Z-Score Calculator
Calculate the z-score (standard score) of a data point. Convert between raw scores, z-scores, and percentiles.
Calculate percentiles and percentile ranks of a data set. Find the value at any percentile or the percentile of any value.
| Percentile | Name | Value (your data) | Common Usage |
|---|---|---|---|
| 10th | P10 | 65.00 | Bottom 10%, cutoff in distributions |
| 25th | Q1 | 73.00 | 1st quartile, lower fence |
| 50th | P50 | 82.00 | Median, center of distribution |
| 75th | Q3 | 89.00 | 3rd quartile, upper fence |
| 90th | P90 | 95.00 | Top 10%, excellence threshold |
| 95th | P95 | 96.00 | Statistical significance cutoff |
| 99th | P99 | 96.80 | Extreme tail, outlier boundary |
The Percentile Calculator finds the value at any given percentile in your data set, or the percentile rank of any given value. The kth percentile is the value below which k% of the data falls.
Percentiles are widely used in standardized testing (SAT scores), pediatric growth charts, income distribution, and performance benchmarking. The 50th percentile is the median, 25th is Q1, and 75th is Q3.
This calculator accepts comma-separated data, computes the requested percentile using linear interpolation, and provides a complete quartile summary. Enter your data and a target percentile to get started.
Finding exact percentiles requires sorting, ranking, and interpolation. This calculator handles all the math and provides a complete quartile summary.
Percentile value using linear interpolation:
Rank = (P/100) ร (nโ1)
Lower index = floor(Rank)
Fraction = Rank โ Lower index
Value = x[lower] + fraction ร (x[lower+1] โ x[lower])Result: 26
Sorted data: 15, 20, 35, 40, 50. Rank = 0.40 ร 4 = 1.6. Value = x[1] + 0.6 ร (x[2] โ x[1]) = 20 + 0.6 ร 15 = 29.
SAT, GRE, and ACT scores are reported with percentile ranks so you can compare across different test dates and versions. A 1200 SAT at the 75th percentile means you beat 75% of test-takers.
BMI, blood pressure, and growth charts use percentiles to identify typical versus unusual values. Values below the 5th or above the 95th percentile often trigger further evaluation.
Box plots visualize Q1, median, Q3, and outliers. The box spans the IQR, and whiskers extend to 1.5 ร IQR. Points beyond that are plotted as individual outliers.
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The kth percentile is the value below which k% of the data falls. The 90th percentile means 90% of values are at or below that point.
Percentile rank is the percentage of values in the data set that are less than or equal to a given value. If your score is at the 85th percentile rank, you scored higher than 85% of the group.
Quartiles divide data into four equal parts. Q1 (25th percentile), Q2 (50th, median), and Q3 (75th percentile). The IQR = Q3 โ Q1 measures the middle 50%.
Yes, there are multiple methods (inclusive, exclusive, interpolation). Different tools may give slightly different results for the same percentile, especially with small data sets.
A percentage is a fraction of a total (e.g. 80% correct). A percentile is a ranking among peers (e.g. 80th percentile means better than 80% of scores). They measure different things.
Pediatricians plot a child's height and weight against age-based percentiles. A child at the 75th percentile for height is taller than 75% of children the same age.
Calculate the z-score (standard score) of a data point. Convert between raw scores, z-scores, and percentiles.
Find the median of any data set. Enter comma-separated numbers to get the middle value.