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Home/Blog/How Is IQ Calculated? The Science Behind the Score
Mathematical equations and statistical charts showing IQ score distribution and standard deviation on a desk
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IQ Basics9 min read·May 16, 2026·Updated: July 11, 2026

How Is IQ Calculated? The Science Behind the Score

Understand the mathematics and psychology behind IQ scoring, standard deviations, and what your percentile ranking really means.

A

Ali J. Mohammed

TEST.IQ Research

You've just finished an IQ test and you're staring at a number. But here's the question: where did that number actually come from?

Is it the percentage of questions you got right? Your raw score out of some maximum? The answer is neither — and understanding how IQ scores are actually calculated will change how you interpret your results.

IQ scores are not raw percentages. They are relative measures — your performance compared to everyone else in your age group, expressed on a standardized scale. Here's exactly how it works.

The Core Concept: Deviation IQ

The modern IQ score is called a Deviation IQ, introduced by David Wechsler in 1939. It answers one simple question: compared to other people your age, how far above or below average are you?

The scale is set so that:

100

Always the mean

The exact middle of the population for your age group

15

Standard deviation

The average distance from the mean in IQ points

68%

Within 1 SD

Percentage of people scoring between 85 and 115

IQ Distribution — Standard Deviations (SD = 15)

0.1%
2.1%
13.6%
34.1%
34.1%
13.6%
2.1%
55-3σ
70-2σ
85-1σ
100Mean
115+1σ
130+2σ
145+3σ

68% of people score between 85 and 115 (within 1 standard deviation of the mean)

Why is the mean always 100?

IQ tests are periodically re-normed — recalibrated against a fresh representative sample of the population. This ensures that 100 always means "average for your age group today," even as populations and education levels change over time.

A Brief History: How IQ Calculation Evolved

The formula for calculating IQ has changed significantly since intelligence testing began. Understanding this history explains why the modern method is far superior to earlier approaches.

1905 — Binet-Simon Scale

Mental Age (MA)

Formula: No IQ score yet — just 'mental age' vs chronological age

Note: A 10-year-old with a mental age of 12 isn't as exceptional as a 5-year-old with the same mental age.

1916 — Stanford-Binet (Stern's Ratio IQ)

Ratio IQ = (MA ÷ CA) × 100

Formula: Mental Age divided by Chronological Age, multiplied by 100

Note: Ratio IQ breaks down in adulthood — mental age doesn't keep growing past ~16.

1939 — Wechsler Scale (Deviation IQ)

Deviation IQ = 100 + 15 × (z-score)

Formula: Your score compared to others your age — not to a fixed 'mental age'

Note: This is the modern standard. No significant problems — it's what virtually all tests use today.

🧠 Want to see how your IQ score is calculated?

Our IQ test uses the same statistical principles described in this article — normed scores, percentiles, and standard deviations. Take it free and see your full breakdown instantly.

Take the Free IQ Test — No Registration Required →

Step-by-Step: How Your IQ Score Is Calculated

Here's the actual process that converts your answers into an IQ score — from raw responses to the final number:

01

Raw Score

You answer a series of questions. Each correct answer adds to your raw score.

Example: You get 47 out of 60 questions correct → Raw Score = 47

02

Scaled Score

The raw score is converted to a scaled score using a lookup table based on your age group.

Example: Raw score 47 for a 28-year-old → Scaled Score = 12 (out of 19)

03

Z-Score (Standard Score)

The scaled score is converted to how many standard deviations you are from the mean.

Example: Scaled score 12 → Z-score = +0.67 (above average)

04

IQ Score (Deviation IQ)

Z-score is converted to the familiar IQ scale: Mean=100, SD=15.

Example: IQ = 100 + (15 × 0.67) = 100 + 10 = 110

05

Percentile Rank

Your IQ score is translated into a percentile — the percentage of people you scored higher than.

Example: IQ 110 → 75th percentile (scored higher than 75% of people your age)

The formula in plain math

IQ = 100 + 15 × Z
Where Z = (your score − population mean) ÷ standard deviation

If you score exactly at the mean → Z = 0 → IQ = 100
If you score 1 SD above the mean → Z = 1 → IQ = 115
If you score 2 SDs above the mean → Z = 2 → IQ = 130

IQ Score to Percentile: The Complete Table

Your percentile tells you what percentage of people your age scored lower than you. Here's how IQ scores map to percentiles:

IQ ScorePercentileWhat It Means
16099.997thExtremely rare — 1 in 30,000
14599.9thTop 0.1% of the population
13097.7thTop 2.3% — gifted range
12091stTop 9% — superior intelligence
11584thTop 16% — high average
11075thTop 25% — above average
10050thExactly average
9025thBottom 25% — low average
8516thOne SD below average
702.3rdBottom 2.3% — extremely low

The Flynn Effect: Why Tests Must Be Re-normed

One of the most fascinating discoveries in intelligence research is the Flynn Effect — named after philosopher James Flynn, who documented it in the 1980s. Average raw IQ scores have risen approximately 3 points per decade throughout the 20th century across many countries.

Think about what that means. If you took a test normed in 1950 today, you'd likely score significantly higher than 100 — not because you're smarter than an average 1950s person, but because education, nutrition, and exposure to abstract thinking have improved the entire population's performance on these specific tasks.

The Flynn Effect

Average raw scores on the same IQ test have risen ~3 points per decade. Tests must be re-normed to keep the average at 100.

1930s
72
1950s
78
1970s
84
1990s
90
2010s
96
Today
100

Raw score equivalent to IQ 100, by decade. Source: Flynn (1984, 2012), Pietschnig & Voracek (2015).

This is why tests must be regularly re-normed. Using outdated norms would systematically inflate IQ scores — a serious issue in legal and clinical settings, known as the obsolescence effect.

Outdated norms = inflated scores

Some popular online IQ tests use norms that are 10–20 years old. This can inflate your score by 5–10 points compared to a properly normed modern test. Always check when a test was last normed before trusting its results.

Confidence Intervals: Why Your Score Has a Range

No IQ test is perfectly precise. Every score comes with a standard error of measurement (SEM) — typically ±5 points for well-constructed tests. This means if your score is 115, your "true" IQ likely falls somewhere between 110 and 120.

This is why psychologists report IQ scores with a confidence interval rather than a single number. A score of "115 ± 5 (90% confidence)" is more honest than simply reporting "115."

Confidence Interval Example — Score: 115

105
125
90% confidence interval (±5)Point estimate (115)

The Bottom Line

IQ is not a raw score or a percentage — it's a standardized measure of where you stand relative to your age group. The Deviation IQ formula converts your raw performance into a number where 100 is always average, 115 is always one standard deviation above average, and so on.

Understanding this helps you interpret your results more accurately — and appreciate both what your score tells you and what it doesn't. A score of 112 doesn't mean you answered 112 questions correctly. It means you performed better than roughly 79% of people your age on a set of carefully normed cognitive tasks.

See your own score — calculated the right way

Our IQ test uses proper statistical norming and gives you your score with full context — including percentile rank and cognitive breakdown.

Take Free IQ Test
#IQ Calculation#Standard Deviation#Bell Curve#Flynn Effect#Percentile#Deviation IQ

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