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Z-Score Calculator

Math Calculators

Standardization, percentile and normal probability

Quick Answer

Z-Score Calculator: Standardization, percentile and normal probability. Z-Score Calculator uses standard math formulas to compute accurate results instantly.

Z 分数

1.300

Percentile 90.3% — beats 90.3% of values

Z1.300
Percentile90.3%
Above (1-Φ)9.7%

Position on normal curve

-3σ~-2σ
-2σ~-1σ
±1σ
1σ~2σ
2σ~3σ

Between 1σ-2σ — less common (27%)

Steps

  1. 1z = (x − μ) ÷ σ = (88 − 75) ÷ 10 = 13.00 ÷ 10 = 1.300
  2. 2Φ(z) = Φ(1.300) = 90.3% percentile

Z-score reference

ZPercentileMeaning
-22.3%Bottom 2.3%
-115.9%Bottom 15.9%
050.0%Exactly average (50%)
184.1%Top 15.9%
1.64595.0%Top 5% (one-tailed 95%)
1.9697.5%Top 2.5% (two-tailed 95%)
297.7%Top 2.3%
399.9%Top 0.13%

💡 Z-score standardizes any normal distribution to μ=0, σ=1, letting you compare across different scales (SAT vs IQ vs height). Rule of thumb: |z|>2 deserves attention, |z|>3 is exceptional. Sample mode uses n−1 (Bessel correction).

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How to Use

  1. Enter values or expressions: type directly into the Z-Score Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Z-Score Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Standardization, percentile and normal probability.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Z-Score Calculator formula

Z-Score Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Z-Score Calculator?
Open the page and fill in the input fields — results update automatically. Standardization, percentile and normal probability.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Z-Score Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/z-score

Results provided by this tool are for reference only and do not constitute professional advice.