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Z-Score Calculator - Quick One-Line Result

z-score calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

z = (X - ฮผ) / ฯƒ | P(Z โ‰ค z) from standard normal CDF

The z-score measures how many standard deviations a value is from the mean. z = 0 is the mean, z = 1 is one SD above. The normal CDF gives the probability of a value being below z.

Worked Examples

Example 1: IQ score of 85

Problem:X=85, ฮผ=100, ฯƒ=15

Solution:z = (85-100)/15 = -1.00. P(Z โ‰ค -1) = 0.1587 (15.87th percentile)

Result:z = -1.00, 15.87th percentile

Frequently Asked Questions

How do I calculate my one-rep max for weightlifting?

The Epley formula estimates 1RM: weight x (1 + reps/30). For example, if you bench press 150 lbs for 8 reps, your estimated 1RM is 150 x (1 + 8/30) = 190 lbs. Use this for programming percentages without the risk of actual max attempts.

How do I get the most accurate result?

Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.

How do I verify Z-Score Calculator - Quick One-Line Result's result independently?

The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.

Why might my result differ from another tool or reference?

Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.

Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy