Arithmetic mean calculator
The average of 2, 4, 6 and 8 is 5: their sum is 20 and there are 4 numbers. Enter any list of numbers to get the arithmetic mean together with the sum and count, so you can check the division yourself. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Numbers
- 2, 4, 6, 8
- N
- 4
- Values
- 2, 4, 6, 8
- Sum
- 20
- Arithmetic mean
- 5
The arithmetic mean is the everyday average: add every number in a list and divide that total by how many numbers you added. Algebra and introductory statistics both start here because the same identity — sum divided by count — is the center of gravity for exam scores, sensor readings, batch measurements, and any dataset where each observation should pull the center with equal weight. This arithmetic mean calculator accepts a non-empty list of finite numbers, including negatives and zeros, sums them, and returns the average together with the count and the sum so you can check the division by hand.
How the arithmetic mean is computed
The arithmetic mean of a finite list is defined by one identity: add every observation and divide that sum by the count of observations. In symbols, if the list is x1 through xn with n at least one, the mean is (x1 + x2 + … + xn) / n, which is also written as one over n times the sum of the xi.
That constant is the unique number that, when subtracted from each value, leaves residuals that add to zero, which is why textbooks call it the center of mass of the sample. Computation is a single forward pass: initialize a running total at zero, add each finite number in input order, then divide the total by n. There is no sorting, no logarithm, and no special treatment of sign — negatives pull the mean down, zeros are valid observations, and a list of identical values returns that common value.
Non-finite tokens, missing fields, and empty strings fail the same way.
Where an arithmetic mean calculator earns its keep
Laboratory and operations teams average repeated instrument readings so a noisy sensor does not stand in for a batch, and they need the same identity a student uses on paper: sum divided by count, including zeros and signed residuals. Gradebooks, sports box scores, and quality-control sheets all reduce a column of numbers to one representative value before anyone talks about spread.
Content sites that already host a mean-median-mode trio still win a distinct long-tail query when learners type arithmetic mean calculator and expect a focused average, not a bundle of other descriptive statistics. If you later need a weighted average, a geometric mean, a harmonic mean, or a five-number summary, treat those as separate search intents and landings rather than overloading this arithmetic mean page.
What you can do with it
Homework and exam answer keys
Generate the count, sum, and arithmetic mean for textbook number lists so teachers and auto-graders share one ground truth.
Repeated measurements and sensor batches
Average a non-empty series of finite instrument readings, including zeros and signed residuals, without inventing a value for an empty batch.
Score and grade summaries
Reduce a column of exam, quiz, or contest scores to one equally weighted average before discussing spread or outliers.
FAQ
How is the arithmetic mean defined?
For a non-empty list of n finite numbers it is the sum of the values divided by n: AM = (x1 + x2 + … + xn) / n.
Can the list include negative numbers and zeros?
Yes. Unlike the geometric mean, the arithmetic mean is defined for any finite real numbers. Negatives pull the average down; zeros are valid observations and count toward n.
How is this different from the geometric or harmonic mean?
This calculator implements only the additive average sum/n. The geometric mean uses an n-th root of a product and the harmonic mean uses reciprocals; those are separate search intents and tools.
What does the arithmetic mean calculator cost?
The browser tool is free and runs locally.
What is the average of 2, 4, 6 and 8?
It is 5. Adding the four numbers gives 20, and dividing 20 by 4, the number of values, gives 5. Each number counts equally toward that result.
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/algebra/arithmetic-mean \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"numbers":[2,4,6,8]}'const res = await fetch("https://api.kit.forhosting.com/algebra/arithmetic-mean", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"numbers": [
2,
4,
6,
8
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/algebra/arithmetic-mean",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"numbers": [
2,
4,
6,
8
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/algebra/arithmetic-mean", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"numbers":[2,4,6,8]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"numbers":[2,4,6,8]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/algebra/arithmetic-mean", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"numbers": [
2,
4,
6,
8
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "algebra.arithmetic_mean",
"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_items | 10000 |
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
An empty list is rejected with a clear invalid_input error instead of returning NaN or dividing by zero.
How the arithmetic mean is computed
An empty list is undefined because division by zero is not a number; this engine rejects it with invalid_input rather than inventing NaN. The pipeline is deterministic floating-point arithmetic with no random seeds, no wall-clock timestamps, and no network calls, so identical inputs always produce identical JSON.
Input contract, response shape, and validation rules
A single finite number is treated as a one-element list whose mean equals itself. The empty-list rejection is the defining contract of this calculator: the arithmetic mean is the sum of the xi divided by n, and n must be at least one. POST a JSON object with one required field named numbers, or the aliases values, data, or list. The field holds either a JSON array of finite numbers or a plain string with numbers separated by commas, spaces, or semicolons. Missing fields, empty arrays, empty strings, non-numeric tokens, NaN, and Infinity fail with invalid_input and are not billed. On success the response includes the count n, the cleaned values array in input order, the scalar sum, the scalar arithmetic_mean, and a short formula string AM = (Σ xi) / n. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance. Because the engine is pure parse code, latency stays sub-millisecond for ordinary classroom lists and modest API payloads. Lists are capped at ten thousand values so a runaway payload cannot exhaust isolate memory.
Where an arithmetic mean calculator earns its keep
Secondary-school algebra and college statistics courses constantly assign arithmetic-mean drills, comparisons against the geometric and harmonic means, and word problems that ask for the average of a score list; a single trusted oracle that returns cleaned JSON speeds grading and demo setup. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance. Keep the list non-empty and finite, pin the rounded arithmetic_mean in tests, and you get a reproducible average for homework, LMS plugins, and edge workers without standing up a statistics library of your own.
Technical questions
Why is an empty list rejected?
The arithmetic mean divides by the count. With zero observations that division is undefined, so the calculator fails with invalid_input instead of returning NaN or dividing by zero.