What does a negative z-score mean?

The value is below the mean. z = −1 is about the 16th percentile.

Is the SAT normally distributed?

Close enough for this estimate; the real distribution is bounded at 400 and 1600 and slightly skewed.

Z-score calculator

standard normal

z-score

Valuethe score you havex
Meanpopulation or sample meanμ
Standard deviationσ

88th percentile

z = (x − μ) ÷ σ. The percentile is the area under the standard normal curve to the left of z. Defaults are the SAT: mean 1050, SD 210.

How many standard deviations a score sits from the mean, and what share of the population sits below it. The defaults are the SAT (mean 1050, standard deviation 210).

Worked examples

SAT 1300: z = (1300 − 1050) ÷ 210 = 1.19, about the 88th percentile.
ACT 24: With mean 19.5 and SD 5.7: z = 0.79, about the 78th percentile.

How it is calculated

z = (x − μ) ÷ σ. The percentile is Φ(z), the standard normal cumulative distribution, computed with the Abramowitz–Stegun approximation (error under 1.5 × 10⁻⁷).

Questions people ask

What does a negative z-score mean?: The value is below the mean. z = −1 is about the 16th percentile.
Is the SAT normally distributed?: Close enough for this estimate; the real distribution is bounded at 400 and 1600 and slightly skewed.

Embed this calculator

Paste this anywhere HTML is allowed. Free; keep the credit link. Teachers and tutoring sites are welcome.

<iframe src="https://thescorecurve.com/embed/z-score" width="100%" height="640" loading="lazy" title="Z-Score Calculator"></iframe>
<p><a href="https://thescorecurve.com/z-score-calculator">Z-Score Calculator</a> by ScoreCurve</p>