Child IQ Calculator

Explore developmental cognitive index scores across Verbal Comprehension, Visual Spatial, Fluid Reasoning, Working Memory, and Processing Speed based on standardized intelligence paradigms (Wechsler WISC-V and Stanford-Binet 5). Calculate composite Full-Scale IQ, 95% confidence intervals, standard deviation bell curve positions, and domain percentile ranks.

Standardized intelligence batteries scale cognitive performance against age-normed peer samples, establishing a Gaussian normal distribution with an international mean (μ) of 100 and a standard deviation (σ) of 15.

• Domain-Weighted Composite FSIQ: FSIQ = 0.25 × VCI + 0.20 × VSI + 0.25 × FRI + 0.15 × WMI + 0.15 × PSI. Composite Full-Scale IQ derived from core cognitive domains (Verbal, Visual, Reasoning, Memory, Speed).
• Standard Score Z-Transformation: z = (FSIQ - 100) / (15). Standard deviation metric indicating distance above or below the general population mean.
• Theoretical Population Percentile Rank: P = Phi(z) = (1) / (2) [1 + erf(fracz√(2))] × 100. Cumulative percentage of the standardized peer group scoring at or below the calculated score.
• 95% Confidence Interval Band: CI_95\% = FSIQ pm 1.96 × SEM ≈ FSIQ pm Delta_test. Measurement error interval reflecting true score probability (typically ±5 for WISC-V, ±4 for Stanford-Binet, ±6 for WPPSI).

• Assessment Framework: WISC-V Normative Standard (Mean = 100, SD = 15, Confidence Band = ±5)
• Verbal Comprehension (VCI): 110 (75th percentile - strong vocabulary and verbal reasoning)
• Visual Spatial Index (VSI): 105 (63rd percentile - solid geometric and architectural assembly)
• Fluid Reasoning Index (FRI): 100 (50th percentile - normative inductive logic)
• Working Memory Index (WMI): 95 (37th percentile - age-appropriate short-term auditory retention)
• Processing Speed Index (PSI): 90 (25th percentile - deliberate, methodical visual scanning)

1. Domain Multiplications: VCI = 110 × 0.25 = 27.50; VSI = 105 × 0.20 = 21.00; FRI = 100 × 0.25 = 25.00
2. Memory & Speed Multiplications: WMI = 95 × 0.15 = 14.25; PSI = 90 × 0.15 = 13.50
3. Full-Scale Sum: 27.50 + 21.00 + 25.00 + 14.25 + 13.50 = 101.25 → 101 FSIQ
4. Z-Score Transformation: z = (101 - 100) / 15 = +0.067
5. Cumulative Normal Percentile: Φ(0.067) = 52.7% → 53rd Percentile
6. 95% Confidence Interval: 101 ± 5 → [96 to 106]
7. Cognitive Discrepancy Check: VCI (110) vs PSI (90) shows a 20-point spread (>15 pts), highlighting an uneven profile (verbal strength with deliberate processing).

The child achieves a solid Full-Scale IQ of 101 (53rd percentile), firmly in the Average range. The 20-point gap between Verbal Comprehension and Processing Speed indicates strong verbal conceptualization paired with a methodical pace, a very common developmental variation.

• Range: 130 and above | Label: Very Superior / Extremely High | Percentile: Top 2.2% | Description: Advanced conceptual, abstract problem solving and rapid knowledge acquisition.
• Range: 120 to 129 | Label: Superior | Percentile: 91st to 97th | Description: Significantly above-average reasoning and high academic learning capacity.
• Range: 110 to 119 | Label: High Average | Percentile: 75th to 90th | Description: Strong cognitive competence across core scholastic and verbal disciplines.
• Range: 90 to 109 | Label: Average | Percentile: 25th to 74th | Description: Normative developmental trajectory encompassing approximately 50% of children.
• Range: 80 to 89 | Label: Low Average | Percentile: 9th to 24th | Description: May benefit from structured scaffolding in demanding or pace-dependent tasks.
• Range: 70 to 79 | Label: Borderline | Percentile: 2nd to 8th | Description: Indicates developmental or learning areas where targeted intervention is beneficial.
• Range: Below 70 | Label: Extremely Low | Percentile: < 2nd percentile | Description: Requires comprehensive clinical assessment for individualized educational plans (IEP).