MihsabaHow to use
A z-score expresses how far a value is from the mean in standard-deviation units. The tool supports raw-to-z, z-to-raw and percentile-to-z modes. Percentile calculations use the standard normal distribution.
- Choose a conversion mode.
- For raw-to-z enter value, mean and standard deviation; reverse mode uses z instead of the raw value.
- For percentile-to-z enter a percentile strictly between 0 and 100.
- Review z, lower/upper percentile areas and two-tail probability; raw value appears when mean and SD are supplied.
How it is calculated
Example
If x=85, mean=75 and SD=10, then z=(85−75)/10=1. Under the standard normal distribution, about 84.13% of the area lies below z=1.
Important notes
The z-score itself is a standardization. Turning it into a normal percentile or tail probability is appropriate only when a normal-model interpretation is reasonable; strongly skewed data may not support that assumption.
Frequently asked questions
What does z=0 mean?
The raw value is exactly at the mean.
Does z=2 mean the top 2%?
Not exactly; under a normal model about 97.72% lies below z=2 and about 2.28% above.
Can I recover the raw score?
Yes, with z, mean and standard deviation: x=μ+zσ.
Is this calculator free?
Yes. It is free to use and requires no account.