Average atomic mass calculator
Get the weighted average behind a periodic-table value: boron's isotopes at 10.012937 u and 11.009305 u, with abundances 0.199 and 0.801, give 10.811027768 u. Abundances that miss one by more than 0.01 are refused. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Masses
- 10.012937, 11.009305
- Abundances
- 0.199, 0.801
- Isotope count
- 2 u
- Abundance sum
- 1
- Average atomic mass
- 10.811027768
The average atomic mass on the periodic table is not the mass of any single atom of that element. It is a weighted average of the masses of the naturally occurring isotopes, each weighted by its fractional abundance in nature. Students, tutors, and lab pipelines need a deterministic way to compute that number from a short list of isotope masses and fractions, to check textbook exercises, regenerate table values, or validate that a set of abundances is complete. This capability multiplies each isotope mass by its fractional abundance, sums the products, and returns both the average and the per-isotope contributions so you can see exactly how much each nuclide pulls the mean. Abundances must be fractions that sum near one; percent values and incomplete sets fail with a clear invalid input error and are not charged.
What average atomic mass means and how to prepare masses and abundances
Every element with more than one stable isotope has a table atomic mass that is a population average, not the mass of one chosen isotope. For two or more isotopes you list each mass in unified atomic mass units and the matching fractional abundance, then form the sum of mass times abundance over all isotopes. Fractional abundance means a value between zero and one, such as zero point one nine nine for about nineteen point nine percent, not the percent figure itself.
Masses must be positive and finite; each abundance must lie in the closed interval from zero to one. Classroom boron with two isotopes, chlorine with chlorine-thirty-five and chlorine-thirty-seven, and copper with copper-sixty-three and copper-sixty-five are the usual first examples; the same contract scales to any short natural set up to the published isotope cap.
What you can do with it
Homework and exam verification
Students submit isotope masses and fractional abundances, compare the weighted average and per-isotope contributions to worked solutions, and get a clear error when abundances do not sum near one.
Lab and data pipelines
Scripts that ingest isotope tables validate abundance completeness and compute table-style average atomic mass without reimplementing the weighted sum in every language.
FAQ
What if my abundances are in percent?
Convert to fractions first (divide by 100). This calculator expects fractional abundances that sum near one; percent values such as 19.9 and 80.1 will fail validation.
What happens if abundances do not sum to one?
Incomplete isotope sets and percent-by-mistake inputs are rejected and not charged.
Is the average atomic mass calculator free?
The browser tool runs free on your device.
Does this look up isotope data automatically?
No. You supply the isotope masses and fractional abundances. The engine only computes the weighted average and contributions so results stay fully deterministic and pin-friendly in tests.
How do I calculate the average atomic mass of boron?
Multiply each isotope mass by its abundance and add the results: 10.012937 u times 0.199 gives 1.992574463 u, 11.009305 u times 0.801 gives 8.818453305 u, and together they make 10.811027768 u.
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/chem/average-atomic-mass \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"masses":[10.012937,11.009305],"abundances":[0.199,0.801]}'const res = await fetch("https://api.kit.forhosting.com/chem/average-atomic-mass", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"masses": [
10.012937,
11.009305
],
"abundances": [
0.199,
0.801
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/average-atomic-mass",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"masses": [
10.012937,
11.009305
],
"abundances": [
0.199,
0.801
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/average-atomic-mass", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"masses":[10.012937,11.009305],"abundances":[0.199,0.801]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"masses":[10.012937,11.009305],"abundances":[0.199,0.801]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/average-atomic-mass", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"masses": [
10.012937,
11.009305
],
"abundances": [
0.199,
0.801
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.average_atomic_mass",
"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.
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
What average atomic mass means and how to prepare masses and abundances
Send the required arrays masses and abundances with the same length; aliases isotope_masses, m, mass, fractions, abundance, and fractional_abundances are accepted when your client already uses those names. The engine checks that the abundances sum near one within a small tolerance so incomplete isotope lists and percent-by-mistake inputs fail early with invalid_input instead of producing a silently wrong average. Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Reading the weighted average, contributions, and abundance sum
The contributions array is the structured heart of the contract: each entry repeats mass and abundance for one isotope and adds contribution equal to their product, which is the amount that isotope adds to the final average. On success the response echoes the normalized masses and abundances arrays, isotope_count, and abundance_sum so you can confirm that the fractions you sent are complete. The average_atomic_mass field is the weighted mean in unified atomic mass units, and unit is always the string u for display next to the number. Summing the contribution values recovers average_atomic_mass within rounding, which is useful when grading software checks work step by step rather than only the final number. The formula field restates A_avg equals the sum of mass_i times abundance_i, and method is always weighted_isotope_average so downstream code can branch without sniffing shapes. Use average_atomic_mass alone when you only need the table-style number; use contributions when a lesson needs to show how a rare heavy isotope still shifts the mean; use abundance_sum when auditing that a third-party data feed still sums to one. Missing arrays, length mismatch, non-positive masses, abundances outside zero to one, and abundance sums far from one all fail with invalid_input and are not charged after the engine rejects the request.
API usage, pricing, classroom workflows, and practical limits
Call the free in-browser average atomic mass from isotopes calculator for homework checks, lecture demos, and quick verification of periodic-table style averages without installing a chemistry package. Keep abundance lists fractional and complete; if your source data is in percent, divide each entry by one hundred before calling. Authors shipping SDKs can map the contributions array directly into UI tables that show isotope mass, fraction, and contribution columns—the same columns students fill when they compute average atomic mass by hand on paper. Send a JSON body with the required masses and abundances arrays of equal length. Use the prepaid API when a tutoring platform, LMS auto-grader, lab notebook service, or curriculum generator needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance. Pair this endpoint with molar mass tools when the next step is building a compound mass from the averaged elemental values, or with stoichiometry calculators once the elemental averages are fixed.
Integration use cases
Tutoring and curriculum generators
Lesson builders produce boron, chlorine, and copper drills with structured JSON for flashcards, step sheets, and auto-graded average atomic mass problems.
Technical questions
How do I calculate average atomic mass from isotopes?
Send JSON with masses and abundances arrays of equal length (for example boron: masses [10.012937, 11.009305] and abundances [0.199, 0.801]). The response includes average_atomic_mass and per-isotope contributions.