Convert a score to a percentile using the z-score method. Enter the score, mean, and standard deviation to get your percentile rank instantly.
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This calculator uses the normal distribution method. It first computes your z-score as z = (score - mean) / standard deviation, which standardizes your score into units of spread around the average. It then feeds the z-score into the cumulative distribution function of the standard bell curve, Phi(z) = (1 + erf(z / sqrt(2))) / 2, using math.erf in Python and the matching Abramowitz and Stegun approximation in JavaScript. Multiplying by 100 converts the probability into a percentile: the percentage of the distribution that falls at or below your score. The approach assumes the underlying data is roughly bell-shaped, like IQ scores, test results, or adult heights.
A percentile tells you what share of a normal distribution falls at or below your score, which is the core of the percentile meaning: rank within a group, not score on a test. First, the calculator converts your score into a z-score with the formula z = (score - mean) / standard deviation. A z-score of 1.0 means you sit one standard deviation above the mean. Then it applies the standard normal cumulative distribution function: percentile = 100 * (1 + erf(z / sqrt(2))) / 2. A z-score of 0 gives the 50th percentile, z = 1 gives about the 84th, and z = 2 gives about the 98th. The method assumes your data follows a bell curve.
Enter three numbers: your score, the mean (average) of the distribution, and its standard deviation. You get two results: your percentile and your z-score. A result at the 90th percentile means you scored at or above 90 percent of the group. Common uses include IQ scores (mean 100, SD 15), SAT and ACT score bands, test grading curves, and performance benchmarks at work. If you only know your rank in a group, such as rank 5 out of 120, use the rank formula percentile = (1 - (rank - 1) / total) * 100 instead. Make sure your data is roughly bell-shaped before trusting the number.
A z-score counts how many standard deviations a value sits above or below the mean. Negative z-scores fall below average, positive ones above, and zero is exactly average. Converting a z-score to a percentile uses the cumulative normal curve: z = 1.0 lands at the 84th percentile, z = 1.28 at the 90th, z = 1.65 at the 95th, and z = 2.33 at the 99th. Going the other way, from a percentile to a z-score, uses the inverse normal function. Because z-scores are standardized, you can compare scores from different tests on one scale: an IQ of 115 and a test score one standard deviation above its mean are both at the 84th percentile.
A percentage measures performance against the test: 72 percent means you earned 72 out of 100 points. A percentile measures position against people: the 72nd percentile means you scored at or above 72 percent of test takers. They are not interchangeable. A score of 60 percent on a very hard exam could still put you in the 90th percentile if everyone else scored lower. This distinction matters for college admissions, job benchmarking, and growth charts, where rank in the group counts more than the raw score.
The terms sound alike but answer different questions. A percentile value is a score: the 90th percentile is the number that 90 percent of values fall below. A percentile rank belongs to a specific score: it is the share of values at or below it, so a score of 115 with mean 100 and SD 15 has a percentile rank of about 84. A related tool is the kth percentile calculator, which takes a dataset and a number k and returns the value at that rank in the sorted data. For single scores on a normal curve, use this page; for full datasets, a kth percentile calculator is the right fit.
Example 1: score 115, mean 100, SD 15. z = (115 - 100) / 15 = 1.0, and the calculator returns the 84.1th percentile: higher than about 84 percent of the group. Example 2: score 100, mean 100, SD 15. z = 0, so the result is exactly the 50th percentile, the midpoint of the distribution. Example 3: score 70, mean 100, SD 15. z = -2.0, giving the 2.3rd percentile. Reading a percentile chart gets easier once you memorize a few landmarks: 68 percent of values sit within one standard deviation (the 16th to 84th percentile), 95 percent within two.
A percentile is the percentage of values in a distribution that fall at or below a given score. If your test result is at the 84th percentile, you scored as well as or better than 84 percent of test takers. The 50th percentile is the median, the exact middle of the group. Percentiles always describe rank within a group, never the share of questions you answered correctly.
Percentile rank is the percentile attached to one specific score. With a normal distribution, first find the z-score: z = (score - mean) / standard deviation. Then convert it to a percentile with 100 * Phi(z). For rank 5 out of 120 in a simple list, an approximation is (1 - (rank - 1) / total) * 100, about the 96.7th. Enter score, mean, and SD above for the exact normal-distribution answer.
No. A percentage compares your score to the maximum possible, like 72 out of 100 points. A percentile compares your score to other people: the 72nd percentile means you beat 72 percent of the group. On a hard test, 60 percent correct can still land you in the 90th percentile. Use percentages for absolute performance and percentiles for relative standing.
A percentile is a value on the scale: the 90th percentile is the score that 90 percent of values fall below. A percentile rank is a position of one score: it tells you what share of values sit at or below it. A score of 130 with mean 100 and SD 15 is at the 97.7th percentile rank, while the 90th percentile value for that distribution is about 119.2. One is a score, the other is a share.
Subtract the mean from the score and divide by the standard deviation: z = (score - mean) / sd. Then plug z into the standard normal cumulative function, 100 * Phi(z), where Phi(z) = (1 + erf(z / sqrt(2))) / 2. For example, a score of 115 with mean 100 and SD 15 gives z = 1.0, which converts to the 84.1st percentile. This page does both steps automatically.
The 50th percentile is the median: exactly half the group scored at or below it and half scored above. In salary data, the 50th percentile is the typical middle pay. In a bell curve it equals the mean. Being at the 50th percentile is perfectly average, neither high nor low, and it is the most common benchmark people compare against.
The 90th percentile salary is the pay level that 90 percent of earners fall at or below, and only 10 percent earn more. If your pay is at the 90th percentile for your role, you are in the top 10 percent of the benchmark group. Salary surveys publish the 10th, 25th, 50th, 75th, and 90th percentiles so candidates and employers can compare offers against the market.
Use =NORM.DIST(score, mean, sd, TRUE) to convert a score to a percentile on a normal curve, which matches this calculator. For a list of data, use =PERCENTILE.INC(range, k) for the kth value with inclusive ranks, or =PERCENTILE.EXC(range, k) for the exclusive variant. Note that PERCENTILE.INC and PERCENTILE.EXC can return slightly different answers because they use different ranking conventions.
Percentile calculators use different ranking methods. For datasets, common conventions include inclusive ranks like Excel PERCENTILE.INC, exclusive ranks like PERCENTILE.EXC, nearest rank, and linear interpolation between data points. They can disagree by a few points on small datasets. This calculator uses the z-score method on a normal distribution, which is exact for bell-shaped data but only an approximation when the data is skewed.
No, not directly. Percentiles are ranks, not quantities, so averaging them gives a misleading number. To combine two test results, average the raw scores or the z-scores first, then convert the average to a percentile. For example, the average of the 50th and 90th percentiles is not the 70th percentile; you must recompute from the underlying scores.
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