Free · Inference, regression, and statistical tests calculators 📉

Raw Score & Z-Score Standardization

Convert between a raw value and its signed standard-deviation distance from a supplied mean.

Calculator inputs

Loading calculator…

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

With mean 100 and standard deviation 15, a z-score of 2 corresponds to raw score 130.

Raw score = mean + standard deviation × z; z = (raw score − mean) / standard deviation

Enter these known values and leave the other values blank.

Standard deviation must be positive. Mean, raw score and z-score may be signed or zero.
Standardization does not require a normal distribution, but translating z into a normal percentile would require an additional distributional assumption.
Mean and standard deviation use the same units as the raw score; z is dimensionless. With z = 0 and raw score equal to mean, standard deviation is not uniquely recoverable.

The raw value is below the reference mean; its magnitude is the number of reference standard deviations below.

No. A percentile depends on the distribution, which this standardization calculation does not determine.

Bookify requires positive standard deviation so the standardized score is defined.