Iq Percentile Calculator

IQ Percentile Calculator

Calculation Results

Percentile Rank:

function calculateIQPercentile() { var iq = parseFloat(document.getElementById('iqScore').value); var mean = parseFloat(document.getElementById('iqMean').value); var sd = parseFloat(document.getElementById('iqSD').value); if (isNaN(iq) || isNaN(mean) || isNaN(sd) || sd = 0.5) { rarity = 1 / (1 – percentile); } else { rarity = 1 / percentile; } var resultDiv = document.getElementById('iqResult'); resultDiv.style.display = 'block'; document.getElementById('percentileValue').innerText = percentileFormatted + "%"; var rarityDescription = ""; if (iq > mean) { rarityDescription = "You scored higher than approximately " + percentileFormatted + "% of the population. This performance is roughly 1 in every " + Math.round(rarity).toLocaleString() + " people."; } else if (iq < mean) { rarityDescription = "You scored higher than approximately " + percentileFormatted + "% of the population. This score is in the bottom " + (100 – percentileFormatted).toFixed(2) + "% of the population."; } else { rarityDescription = "Your score is exactly at the average. You scored higher than 50% of the population."; } document.getElementById('rarityText').innerText = rarityDescription; document.getElementById('zScoreText').innerText = "Z-Score: " + z.toFixed(4); } // Approximation of the error function (erf) function erf(x) { var a1 = 0.254829592; var a2 = -0.284496736; var a3 = 1.421413741; var a4 = -1.453152027; var a5 = 1.061405429; var p = 0.3275911; var sign = (x < 0) ? -1 : 1; x = Math.abs(x); var t = 1.0 / (1.0 + p * x); var y = 1.0 – (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * Math.exp(-x * x); return sign * y; }

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Understanding the IQ Percentile Calculator

An IQ percentile indicates how your intelligence quotient score compares to the rest of the population. IQ scores follow a Normal Distribution, commonly known as the Bell Curve. By understanding your percentile, you can determine exactly where you stand in relation to others.

What is a Percentile Rank?

A percentile rank is not the same as a percentage score on a test. If you are in the 90th percentile, it does not mean you got 90% of the questions correct. Instead, it means you performed better than 90% of the people who took the same test.

The Role of Mean and Standard Deviation

Most modern IQ tests, such as the Wechsler Adult Intelligence Scale (WAIS) or the Stanford-Binet, use a specific mathematical framework:

• Mean (Average): Usually set at 100. This is the peak of the bell curve.
• Standard Deviation (SD): Usually 15. This measures the spread of the scores.

With an SD of 15, about 68% of the population falls between an IQ of 85 and 115. About 95% falls between 70 and 130.

Common IQ Percentile Examples

IQ Score (SD 15)	Percentile Rank	Classification
145	99.8th	Very Gifted
130	97.7th	Gifted (Mensa Level)
115	84.1st	High Average
100	50.0th	Average
85	15.9th	Low Average

How the Calculation Works

To find the percentile, we first calculate the Z-score, which tells us how many standard deviations a score is from the mean. The formula is:

Z = (Score – Mean) / SD

Once we have the Z-score, we use the cumulative distribution function (CDF) of the standard normal distribution to determine the area under the curve to the left of that score, which represents the percentile.

Why Percentiles Matter

Raw IQ scores can be confusing because different tests might use different scales (e.g., Cattell uses an SD of 24). Percentiles provide a universal language. Being in the 98th percentile means the same thing regardless of whether the test mean is 100 or 1000—it means you are in the top 2% of the population.