Percentile Calculator

About Percentile Calculator

What Is a Percentile?

The kth percentile is the value below which k% of the data falls. If your test score is at the 85th percentile, you scored higher than 85% of test takers.

Worked example: Find the 25th percentile of: 3, 7, 8, 12, 14, 18, 21, 24, 29, 35

1. Data is already sorted (n = 10)
2. Index = (25/100) × (10 - 1) = 2.25
3. This falls between the 3rd value (8) and 4th value (12)
4. Interpolate: 8 + 0.25 × (12 - 8) = 8 + 1 = 9
5. P25 = 9

Percentile vs Percentile Rank

	Percentile (Value)	Percentile Rank
Question	"What value is at the 75th percentile?"	"What percentile is the value 42?"
Input	A percentile number (0-100)	A data value
Output	A data value	A percentile number (0-100)
Formula	Uses index and interpolation	Count values ≤ x, divide by n, multiply by 100

Quartiles and the Five-Number Summary

Quartiles divide sorted data into four equal parts:

Quartile	Percentile	Meaning
Q1 (Lower quartile)	25th	25% of data falls below this
Q2 (Median)	50th	50% of data falls below this
Q3 (Upper quartile)	75th	75% of data falls below this

The five-number summary combines: Minimum, Q1, Median (Q2), Q3, Maximum. These five values give a complete picture of the data's distribution.

Example: Dataset 2, 4, 6, 8, 10, 12, 14, 16

Statistic	Value
Minimum	2
Q1 (P25)	5
Median (P50)	9
Q3 (P75)	13
Maximum	16

Interquartile Range (IQR) and Outliers

The IQR is the range of the middle 50% of data:

IQR = Q3 - Q1

Outliers are values that fall far from the central data. The standard rule uses 1.5 × IQR:

Boundary	Formula	Classification
Lower fence	Q1 - 1.5 × IQR	Values below this are mild outliers
Upper fence	Q3 + 1.5 × IQR	Values above this are mild outliers
Lower extreme	Q1 - 3 × IQR	Values below this are extreme outliers
Upper extreme	Q3 + 3 × IQR	Values above this are extreme outliers

Example: Q1 = 20, Q3 = 40, IQR = 20

• Lower fence: 20 - 30 = -10
• Upper fence: 40 + 30 = 70
• Any value below -10 or above 70 is an outlier

How to Read a Box Plot

The box plot (box-and-whisker plot) is a visual summary of the five-number summary:

• Box: Spans from Q1 to Q3 (the middle 50% of data)
• Line inside the box: The median (Q2)
• Whiskers: Extend to the most extreme data points within 1.5 × IQR of the box
• Dots beyond whiskers: Individual outlier values

A symmetric box plot suggests normally distributed data. A box with whiskers of very different lengths suggests skewed data.

Common Percentiles in Real Life

Context	Common Percentiles Used	What They Mean
Standardised tests (SAT, GRE)	P25, P50, P75, P90, P99	Compare your score to all test takers
Child growth charts	P3, P15, P50, P85, P97	Compare height/weight to same-age children
Income distribution	P10, P25, P50, P75, P90, P99	Compare earnings across the population
Website performance	P50, P90, P95, P99	Page load times - P99 catches worst-case scenarios
Network latency	P50, P95, P99, P99.9	API response times for SLA monitoring

Which Percentile Formula Does This Tool Use?

This calculator uses linear interpolation between closest ranks (the NIST recommended method and Excel's default PERCENTILE.INC), so results match Excel, Google Sheets, NumPy's default, and most statistics textbooks. Percentile software actually disagrees at the edges - Hyndman and Fan (1996) catalogued nine different definitions still in use.

Method	Where It's Used	Notes
Linear interpolation (R-7)	Excel PERCENTILE.INC, Google Sheets, NumPy default, this tool	Index = p(n-1), interpolate between neighbours. Most common.
Exclusive method (R-6)	Excel PERCENTILE.EXC, SAS default, Minitab	Index = p(n+1). Can't return values below P(1/(n+1)) or above P(n/(n+1)).
Nearest rank	NIST handbook, older textbooks	No interpolation - picks the closest actual data value.
Tukey's hinges	Box plots in John Tukey's original 1977 definition	Q1/Q3 use the median of each half of the data.

For small datasets the methods can give results that differ by several percent. For datasets over ~100 values the difference is negligible. The variance calculator and standard deviation calculator complement percentiles when describing spread.

What Do Percentiles Mean for Income and Wealth?

Income percentiles are the most-quoted real-world use of the statistic. In the UK, ONS data for financial year ending 2024 put median (P50) household disposable income at £36,700, a 0.8% rise on the previous year, with the gap between top and bottom quintiles the widest in a decade. In the US, the Census Bureau's 2023 figures show median household income at $80,610 (a 4.0% real rise on 2022), with the 80/20 ratio wider than the UK because top-end incomes stretch further.

• P50 (median) is preferred over the mean for income because very high earners pull the mean up - in 2023 the UK mean was roughly 27% above the median for this reason.
• P99 is the common threshold for "top 1%" reporting. HMRC data for 2023/24 put the UK top 1% threshold at around £190,000 of total pre-tax income.
• Percentile ranks within a single company (salary bands, bonus distributions) are usually calculated with the same R-7 interpolation this tool uses.

Percentiles in Child Growth Charts

Paediatricians read height and weight as percentiles because absolute values are meaningless without reference to age. The WHO Child Growth Standards (birth to 5 years) and the NHS/CDC charts for older children use P3, P15, P50, P85, and P97 as key bands. A child tracking along P25 from age 2 to 10 is usually considered healthy; the clinical concern is crossing percentile bands, not the band itself.

Worked example: A 7-year-old boy's weight is at P15 on the CDC chart, meaning 15% of 7-year-old boys weigh less than he does and 85% weigh more. If at age 10 he has dropped to P3, that is a faster-than-expected growth deceleration and typically prompts further assessment, even though P3 itself is within the "normal" range (defined as P3 to P97).

Percentiles in Web Performance and SLAs

Engineering teams report page-load and API-response times as P50/P90/P95/P99 because the average hides tail latency. A service with a mean response of 100ms can still have a P99 of 2,000ms - meaning 1 in 100 requests takes 20x longer. Google's Core Web Vitals use P75 across all page loads as the threshold for "good" performance, on the basis that P75 captures the experience of the typical user without being dragged down by outlier cases.

Metric	Good (P75 target)	Needs Improvement	Poor
Largest Contentful Paint (LCP)	≤ 2.5s	2.5-4.0s	> 4.0s
Interaction to Next Paint (INP)	≤ 200ms	200-500ms	> 500ms
Cumulative Layout Shift (CLS)	≤ 0.1	0.1-0.25	> 0.25

SLA contracts often specify "P99 latency < 300ms" because promising an average of 300ms leaves the provider free to serve the worst 1% of requests arbitrarily slowly. Tail-latency thinking was popularised by Jeff Dean and Luiz Barroso's 2013 CACM paper "The Tail at Scale".

Common Mistakes When Using Percentiles

• Confusing "75th percentile" with "75%". P75 is a value, not a proportion. If test scores have P75 = 82, it means 75% of students scored 82 or below - not that they scored 75%.
• Averaging percentiles. The average of P90s from multiple services is not the overall P90 - you need the raw data. This is a classic monitoring bug.
• Using a single tool-specific percentile across tools. Excel PERCENTILE.EXC and PERCENTILE.INC give different answers on small datasets. Pick one and stick with it when comparing.
• Reading outliers as errors. The 1.5 × IQR rule is a guideline popularised by Tukey, not a statistical test. Genuinely skewed distributions (income, insurance claims) produce many flagged values that are not errors.
• Interpreting percentiles with too few data points. With 10 values, P25 and P75 are almost arbitrary - always include the sample size when reporting.

For converting percentile ranks to z-scores under a normal-distribution assumption, use the z-score calculator. All calculations in this tool run in your browser; the data you paste never leaves your device.

Sources

• NIST/SEMATECH e-Handbook - Percentiles
• Hyndman & Fan (1996) - Sample Quantiles in Statistical Packages, American Statistician
• ONS - Household Disposable Income and Inequality
• US Census Bureau - Income in the United States 2023
• WHO - Child Growth Standards
• Google - Core Web Vitals thresholds
• Dean & Barroso (2013) - The Tail at Scale, CACM