Z-Score Calculator

z = (x − μ) / σ — how many standard deviations a value is above or below the mean.

Inputs

Result

Loading calculator…
—

General calculation reads

Amazon affiliate
How Not to Be Wrong
Jordan Ellenberg - math thinking
Shop on Amazon
The Joy of X
Steven Strogatz - accessible math
Shop on Amazon
Scientific calculator (Casio fx-991EX)
Shop on Amazon

As an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.

How to use this calculator

  • Enter the value, mean, and standard deviation.
  • Read the z-score and approximate percentile.

About this calculator

A z-score expresses how many standard deviations a value is from the mean. Positive = above the mean; negative = below. z=1 means one σ above; z=−2 means two σ below. For a normally distributed dataset, z translates directly to a percentile via the normal CDF.

Frequently asked

How big is a "high" z-score?+
|z| > 2 is unusual (~5% chance for normal data). |z| > 3 is rare (~0.3%).
Can z-score be negative?+
Yes — values below the mean produce negative z-scores.
Does z-score require normal data?+
The formula doesn't — it works on any data with a defined mean and SD. The percentile interpretation only holds for approximately normal data.
How does z-score relate to standardization?+
Computing z-scores for every value standardizes the dataset to mean 0, SD 1. Useful for comparing variables on different scales.
Is z-score the same as t-score?+
Similar idea but t-score uses sample SD and a slightly different distribution; t is used for small samples (n < 30).

Related calculators

T-Score Calculator
t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.
Standard Deviation Calculator
Compute sample (n−1) and population (n) standard deviation from a list of numbers.
Mean (Average) Calculator
Compute the arithmetic mean of a list of numbers.
Percentile Calculator
Find the value at the kth percentile in a dataset (linear interpolation).
Normal Distribution Calculator (PDF + CDF)
Compute probability density and cumulative probability at x for given μ, σ.
P-Value Calculator (z to p)
Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.

T-Score Calculator
Calc

t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.

P-Value Calculator (z to p)
Calc

Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.

Standard Deviation Calculator
Calc

Compute sample (n−1) and population (n) standard deviation from a list of numbers.

Percentile Calculator
Calc

Find the value at the kth percentile in a dataset (linear interpolation).

Normal Distribution Calculator (PDF + CDF)
Calc

Compute probability density and cumulative probability at x for given μ, σ.

Auto Lease Calculator
Finance

Monthly lease payment from MSRP, capitalized cost, residual value, money factor, term, sales tax, and down payment — using the standard lease-payment formula (depreciation + finance + tax).