Z-Score Calculator
Standardize one raw value using your supplied reference mean and SD.
One raw value, one supplied reference
The z-score is (raw value − reference mean) ÷ reference SD. With a raw value of 85, mean of 70 and SD of 10, the difference is 15 and the z-score is 1.5. Changing only the raw value to 55 gives −1.5.
Standardization does not require a normal-distribution claim
You can describe a value's distance from a supplied mean without assuming the source data are normal. Normal-model probability areas are a separate, optional interpretation. They stay off until you select the assumption, and the caveat stays beside the areas and in copied or exported text.
Method and numerical limits
The standardization and normal-model definitions follow the NIST statistical handbook. The browser calculates with double-precision numbers and a numerical normal-CDF approximation; it does not round the z-score before computing areas. Tiny tails are shown as inequalities rather than false exact zero or one.
This is an educational calculator, not a clinical growth-chart score, official grade, employee-selection decision or hypothesis-test selector. It does not validate the reference statistics or establish an empirical percentile.
Frequently asked questions
How do I calculate a z-score from a raw value?
Subtract the supplied reference mean from the raw value, then divide by the supplied reference standard deviation: z = (x − mean) / SD. For 85, 70 and 10, z = 1.5. This calculator uses your supplied reference values; it does not estimate them from a dataset.
Which mean and standard deviation should I enter?
Use the same reference group and measurement units for all three fields. Check whether your source reports population SD or sample SD. The calculator does not choose a reference group or convert sample statistics into population parameters.
Does a z-score give my actual percentile?
No. A z-score gives distance from the supplied mean in supplied SD units. Optional tail areas assume a normal distribution; they do not establish the observed rank of a value in your dataset.
Is the two-sided area a p-value?
Not automatically. This tool only reports a symmetric area under an assumed standard normal model. A hypothesis-test p-value also requires an appropriate test statistic, null model, sampling assumptions and test design.
What does a negative z-score mean?
It means the raw value is below the supplied mean. For 55, 70 and 10, z = −1.5. A z-score of zero means the raw value equals the reference mean; neither result is a judgment about an individual.
Why must standard deviation be positive?
Standard deviation supplies the scale for the calculation. Zero would divide by zero, and a negative SD is not a valid scale. This tool supports positive SD from 0.000000001 to 1,000,000,000.
How is this different from a z table?
This page starts with a raw value, mean and SD. The Interactive Z Table starts with a known z-score or normal-model probability. Transfer a z-score manually; the result link does not put your values in the URL.
What are the input and rounding limits?
Use complete decimal numbers with a period and no more than 10 significant digits; no commas or scientific input notation. Raw value and mean range from −1,000,000,000 to 1,000,000,000. Z-scores normally display up to four decimal places; model areas use the unrounded z-score and display six decimals or an inequality near zero or one. Extreme z-scores use scientific display notation.