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Z-Score Calculator

Standardize a value: z = (x − μ) / σ.

Best for: Comparing scores from different tests, flagging outliers, and standardising data before further analysis.

Complete guide
Why this result happened View assumptions

Input

How it's calculated & sources
The Z-Score Calculator uses the standard, deterministic formula, so the same inputs always produce the same result. It runs entirely in your browser, so your inputs are never uploaded. Last reviewed June 2026.
Key assumptions
  • Approximately normal distribution

Free & no sign-up · runs entirely in your browser. Results are estimates for general information, not professional advice — verify important decisions with a qualified expert. Last reviewed June 2026.

How it works

z = (x − μ) / σ. Tells how many standard deviations x is from the mean.

Example

x=85, μ=75, σ=5 → z = 2 (2 SD above mean)

Frequently asked questions

How to interpret z?+

|z| > 2 is unusual, |z| > 3 is very unusual under a normal distribution.

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Complete guide

Quick answers

Short, sourced answers to the questions people (and AI assistants) ask most.

What is Z-Score?
A z-score calculator tells you how many standard deviations a value sits above or below the mean of its dataset.
Why does Z-Score matter?
The z-score puts values from different scales on a common footing. For a normal distribution it also maps to a percentile — a z of 0 is the 50th percentile, +1 is about the 84th.
How is Z-Score calculated?
It computes z = (x - mean) / standard deviation. A z of +2 means the value is two standard deviations above the mean; -1.5 means one and a half below. Formula: z = (x - mean) / standard deviation.
What are common z-score mistakes?
Mixing population and sample standard deviations between steps.
When should you use the Z-Score Calculator?
Comparing scores from different tests, flagging outliers, and standardising data before further analysis.

What is the Z-Score Calculator?

A z-score calculator tells you how many standard deviations a value sits above or below the mean of its dataset.

How the Z-Score Calculator works

It computes z = (x - mean) / standard deviation. A z of +2 means the value is two standard deviations above the mean; -1.5 means one and a half below.

z = (x - mean) / standard deviation

What impacts results most

  1. 1.
    Value (High impact)How far it sits from the mean.
  2. 2.
    Mean (High impact)The reference point.
  3. 3.
    Standard deviation (High impact)Scales the distance.

Key assumptions

  • Approximately normal distribution

Z-score to percentile (standard normal distribution)

-30.13%99.87%
-2.580.49%99.51%
-1.962.50%97.50%
-1.655.00%95.00%
-115.87%84.13%
-0.530.85%69.15%
050.00%50.00%
0.569.15%30.85%
184.13%15.87%
1.2889.97%10.03%
1.6595.00%5.00%
1.9697.50%2.50%
2.5899.51%0.49%
399.87%0.13%

Key terms

Standardisation:
Rescaling values to a mean of 0 and standard deviation of 1.
Percentile:
The share of values that fall below a given point.

Common mistakes to avoid

  • Mixing population and sample standard deviations between steps.
  • Reading a percentile from the z-score when the data is not approximately normal.
  • Sign confusion — a negative z is below the mean, not an error.

Keywords: z, score, standardize.

Sources: NIST/SEMATECH e-Handbook of Statistical Methods

Reviewed by the Free Tools Galaxy editorial team · Updated June 2026 · Calculated privately in your browser.

Frequently asked questions

Is the Z-Score Calculator free to use?+

Yes. Every tool on Free Tools Galaxy is 100% free, runs in your browser and requires no signup.

How accurate is the Z-Score Calculator?+

Z-Score Calculator uses the standard z-score formula in double-precision arithmetic, so the same inputs always produce the same result and you can verify any figure by hand. It is an educational estimate — real-world outcomes depend on your actual rates, rules and assumptions.

Do you store my inputs?+

No. The Z-Score Calculator runs entirely in your browser. Nothing is uploaded or saved to a server.

Can I use the Z-Score Calculator on mobile?+

Yes — the interface is fully responsive and works on phones, tablets and desktops.

What are common mistakes to avoid?+

The most frequent mistake is mixing units. Double-check your inputs use a single, consistent unit before clicking Calculate.

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Standardize a value: z = (x − μ) / σ.

Try it: https://freetoolsgalaxy.com/tools/z-score-calculator
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