z Z-Score Calculator (with Percentile & Probability)

How many standard deviations from the mean — and what share of people score lower?

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Formula at a glance

Z-Score Calculator: z-score — z = (x − μ) / σ. Example: Score 85, mean 70, SD 10 → z-score: 1.5
How the Z-Score Calculator works: z-score — z = (x − μ) / σ

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📘 About the Z

A z-score (standard score) tells you how many standard deviations a value is above or below the mean. It puts different scales on a common footing — comparing an IQ score with an SAT score, or a child’s height with growth charts — and turns values into normal-distribution probabilities and percentiles.

Enter the value, mean and standard deviation (or paste data). The calculator gives z, the percentile (the probability of a lower value), the probability of a higher value, the central area and two-tailed p-value, and shades the area on the bell curve.

🧮 Formula

z-score
z = (x − μ) / σ
Percentile
P(X < x) = Φ(z)
Back to a value
x = μ + z·σ

✏️ Worked examples

Score 85, mean 70, SD 10

You enter
Value x85
Mean μ70
Standard deviation σ10
You get
z-score1.5
Meaning1.5 standard deviations above the mean
P(X < 85)0.933193 (93.3193% — percentile)
P(X > 85)0.0668072 (6.68072%)
P(between −|z| and |z|)0.866386
Two-tailed p-value0.133614
Mean · SD used70 · 10

z = 1.5.

IQ of 130

You enter
Value x130
Mean μ100
Standard deviation σ15
You get
z-score2
Meaning2 standard deviations above the mean
P(X < 130)0.97725 (97.725% — percentile)
P(X > 130)0.0227501 (2.27501%)
P(between −|z| and |z|)0.9545
Two-tailed p-value0.0455003
Mean · SD used100 · 15

z = 2.

🧭 How to use this calculator

What you enter

  • Value x
  • Mean μ
  • Standard deviation σ
  • Or paste data to use its mean and SD (optional)Separate numbers with commas, spaces or new lines.

What you get

  • z-score
  • Meaning
  • P(X < 85)
  • P(X > 85)
  • P(between −|z| and |z|)
  • Two-tailed p-value
  • Mean · SD used

❓ Frequently asked questions

What is a good z-score?

It depends on the context: z = 0 is average, z = 1 beats about 84% and z = 2 about 97.7% of a normal population.

Can a z-score be negative?

Yes — a negative z means the value is below the mean.

What z-score is 95% confidence?

±1.96 for a two-sided 95% interval; 1.645 for one-sided 95%.