Math & Statistics
Z-Score Calculator
Standardize an observation by measuring how many standard deviations it lies above or below a mean. The calculator uses z = (observation − mean) ÷ standard deviation. It returns more than one result so you can check the main answer against a useful secondary measure. A positive z-score is above the mean and a negative score is below it. Interpreting z-scores as probabilities requires an appropriate distribution model.
Check the displayed units, assumptions, and rounding before relying on the result.
Calculate and compare
Use the number box for precision or the slider for fast scenario testing.
Scenario results
Z-score
1.5
Above the entered mean.
Raw difference
12
Observation minus mean.
Distance in SD units
1.5
Absolute standardized distance.
How the calculation works
Use consistent units and retain full precision until the final display step.
Worked example
Reproduce the displayed scenario, then change one assumption at a time.
Assumptions behind the result
- • Inputs use the units shown beside each control.
- • The displayed formula is applied without hidden market or demographic data.
- • Rounding occurs only for display; calculations keep full numeric precision.
- • A positive z-score is above the mean and a negative score is below it.
- • Interpreting z-scores as probabilities requires an appropriate distribution model.
Mistakes that change the answer
- • Mixing percentages with decimals or mixing incompatible units.
- • Relying on a rounded intermediate value instead of the full result.
- • Changing several assumptions at once instead of testing observation separately.