Rank IQ Score Calculator

By CalculatorBolt Team | Published: | Updated: | Reviewed by: Test Prep/Quant Editor

Convert between raw scores, z-scores, percentiles, and IQ-style standardized scores. You can also estimate your expected rank in a cohort and find top-x% cutoffs. This is an educational approximation.

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Find the percentile/z needed to be in top X%

Note: The normal model extends to infinity in both directions. In practice, test scores are bounded and distributions may deviate from normal at the tails.

How It Works

We use the normal (Gaussian) model to convert among raw, z, percentile, and standardized scores. IQ-style scores use a configurable mean and SD (default 100/15). For cohort rank, we map percentile to an expected rank out of N.

  • Z-score: z = (x − μ) / σ
  • Percentile: p = Φ(z) × 100, where Φ is the standard normal CDF
  • IQ score: IQ = IQ_mean + z × IQ_SD
  • T-score: T = 50 + z × 10
  • Stanine: Maps z to 1–9 scale using standard cutpoints
  • Expected rank: rank ≈ N × (1 − p/100) + 1

Inputs Explained

  • Raw → Z/Percentile/IQ: Enter your test mean and SD to compute z, percentile, IQ, T, and stanine.
  • Percentile ↔ IQ: Convert either direction; see z and T at the same time.
  • Rank & Cutoff: Give a cohort size and your percentile to estimate expected rank; compute top-x% thresholds.

Examples

Example 1 (Raw → IQ)

x = 82, μ = 70, σ = 10 → z = 1.20 → p ≈ 88.5% → IQ ≈ 118 → T ≈ 62

Example 2 (Percentile → IQ)

p = 95% → z ≈ 1.645 → IQ ≈ 125 (100/15) → T ≈ 66

Example 3 (Rank)

N = 12,000, p = 93% → rank ≈ 12,000 × (1 − 0.93) + 1 = 841 (approx)

Top 10% cutoff → p* = 90%, z* ≈ 1.282

Tips & Notes

  • Real exams may not be perfectly normal; distributions can be skewed or bounded.
  • If you know a published curve, match IQ mean/SD to that standard or use the composite mode.
  • For ranks, the estimate is smoother for large N; small cohorts show more variability.

FAQs

It assumes a normal distribution. Many tests approximate normal, but not all. Treat results as rough guides.

Psychometric IQ tests commonly use 100/15. Some "T-IQ" variants use different parameters—configure as needed.

Yes—use the Percentile ↔ IQ tab to convert either direction and see z and T simultaneously.

Expected rank ≈ N×(1−p/100)+1 under a normal-percentile model. It's an estimate, not an official rank.

No. Everything runs in your browser. Use the Share Link to keep or share your settings.

No. It's an educational tool. For psychological assessment, see a qualified professional and standardized tests.

Disclaimer

Educational estimate only. Not psychological or clinical advice. Scales and distributions vary by exam and population.

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