How IQ Scores Are Calculated

If you take an IQ test and answer 40 out of 60 questions correctly, your IQ isn't 40, and it isn't a percentage. It's a completely different number, like 112, that comes from comparing your performance to thousands of other people. Here's exactly how that comparison works, step by step.

Step 1: Your score only means something next to other people's scores

Before any test is sold or used, the company that made it gives it to a large group of people — often several thousand — who are meant to represent the general population: different ages, backgrounds, and regions. This group is called the norm group (or standardization sample).

The point of the norm group is simple: it tells the test maker what a "typical" score looks like, and how much scores normally vary from person to person. Without it, a raw score like "40 correct answers" is meaningless — you'd have no way to know if that's impressive or below average.

This is also the reason two people can get the same number of questions right on two different IQ tests and end up with different IQ scores. Each test has its own norm group, its own questions, and its own difficulty level, so "40 correct" means something different on each one.

Step 2: Most people cluster near the middle — the bell curve

When you plot the norm group's scores on a graph, they form a pattern that shows up again and again in nature and in testing: a bell curve (technically, a normal distribution). Most people land somewhere near the middle. Fewer people score very high or very low. Almost nobody lands at the extreme edges.

Two numbers describe that curve completely:

• The average (also called the mean) — the score right in the middle of the curve.
• The standard deviation — a measure of how spread out scores typically are from that average. A small standard deviation means most people score close to the average. A large one means scores are more spread out.

Standard deviation is the part people find hardest to picture, so it's worth pausing on it before going further.

What "standard deviation" actually means

Standard deviation answers one question: on average, how far does a typical person's score sit from the mean? It's calculated by measuring how far every person's score is from the average, squaring those differences (so a score 10 points above and 10 points below both count the same), averaging them, and then taking the square root to bring the number back to a normal, readable scale.

You don't need to run that calculation yourself — the test publisher already has. What matters is what the result lets you do: once you know the average and the standard deviation of a test, you can say precisely how unusual any given score is, using a rule that holds for every bell curve:

• About 68% of people score within 1 standard deviation of the average
• About 95% of people score within 2 standard deviations of the average
• About 99.7% of people score within 3 standard deviations of the average

This is sometimes called the 68–95–99.7 rule, and it's the same rule that describes height, blood pressure, and most other traits that vary naturally across a population (Neisser et al., 1996).

Try it: flatten or sharpen the curve

The standard deviation is what controls the shape of the bell curve — how concentrated or spread out scores are around the average. Drag the slider to make the curve narrower (a smaller standard deviation) or flatter (a larger one), and watch how the ±1 SD range changes even though the average always stays at 100.

Step 3: Nearly every major test uses the same ruler — mean 100, standard deviation 15

Once a publisher knows its norm group's average and standard deviation, it rescales every future score onto a fixed, easy-to-read scale. The overwhelming convention today, used by the Wechsler Adult Intelligence Scale (WAIS), the Wechsler Intelligence Scale for Children (WISC), and the Stanford-Binet Intelligence Scales, is:

• Average = 100
• Standard deviation = 15

That means, on any of these tests, a score of 115 is one standard deviation above average, and a score of 130 is two standard deviations above average — regardless of how many raw questions each test contains. This shared scale (known as the deviation IQ) is what makes it possible to say "an IQ of 130" and have it mean roughly the same thing across different tests (Kaufman & Lichtenberger, 2006).

The underlying math for converting a raw score to this scale uses a z-score — how many standard deviations a raw score sits from the norm group's average:

z-score = (your raw score − norm group average) / norm group standard deviation

That z-score is then stretched onto the familiar 100/15 scale:

IQ score = 100 + (z-score × 15)

A z-score of 0 becomes an IQ of exactly 100. A z-score of +2 becomes an IQ of 130.

How popular IQ tests actually compare

Not every test uses the exact same convention, and knowing the differences matters if you're comparing scores across tests or aiming for a specific admission cutoff.

| Test | Typical scale | Notes | |---|---|---| | WAIS-IV / WAIS-5 (adults) | Mean 100, SD 15 | The most widely used clinical IQ test for adults; scores are built from several subtests covering verbal comprehension, working memory, processing speed, and perceptual reasoning. | | WISC-V (children) | Mean 100, SD 15 | Same scale and structure as WAIS, adapted for ages 6–16. | | Stanford-Binet 5 | Mean 100, SD 15 | One of the oldest IQ tests still in use, now aligned to the same 100/15 convention as Wechsler scales. | | Raven's Progressive Matrices | Percentile-based, often converted to mean 100, SD 15 | A nonverbal, pattern-based test; raw scores are typically reported as percentiles first, then optionally converted to the standard IQ scale. | | Cattell Culture Fair III | Historically mean 100, SD 24 | An older test that used a wider standard deviation, meaning the same relative standing produces a visibly higher-looking number than on a SD-15 test. | | Mensa admission tests | Cutoff at the 98th percentile | Mensa doesn't use one fixed test — it accepts scores from several supervised tests (often Wechsler or Cattell scales), as long as the result lands at or above the 98th percentile on that test's own norms. |

The Cattell example is a useful warning sign: a raw "IQ of 148" on an SD-24 test is not more impressive than a 132 on a standard SD-15 test — both represent the same 98th-percentile standing, just expressed on different rulers. Always check which standard deviation a reported score is based on before comparing it to another test.

Try it: turn a score into a percentile

Move the marker below to see how a score translates into a z-score and a percentile — the same conversion every standardized IQ test performs internally. For more on the reasoning behind standard deviation specifically, see our companion article, what is standard deviation?

Scores above 145 or below 55 are correspondingly rare on a standard SD-15 test — under 1 in 1,000 people — and get rarer very quickly beyond that, since the bell curve's density drops off sharply the further out you go.

What the number is actually estimating

IQ scores are a proxy for general cognitive ability (often called g), not a single fixed trait, and not a direct measurement of "intelligence" in the everyday sense — see our deeper dive on what IQ actually measures for the evidence on that distinction. Performance can also shift with practice, sleep, stress, and familiarity with the question formats, which is the entire premise behind targeted practice with varied question formats — number series, matrices, spatial reasoning.

If you're prepping for a specific admission test, see our test guides for format-by-format breakdowns.

---

Sources

• Neisser, U., Boodoo, G., Bouchard, T. J., et al. (1996). Intelligence: Knowns and unknowns. American Psychologist, 51(2), 77–101.
• Kaufman, A. S., & Lichtenberger, E. O. (2006). Assessing Adolescent and Adult Intelligence (3rd ed.). Wiley.