Z-Score Calculator

Calculate z-score from value, mean, and standard deviation — with percentile lookup.

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Find the z-score and percentile for any value

Calculate Z-scoreFind value from Z

Value (x)

Mean (μ)

Standard deviation (σ)

Z-score (z)

Mean (μ)

Standard deviation (σ)

Decimals: use a period or a comma — 99.5 or 99,5.

—Z-score

—Percentile

Reference table: common Z-scores

Z-score	Percentile	Meaning
−3.0	0.13%	3σ below — extreme outlier
−2.576	0.50%	99% lower bound
−2.0	2.28%	2σ below the mean
−1.96	2.50%	95% lower bound (standard CI)
−1.645	5.00%	90% lower bound
−1.0	15.87%	1σ below the mean
0	50.00%	Exactly at the mean
1.0	84.13%	1σ above the mean
1.645	95.00%	90% upper bound
1.96	97.50%	95% upper bound (standard CI)
2.0	97.72%	2σ above the mean
2.576	99.50%	99% upper bound
3.0	99.87%	3σ above — extreme outlier

In Excel and Google Sheets

These formulas are identical in Microsoft Excel and Google Sheets.

Z-score (value in A2, mean in B2, std dev in C2):
=STANDARDIZE(A2, B2, C2)

Percentile (cumulative proportion) from Z-score in D2:
=NORM.S.DIST(D2, TRUE)

Value from Z-score (inverse):
=B2 + D2 * C2

Z-score for a given percentile (e.g. 0.95):
=NORM.S.INV(0.95)

In SQL

Compute each row's Z-score relative to the column mean and standard deviation. Works in PostgreSQL, BigQuery, and other engines with window functions.

SELECT
    value,
    (value - AVG(value) OVER())
      / NULLIF(STDDEV_POP(value) OVER(), 0) AS z_score
FROM measurements;

NULLIF avoids division by zero when all values are equal (σ = 0). STDDEV_POP uses the population standard deviation (N); for sample (N−1) use STDDEV_SAMP.

About this z-score calculator

Enter a value, the population mean, and the standard deviation to calculate the z-score: z = (x − μ) / σ. The result tells you how many standard deviations a value is above or below the mean. A z-score of 1.96 means the value is at the 97.5th percentile — only 2.5% of values in a normal distribution fall above it. The calculator also works in reverse: enter a z-score, mean, and standard deviation to find the original value.

Z-scores are the foundation of hypothesis testing, quality control (Six Sigma), grading on a curve, and comparing measurements across different scales. The built-in reference table shows common z-scores and their percentiles so you can interpret results without a separate lookup. Excel and SQL formulas are included for use in your own analysis.

Reference tables

Z-Score Table — Standard Normal DistributionLook up the area to the left of any z-score, positive or negative, to four decimal places.

FAQ

What does a negative z-score mean?

A negative z-score means the value is below the mean. A z-score of −1.5 means the value is 1.5 standard deviations below average. About 6.68% of values in a normal distribution fall below −1.5.

What z-score corresponds to the 95th percentile?

A z-score of 1.645 corresponds to the 95th percentile (one-tailed), and ±1.96 covers the middle 95% (two-tailed). These are the most commonly used thresholds in statistics.

Can I compare z-scores from different datasets?

Yes — that is exactly what z-scores are for. By standardizing to units of standard deviation, you can compare a test score from one exam to a score from a completely different exam, or compare height and weight on the same scale.