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IQ Standard Deviation Score Calculator

Work out iq standard deviation score instantly with clear inputs, formula shown and shareable results.

About IQ Standard Deviation Score Calculator

IQ scales set the mean at 100 with a standard deviation of 15 on Wechsler tests and 16 on Stanford-Binet, so the same ability gives different numbers. An IQ of 130 is exactly two standard deviations up on the SD 15 scale - the 97.7th percentile, about one person in 44 - and would read 132 on an SD 16 scale.

Formulas

Deviations from the mean

z = (IQ - 100) / scale standard deviation

Rarity

one in 100 / (100 - percentile) for above-average scores

Worked example

With the default values below, IQ Standard Deviation Score Calculator returns Standard Deviations From The Mean of 2.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

IQ scoreaccepts 40–200
130
Scale standard deviationminimum 1
15

Results

Standard Deviations From The Mean
2.000
Percentile Rank
97.725%
Rarity, One In
44.0
Equivalent On An SD 16 Scale
132.0

Step by step

  1. 1Values used
  2. 2Deviations from the mean
  3. 3Rarity
  4. 4Standard Deviations From The Mean= 2.000
  5. 5Percentile Rank= 97.725
  6. 6Rarity, One In= 44.0
  7. 7Equivalent On An SD 16 Scale= 132.0

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do different tests give different IQs?

Because of differing standard deviations and norming samples. A score is only meaningful with the scale and norm date stated.

What is the Flynn effect?

Raw performance has risen about three IQ points a decade, so norms must be restandardised or scores drift upwards over time.

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