IQR calculator
Get the spread of the middle half of your data: for the numbers 1 to 8, Q1 is 2.5, Q3 is 6.5 and the interquartile range is 4. One extreme value cannot stretch it the way it stretches the full range. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
The interquartile range, written IQR, is the width of the middle half of a numeric dataset: the third quartile minus the first quartile. Unlike the full range, IQR ignores the most extreme tails, so a single outlier does not stretch the result the way max minus min does. Students, analysts and quality engineers search for an IQR calculator when they need that robust spread number for a box plot, a homework check or a process-control report. This capability accepts a list of at least four finite numbers, sorts them, locates Q1 and Q3 with exclusive Tukey hinges, and returns IQR as Q3 minus Q1.
What the interquartile range measures and why Q3 minus Q1
The interquartile range is the difference between the third quartile and the first quartile of a sorted numeric sample. After the observations are placed in ascending order, Q1 marks the cut that leaves roughly one quarter of the values below it and Q3 marks the cut that leaves roughly one quarter above it. Subtracting those two hinges yields IQR, the length of the central fifty percent of the list.
That single number is the robust cousin of the full range: max minus min uses only the two most extreme points, so one typo or one storm reading can dominate the story, whereas IQR is built from the interior of the ordered sample and stays stable when the tails move. Textbooks introduce IQR next to the five-number summary and the box plot, where the box itself is drawn from Q1 to Q3 and its width is exactly this statistic.
Quality engineers use the same width later to flag mild outliers with the fences Q1 minus one and a half IQR and Q3 plus one and a half IQR, even when they only need the width first. Students search for an IQR calculator when a homework prompt asks for Q3 minus Q1 and they want a second pair of eyes on the hinges.
A dataset with fewer than four finite numbers cannot support two non-empty halves in an honest hinge construction, so those requests fail instead of inventing a quartile from a singleton or a pair.
What you can do with it
Homework and introductory statistics labs
Students and graders verify IQR as Q3 minus Q1 on the same list, including the hard rule that fewer than four numbers or a non-numeric token is invalid.
Box-plot width and robust process spread
Analysts and quality engineers turn a finished batch of readings into a stable middle-half width without pulling the two extremes or a full five-number summary.
FAQ
Which quartile method does this IQR calculator use?
Exclusive Tukey hinges: sort the list, split into lower and upper halves, take each half's median. When n is odd the overall median is left out of both halves. IQR is then Q3 minus Q1.
Why does the dataset need at least four numbers?
Two non-empty halves are required to form Q1 and Q3 honestly. Validation failures are not charged.
What happens if a value is not numeric?
Every entry must be a finite number. Empty strings, NaN, Infinity and words are not observations.
What does the IQR calculator cost?
The browser tool runs free on your device.
Why use the interquartile range instead of the full range?
The full range uses only the two most extreme values, so a single typo or freak reading can dominate it. The interquartile range is built from the middle of the sorted list and stays stable when the tails move.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/stat/iqr \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"values":[1,2,3,4,5,6,7,8]}'const res = await fetch("https://api.kit.forhosting.com/stat/iqr", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"values": [
1,
2,
3,
4,
5,
6,
7,
8
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/iqr",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"values": [
1,
2,
3,
4,
5,
6,
7,
8
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/iqr", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"values":[1,2,3,4,5,6,7,8]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"values":[1,2,3,4,5,6,7,8]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/iqr", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"values": [
1,
2,
3,
4,
5,
6,
7,
8
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.iqr",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_values | 100000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Lists shorter than four observations, empty tokens and non-numeric entries fail with invalid_input instead of inventing a silent zero. The same deterministic arithmetic runs free in the browser and over the API at $0.002 per successful request.
What the interquartile range measures and why Q3 minus Q1
This endpoint answers that search directly: it is not a full quartile suite, not a five-number summary and not an outlier reporter. It computes Q1 and Q3 with exclusive Tukey hinges, subtracts them, and returns the IQR together with the two quartiles and the count so you can audit the subtraction.
Input contract, exclusive Tukey hinges, and the response shape
After validation the core coerces every entry, sorts a copy in ascending order, and applies exclusive Tukey hinges. The lower half is the first floor of n over two values and the upper half is the last floor of n over two values; when n is odd the overall median is excluded from both halves. Q1 is the median of the lower half and Q3 is the median of the upper half. IQR is Q3 minus Q1. Example: the eight numbers one through eight have Q1 equal to two and a half, Q3 equal to six and a half, and IQR equal to four. Send a JSON body whose required field is values: an array of at least four finite numbers. The same list is also accepted under the aliases numbers, data and list, and as a comma-separated, semicolon-separated or whitespace-separated string so a pasted column from a spreadsheet does not need a rename step. Each entry may arrive as a JSON number or as a numeric string; empty strings, NaN, Infinity, objects and words are rejected with invalid_input naming the offending index. A missing field, a non-array non-string payload, a list shorter than four, and a list longer than the published maximum also fail, and those failures do not consume balance. The response echoes n, q1, q3, iqr and method set to tukey_exclusive so a client can reprint the subtraction without a second request.
Where an IQR calculator earns its keep
Use the browser tool when you want an immediate interquartile range while checking a homework answer, sizing the box on a sketch of a box plot, or explaining why a mean without a robust spread is incomplete. Results are fully deterministic: the same values always yield the same n, Q1, Q3 and IQR. There is no language model, no external statistics service and no randomness, so the capability is safe to pin in continuous-integration checks and reproducible lesson materials. Pair it with a dedicated quartile or five-number-summary neighbour if you also need the median, the extremes or Tukey outlier fences; this landing answers the search for an IQR calculator, not a full descriptive-stats suite. Each successful request is one billable item at $0.002; failed validation does not consume balance. Accepted lists stay bounded for Worker isolates: up to one hundred thousand values cover classroom tables, laboratory excerpts and typical analytics samples while still finishing quickly. Wire the endpoint into data-science tutorials, spreadsheet-migration tests, coding-interview sandboxes, or preprocessing steps where you already prefer a closed-form hinge width over an approximate streaming sketch.
Integration use cases
Scripts and CI numeric fixtures
Pipelines and interview sandboxes call a deterministic IQR contract instead of reimplementing sort, exclusive hinges and Q3 minus Q1 in every language.
Technical questions
How do I compute the interquartile range with this calculator?
Send JSON with values (an array of at least four finite numbers) to stat.iqr. The response returns iqr as Q3 minus Q1, plus q1, q3, n and the hinge method.