01
How to use this calculator
- Identify the observed value, mean and standard deviation.
- Subtract the mean from the observed value.
- Divide by a strictly positive standard deviation.
02
A little understanding goes a long way.
A positive z score lies above the mean; a negative score lies below it. Standardization does not require a normal distribution.
THE FORMULA
z = (x − μ) ÷ σ
TRY IT ON PAPER
A worked example
For x = 85, mean μ = 70 and standard deviation σ = 10, z = (85 − 70)/10 = 1.5.
03
A few common questions
Can standard deviation be zero?
The formula is undefined when standard deviation is zero. Use a positive value.
Does z = 0 mean the value is zero?
No. It means the observed value equals the mean.