Iq Calculator Percentile

IQ Percentile Calculator

Enter your IQ score to find out what percentile it falls into, based on a mean IQ of 100 and a standard deviation of 15.

// Function to approximate the Error Function (erf) // Based on Abramowitz and Stegun, formula 7.1.26 function erf(x) { // constants var a1 = 0.254829592; var a2 = -0.284496736; var a3 = 1.421413741; var a4 = -1.453152027; var a5 = 1.061405429; var p = 0.3275911; // Save the sign of x var sign = 1; if (x < 0) { sign = -1; x = -x; } // A&S formula 7.1.26 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; } // Function to calculate the Cumulative Distribution Function (CDF) for a standard normal distribution function normalCDF(z) { return 0.5 * (1 + erf(z / Math.sqrt(2))); } // Main calculation logic function calculateIQPercentile() { var iqScoreInput = document.getElementById("iqScore").value; var iqScore = parseFloat(iqScoreInput); var resultDiv = document.getElementById("iqPercentileResult"); // Validate input if (isNaN(iqScore) || iqScore 200) { // Reasonable range for IQ resultDiv.innerHTML = "Please enter a valid IQ score between 40 and 200."; return; } // Standard mean and standard deviation for IQ scores var mean = 100; var stdDev = 15; // Calculate Z-score var zScore = (iqScore – mean) / stdDev; // Calculate percentile using the normal CDF var percentile = normalCDF(zScore) * 100; // Display result resultDiv.innerHTML = "An IQ score of " + iqScore + " is approximately in the " + percentile.toFixed(2) + "th percentile." + "This means that approximately " + percentile.toFixed(2) + "% of the population scores at or below this IQ level."; } // Initialize with a default calculation on page load (optional, but good for user experience) document.addEventListener('DOMContentLoaded', function() { calculateIQPercentile(); });

Understanding Your IQ Percentile

An IQ (Intelligence Quotient) score is a measure of a person's cognitive abilities relative to the general population. While IQ tests are often debated, they generally aim to assess reasoning, problem-solving, and learning capabilities.

The Normal Distribution of IQ Scores

IQ scores are typically designed to follow a normal distribution, often visualized as a bell curve. This means that most people score around the average, with fewer people scoring very high or very low. The standard model for IQ scores uses:

• Mean (Average) IQ: 100
• Standard Deviation: 15

The standard deviation indicates how much scores typically vary from the mean. For example, about 68% of people have an IQ between 85 and 115 (within one standard deviation of the mean).

What is a Percentile?

A percentile indicates the percentage of people whose score falls at or below a given score. For instance, if your IQ score is in the 90th percentile, it means you scored as well as or better than 90% of the population.

Our calculator uses your IQ score, along with the standard mean (100) and standard deviation (15), to determine your position on this bell curve and translate it into a percentile rank. This involves calculating a "Z-score," which measures how many standard deviations your IQ is from the mean, and then converting that Z-score into a percentile using the cumulative distribution function of the standard normal distribution.

Interpreting Your IQ Percentile

Here are some common IQ scores and their approximate percentiles:

• IQ 70: Approximately 2nd percentile. This is often considered the threshold for intellectual disability.
• IQ 85: Approximately 16th percentile. One standard deviation below the mean.
• IQ 100: 50th percentile. This is the average IQ score.
• IQ 115: Approximately 84th percentile. One standard deviation above the mean.
• IQ 130: Approximately 98th percentile. Two standard deviations above the mean, often considered the threshold for giftedness.
• IQ 145: Approximately 99.87th percentile. Three standard deviations above the mean.

It's important to remember that IQ scores are just one measure of intelligence and do not encompass all forms of human ability or potential. Factors like emotional intelligence, creativity, practical skills, and social aptitude are also crucial aspects of overall capability.