Percentile Calculator

How to use the percentile calculator

1. Choose what to find. “Value at a percentile” answers questions like “what score marks the 70th percentile?” “Percentile of a value” answers “what percentile is a score of 58?”
2. Paste the data. Separate values with commas, spaces or line breaks. They don’t need to be sorted.
3. Enter k or the value. For a percentile, also pick the method. The other two methods appear in the cards for comparison.

The calculator opens on the ages of 29 Academy Award winners in the lead-actor category from OpenStax’s Introductory Statistics 2e, section 2.3. Their 70th percentile is 64 years.

What a percentile means

The kth percentile is a value with about k percent of the data at or below it. If your test score is at the 90th percentile, you scored as well as or better than about 90% of test takers. That is not the same as getting 90% of the questions right; percentiles describe position within a group, not a score out of 100.

Some percentiles have their own names. The 25th percentile is the first quartile (Q1), the 50th is the median, and the 75th is the third quartile (Q3). The textbook stresses that a percentile may or may not carry a judgment of “good” or “bad”: a high percentile for test scores is good, but a high percentile for the time taken to finish a timed test may not be, since taking too long can leave questions unanswered.

Finding the value at the kth percentile

The textbook method first finds a position in the sorted list:

If i is a whole number, the kth percentile is the ith value. If not, round i down and up and average the two values at those positions.

• 70th percentile of the 29 ages: i = 0.70 × 30 = 21, a whole number. The 21st age is 64.
• 83rd percentile: i = 0.83 × 30 = 24.9. The 24th and 25th ages are 71 and 72, so the 83rd percentile is 71.5.
• 80th percentile of 50 sleep times (Example 2.17): i = 0.80 × 51 = 40.8. The 40th value is 8 hours and the 41st is 9, so the 80th percentile is 8.5 hours.

Positions below 1 or above n take the smallest or largest value.

Finding the percentile rank of a value

To go the other way, count the values below the one you care about, x, and the values equal to it, y. Then:

Round to the nearest whole number. In Example 2.18, 18 of the 29 actors’ ages are below 58 and one equals 58, so the rank is (18 + 0.5) ÷ 29 × 100 = 63.8, the 64th percentile. For an age of 25, three ages are below and one is equal: (3 + 0.5) ÷ 29 × 100 ≈ 12.07, the 12th percentile.

Counting half of the tied values places a value in the middle of its own group, so repeated values don’t all get pushed to the top or the bottom.

Textbook, PERCENTILE.INC and PERCENTILE.EXC

The textbook itself notes that calculators and computers use a variety of percentile methods. The three in this calculator are the most common:

For the 83rd percentile of the actors’ ages, the textbook gives 71.5, PERCENTILE.EXC gives 71.9 (nine-tenths of the way from 71 to 72), and PERCENTILE.INC gives 71.24. PERCENTILE.EXC is not defined near the extremes: with 29 values it needs k between about 3.33 and 96.67, and it returns an error outside that range, as does the calculator.

For large data sets the three methods agree closely. For small ones, use whichever your teacher, textbook or organization specifies, and say which you used.

Where percentiles are used

• Test scores: standardized tests report percentile ranks so a score can be compared with other test takers.
• Growth charts: a child at the 40th percentile for height is taller than about 40% of children of the same age and sex.
• Response and wait times: a 95th-percentile response time says how slow the slowest 5% of requests are, which the average can hide.
• Salaries and prices: the 25th and 75th percentiles describe a typical range better than the minimum and maximum.

Common percentile mistakes

• Forgetting to sort. Positions only make sense in ordered data. The calculator sorts for you, but a hand calculation on unsorted values gives a meaningless answer.
• Mixing up the two directions. “What is the 90th percentile?” asks for a value in the data’s units, such as 71.5 years. “What percentile is 58?” asks for a rank between 0 and 100. Pick the matching mode.
• Reading a percentile as a percent correct. Scoring at the 60th percentile on a hard exam may mean answering only half the questions correctly, if most people answered fewer.
• Over-reading small samples. With 10 values, each one moves the 90th percentile a lot. Percentiles from small data sets are rough, and the method choice matters more.
• Averaging percentiles. The average of two percentile ranks isn’t generally the percentile rank of the averaged score. Recompute from the data instead.

Percentiles without the raw data

This calculator needs the individual values. If you only know a mean and standard deviation, you can still estimate percentiles, but only by assuming a shape for the data. For data that follow a bell curve, the z-score calculator converts a value to a percentile and back: about 84% of values lie below one standard deviation above the mean, and about 97.7% below two. For skewed data such as incomes or wait times, that assumption can be badly off, so use the raw data when you have it.

A quick class example

Suppose 25 students take a quiz and your score of 17 is beaten by 15 students, tied by 2 (including you) and above 8. The percentile rank is (8 + 0.5 × 2) ÷ 25 × 100 = 36, so you scored at the 36th percentile. If the teacher curves the grades, your percentile stays the same, since the curve shifts everyone’s score and the order doesn’t change. Paste the class scores to check a rank like this in one step.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Textbook method: position i = (k/100)(n + 1); a whole-number i takes that value, otherwise the two values around it are averaged; positions beyond the ends take the minimum or maximum.
• Excel PERCENTILE.INC interpolates at rank (n − 1)p + 1; PERCENTILE.EXC interpolates at rank (n + 1)p and is undefined near 0 and 100.
• Percentile rank = (values below + 0.5 × values equal) ÷ n × 100, rounded to the nearest whole percentile.

Sources

1. OpenStax (Rice University), Introductory Statistics 2e, 2.3 Measures of the Location of the Data. Quartiles, IQR and the 1.5 × IQR rule (Example 2.13: home prices; Example 2.14: day and night classes); kth percentile index (k/100)(n + 1) (Example 2.16: 70th → 64, 83rd → 71.5); percentile rank (x + 0.5y)/n × 100 (Example 2.18: 58 → 64th).
2. Microsoft Support, PERCENTILE.INC function. Returns the kth percentile for k from 0 to 1 inclusive, interpolating between values.
3. Microsoft Support, PERCENTILE.EXC function. Returns the kth percentile for k strictly between 0 and 1, with an error when k is outside the range the data supports.

Last reviewed November 2, 2026. For a percentile under a normal curve from a mean and standard deviation, use the z-score calculator.