Skewness calculator
The list 1, 2, 3, 4, 10 has a mean of 4 and a positive skewness, because the 10 stretches the right tail. Paste at least three numbers and see which way your data lean, with the mean, the standard deviation and both skewness figures. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Values
- 1, 2, 3, 4, 10
- N
- 5
- Mean
- 4
- Std dev
- 3.5355339059
- Skewness
- 1.6970562748
Skewness is the number that tells you whether a list of values leans to one side of its mean: a long right tail produces a positive coefficient, a long left tail a negative one, and a roughly symmetric sample sits near zero. This calculator takes a numeric data set, requires at least three finite numbers, and returns the sample Fisher-Pearson G1 skewness coefficient together with the mean, the sample standard deviation, the matching population moment coefficient, and a short shape label. Constant series, where the sample standard deviation is zero, are rejected because standardized third moments are undefined.
What the skewness coefficient measures on a list of numbers
Each point then contributes a cubed standardized residual from that mean; the sign of those cubes is what makes skewness able to tell left from right, unlike variance, which squares distances and therefore forgets direction. Sample skewness G1, the coefficient this calculator treats as the primary result, scales the sum of cubed residuals standardized by the sample standard deviation by n over (n minus one) times (n minus two).
Population skewness g1 is the third central moment divided by the population standard deviation cubed, which is the textbook moment coefficient when the list is the entire finite set of interest rather than a sample from a larger population. Positive coefficients mean the right tail is longer or heavier than the left; negative coefficients mean the opposite; values near zero suggest approximate symmetry, though small samples can look mildly skewed by chance.
Fewer than three finite numbers is also invalid: G1's denominator involves n minus two, and a two-point list cannot describe a third-moment shape. Together mean, sample standard deviation, sample G1, population g1, and a short interpretation label give a compact portrait of tail direction without fitting a full density model or inventing a silent zero for broken input.
Practical use, limits, pricing, and when to call this tool
Use the browser tool when you want an immediate skewness coefficient while checking a homework answer, screening a small sensor batch, or explaining why a mean is a poor summary of a lopsided list. Accepted lists stay bounded so isolates stay safe: up to one hundred thousand values cover classroom tables, sensor batches, and typical analytics excerpts while still finishing quickly. Results are fully deterministic: the same values always yield the same mean, sample standard deviation, sample G1, and population g1.
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. This landing answers people who searched for a skewness calculator on a plain list of numbers and want the coefficient itself, not a combined shape report and not a Pearson mode formula that already assumes you know the mean, the mode, and the standard deviation.
What you can do with it
Homework and introductory statistics labs
Students and graders verify the sample G1 skewness coefficient for a short numeric list, including the hard rule that fewer than three values is invalid.
Quality control and sensor batches
Engineers flag a finished batch whose readings suddenly lean right or left of the mean before that lopsidedness pollutes downstream averages.
FAQ
What is the difference between sample G1 and population g1?
Sample skewness G1 is the bias-adjusted Fisher-Pearson coefficient (Excel SKEW) using the sample standard deviation. Population g1 is the third central moment divided by the population standard deviation cubed. Both are returned so you do not have to guess the formula.
What happens if fewer than three values are provided?
Skewness requires at least three finite numbers because G1's denominator includes n minus two. Validation failures are not charged.
Why is a constant list rejected?
When every value is equal, sample standard deviation is zero and standardized third moments are undefined.
Is the skewness calculator free?
The browser tool runs free on your device.
How do I read a positive or negative skewness?
A positive value means the right tail is longer or heavier than the left, a negative value means the opposite, and a value near zero suggests a roughly symmetric list. Small samples can look slightly skewed just by chance.
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/skewness \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"values":[1,2,3,4,10]}'const res = await fetch("https://api.kit.forhosting.com/stat/skewness", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"values": [
1,
2,
3,
4,
10
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/skewness",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"values": [
1,
2,
3,
4,
10
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/skewness", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"values":[1,2,3,4,10]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"values":[1,2,3,4,10]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/skewness", 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,
10
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.skewness",
"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_n | 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
The arithmetic is fully deterministic, runs free in your browser, and is available over the API at $0.002 per successful request with no language model and no external statistics service on the hot path.
What the skewness coefficient measures on a list of numbers
Start with the arithmetic mean of the list: add every finite value and divide by how many values you have. That bias-adjusted Fisher-Pearson formula is the definition used by common spreadsheets under the name SKEW, so a classroom answer key, an Excel workbook, and this API can agree on the same number.
How this calculator validates the list and computes G1
After validation the core walks the list once to accumulate the sum and form the mean, then walks again to accumulate the second and third central power sums. Sample standard deviation uses Bessel's correction. Sample skewness G1 is then formed from the cubed z-scores, and population skewness g1 is formed from the raw moments m3 over m2 to the power three-halves. Call the capability with a required array field named values: a list of at least three finite numbers. The engine also accepts the aliases numbers, data, list, and x, so scripts that already speak in those terms do not need a rename step. A comma-separated or whitespace-separated string is accepted for simple text forms that post a plain line instead of a JSON array. Validation rejects a missing field, a non-array, an empty array, lists of one or two points, lists longer than the published maximum, any entry that is not a finite number, and constant series whose sample standard deviation is zero or numerically zero, all with invalid_input and without charging balance. The interpretation field maps G1 through a simple plus or minus one-half threshold into right_skewed, left_skewed, or approximately_symmetric so a dashboard can show a label without running a hypothesis test.
Practical use, limits, pricing, and when to call this tool
Each successful request is one billable item at $0.002; failed validation does not consume balance. Wire the endpoint into data-science tutorials, coding-interview sandboxes, or preprocessing steps where you already prefer a closed-form third-moment coefficient over opaque black-box shape flags that hide whether they divide by n or apply the bias adjustment when they print a single skewness field.
Integration use cases
Scripts and CI numeric fixtures
Pipelines and interview sandboxes call a deterministic skewness contract instead of reimplementing Fisher-Pearson G1 in every language.
Technical questions
How do I compute skewness with this calculator?
Send JSON with values (an array of at least three finite numbers) to stat.skewness. The response returns n, mean, std_dev, skewness (sample G1), population_skewness, interpretation, min, max, and formula.