.45%
How it is calculated
- z = (value − mean) ÷ standard deviation.
- Percentile = Φ(z), the area under the normal curve left of z.
- Φ(z) = (1 + erf(z ÷ √2)) ÷ 2, computed to at least 10 decimal places.
Example
IQ of 130 (mean 100, standard deviation 15): z = 2, about 97.72% of values below.
Good to know
- The percentile only makes sense if the data roughly follow a bell curve.
- The standard deviation must be strictly positive.
Frequently asked questions
What is this tool used for?
A z-score tells how many standard deviations a value is from the mean.
How is the result calculated?
z = (value − mean) ÷ standard deviation.
What should I check before using the result?
The percentile only makes sense if the data roughly follow a bell curve.