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IQ rarity calculator

Turn an IQ into “1 in N score this high or higher,” with percentile cross-check. Normal-curve illustration only.

Defaults to your region. Switch to compare any other scale.

WAIS/WISC-style: mean 100, SD 15.

Rarity answers “how many people score this high or higher?” (one-tailed).

Result

1 in 44

Rarity (this high or higher)

About 2.3% of people score ≥ this IQ

  • Percentile (context)97.7%
  • Qualitative bandVery superior / gifted band (≥130)
  • z-score2.00
  • Scale SD (σ)15
  • Upper-tail probability2.28%

One-tailed rarity

Educational estimate from a normal curve (μ=100). Not a clinical assessment, not WAIS/WISC, and not a substitute for a licensed psychologist.

About this tool

IQ rarity answers how uncommon a score is on a normal curve (mean 100). You get a 1-in-N figure for scoring this high or higher, plus the matching percentile, under SD 15 or SD 16 assumptions.

Rarity language is easy to over-read. It is a mathematical tail probability, not a membership card for any society and not a substitute for supervised testing. Extremely high or low inputs are especially sensitive to the SD choice.

Cross-check the percentile view on the IQ percentile calculator. Both tools are educational illustrations of the normal model used in many textbooks.

Formula

  • z = (IQ − 100) / σ
  • P(X ≥ IQ) = 1 − Φ(z)
  • rarity = 1 / P(X ≥ IQ) → “1 in N score this high or higher”

How it is calculated

  1. Enter the IQ score.
  2. Pick Wechsler SD=15 (default) or SD=16.
  3. We report one-tailed rarity (this high or higher) plus percentile for context.
  4. If your country, school or provider uses different rules, pick another option in the “Standard” menu at the top.

Questions

Is rarity one-tailed or two-tailed?

This tool uses the common “gifted / high-IQ” UX: one-tailed — how many people score this high or higher (1 / (1 − Φ(z))). Two-tailed rarity (either extreme) would be about half as large a “1 in N” for the same |z|.

Why does IQ 100 say about 1 in 2?

By design half the population is at or above the mean. So “this high or higher” at IQ 100 is roughly 50% → about 1 in 2.

Is this a clinical IQ test?

No. It converts a score you already have into rarity under a normal model. Not WAIS/WISC and not a diagnosis.

When should I change the “Standard” setting?

When the rules you work with differ from the default chosen for your language. Options on this page: Wechsler (SD = 15); Stanford–Binet / Cattell-style (SD = 16). The formula, steps and result update to match your choice.

Sources

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