ganak.appPercentile Calculator
Free percentile calculator: find the P-th percentile from a dataset, calculate percentile rank of a value, or convert between z-scores and percentiles. Step-by-step solutions.
10 values parsed. Supports commas, spaces, tabs, or new lines.
69.7500
Percentile Summary
Key percentiles & statistics from your dataset
Distribution Overview
Where values fall across percentiles
Step-by-Step Solution
How this result was calculated
Formula
rank = (P / 100) × (n − 1)
Step 1: Sort the 10 values in ascending order
Step 2: Calculate the rank index
rank = (75 / 100) × (10 − 1) = 6.7500
Step 3: Interpolate between positions 6 and 7
63 + 0.7500 × (72 − 63) = 69.7500
Sorted Dataset
10 values, sorted ascending
What Is a Percentile?
Understanding percentiles in statistics
A percentile indicates the value below which a given percentage of observations fall. If you score at the 90th percentile on a test, 90% of test-takers scored lower than you. Percentiles are widely used in standardized testing, growth charts, income analysis, and any context where you need to understand relative standing.
Excel-compatible formula (interpolation)
rank = (P / 100) × (n − 1)
Percentile vs. percentage: A percentage is a fraction of 100 (e.g., you got 85% of questions right). A percentile is a ranking among a group (e.g., your score is higher than 85% of all test-takers). They measure different things — one is absolute, the other is relative.
Calculation Methods Compared
How different formulas produce different results
Interpolation (Excel / Google Sheets)
Calculates a fractional rank and linearly interpolates between adjacent values. This is the method used by Excel's PERCENTILE() function, Google Sheets, and most spreadsheet software. It produces smooth results even for small datasets.
rank = (P/100) × (n−1), then interpolate
Nearest Rank
Rounds up to the nearest whole rank and returns that value directly. Simpler and commonly taught in statistics courses. Always returns an actual value from the dataset, never an interpolated one.
rank = ⌈(P/100) × n⌉
Example: 75th percentile of {3, 6, 7, 8, 8, 10, 13, 15, 16, 20}
- Interpolation: rank = 0.75 × 9 = 6.75 → 13 + 0.75 × (15 − 13) = 14.5
- Nearest rank: rank = ⌈0.75 × 10⌉ = 8 → value at position 8 = 15
Different methods, different answers — choose based on your use case.
Normal Distribution & Z-Scores
Converting between values, z-scores, and percentiles
When data follows a normal (bell curve) distribution, you can convert any value to a percentile using the z-score formula: z = (x − μ) / σ. The z-score tells you how many standard deviations a value is from the mean.
Common Z-Score to Percentile Conversions
The normal distribution mode in this calculator lets you convert in both directions: enter a value to find its percentile, or enter a percentile to find the corresponding value. Useful for test scoring, quality control, and scientific research.
Percentiles in Excel & Google Sheets
Built-in formulas for percentile calculations
Find a Percentile Value
- =PERCENTILE(A1:A100, 0.75)
- =PERCENTILE.INC(A1:A100, 0.75)
- =PERCENTILE.EXC(A1:A100, 0.75)
- =QUARTILE(A1:A100, 3)
Find Percentile Rank
- =PERCENTRANK(A1:A100, 50)
- =PERCENTRANK.INC(A1:A100, 50)
- =PERCENTRANK.EXC(A1:A100, 50)
- =NORM.DIST(x, mean, sd, TRUE)
Note: PERCENTRANK uses linear interpolation. This calculator uses the midrank formula, which may give different results for small datasets or tied values.
INC vs EXC: PERCENTILE.INC includes 0 and 1 as valid percentile inputs (inclusive), while PERCENTILE.EXC excludes them (exclusive). For most uses, the inclusive version (which matches our interpolation method) is standard.
Frequently Asked Questions
Common questions about percentiles, percentile rank, z-scores, and quartiles
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