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Percentile Calculator

Find percentiles from raw data or from Z-scores.

Inputs

Enter comma-separated numbers.

About this topic

What is a Percentile? The value below which a given percentage of observations fall.

The p-th percentile is the value at which p% of the data lies below it. For example, the 90th percentile is the value below which 90% of the data falls.

Key formulas & rules

  • •P50 = median (middle value)
  • •P25 = Q1 (first quartile)
  • •P75 = Q3 (third quartile)
  • •Also called the 'centile'
  • •Percentiles range from 0 to 100
  • •Uses linear interpolation between points

Examples

Input Output Note
Data: 1, 2, 3, 4, 5 P50 = 3 Median
Data: 1..100 P90 = 90.1 Near top
Data: 1..10 P25 = 3.25 First quartile
Data: 1..10 P75 = 7.75 Third quartile

Real-world uses

Test scores Height/weight growth charts Income distribution
Percentile from Z-Score Convert a standard score to its cumulative probability.

The Z-score tells you how many standard deviations from the mean a value is. The percentile is the cumulative probability up to that Z.

Key formulas & rules

  • •Z = (x − μ) / σ
  • •Uses the standard normal CDF Φ(z)
  • •Z = 0 → 50th percentile (median)
  • •Z = 1.645 → 95th percentile
  • •Z = 1.96 → 97.5th percentile
  • •Z = −1.96 → 2.5th percentile

Examples

Input Output Note
z = 0 50th Mean
z = 1.28 90th Common cutoff
z = 2 97.7th Unusually high
z = −1 15.9th Below average

Real-world uses

IQ scores Standardized tests Quality control
Quartiles & IQR Divide data into four equal parts.

Quartiles split the ordered data into four groups. The Interquartile Range (IQR) = Q3 − Q1 captures the middle 50% of the data.

Key formulas & rules

  • •Q1 = P25, Q2 = P50, Q3 = P75
  • •IQR = Q3 − Q1
  • •Outlier if x < Q1 − 1.5·IQR
  • •Outlier if x > Q3 + 1.5·IQR
  • •Robust to extreme values
  • •Used in box-and-whisker plots

Examples

Input Output Note
1, 2, 3, 4, 5 Q1=2, Q3=4, IQR=2 Simple case
1..100 Q1=25.75, Q3=75.25 Uniform
1, 2, 100, 101 Detects outlier IQR test
1, 2, 3, 4 Q1=1.75, Q3=3.25 Interpolation

Real-world uses

Data cleaning Descriptive statistics Statistical process control
Common Distributions Percentile interpretation across distribution types.

Percentiles have special meaning in different distributions. In a normal distribution, percentiles are determined by Z-scores. In skewed distributions, percentiles shift.

Key formulas & rules

  • •Normal: symmetric, mean = median
  • •Right-skewed: mean > median
  • •Left-skewed: mean < median
  • •Bimodal: two peaks, percentile jumps
  • •Uniform: every value equally likely
  • •Percentile ≠ percentage of correct answers

Examples

Input Output Note
Normal dist P50 = mean Symmetric
Right skewed P50 < mean Tail on right
Bimodal P50 in valley Two peaks
Left skewed P50 > mean Tail on left

Real-world uses

Standardized testing Population studies Market research

Modes & formulas

1

From Raw Data

• Enter a comma-separated dataset. • Specify the target percentile (0–100). • The calculator sorts the data and uses linear interpolation to find the exact percentile value.
rank = (p / 100) × (n − 1) | P = arr[floor(rank)] + frac × (arr[ceil(rank)] − arr[floor(rank)])

This matches Excel's PERCENTILE.INC function. It interpolates between adjacent sorted values for a smooth result rather than snapping to the nearest value.

2

From Z-Score

• Enter a Z-score (number of standard deviations from the mean). • The calculator computes the cumulative probability up to that Z. • The result is the percentile corresponding to the given Z-score.
Percentile = Φ(z) × 100

Φ(z) is the standard normal cumulative distribution function, approximated by the Abramowitz–Stegun method. For example, z = 1.28 corresponds to about the 90th percentile.

How to use it

Choose From Raw Data or From Z-Score. Enter your values. The tool displays the percentile, quartiles (Q1, Q2, Q3), and the interquartile range (IQR).

Frequently asked questions

What is the difference between a percentile and a percentage?
A percentage is a fraction of 100. A percentile is a position in a distribution — the 90th percentile is the value below which 90% of the data falls.
What is the IQR?
The interquartile range is Q3 − Q1, capturing the middle 50% of the data. It's robust against outliers.
What is a percentile?
A measure indicating the value below which a given percentage of observations fall. For example, the 90th percentile is the value below which 90% of the data lies.
What is the median?
The median is the 50th percentile. It is the exact middle value of the dataset.
What is a quartile?
Quartiles divide the data into four equal parts: Q1 (25th percentile), Q2 (50th percentile/median), and Q3 (75th percentile).
What is the Interquartile Range (IQR)?
The difference between the 75th and 25th percentiles (Q3 - Q1). It represents the middle 50% of the data.

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Read the full Percentile Calculator guide — examples & 18 FAQs