Segment addition postulate calculator
If AB is 5 and BC is 8, the whole segment AC is 13, because the two parts of a segment add up to the whole. Enter any two of the three lengths and get the missing one, whether it is a part or the whole. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Ab
- 5
- Bc
- 8
- Ac
- 13
- Missing
- ac
- Length
- 13
The segment addition postulate is the first length identity of Euclidean geometry: if point B lies between points A and C on a straight line, then the two parts add exactly to the whole, written AB + BC = AC. Every later result about collinear points, midpoints, and congruent segments rests on that one sentence. This calculator applies the postulate in the form students actually need at a desk: supply any two of the three finite lengths AB, BC, and AC, and it returns the missing length together with the completed triple.
What the segment addition postulate says
Take three collinear points A, B, and C with B between A and C. The ray that starts at A and ends at C is one segment of length AC, and the interior point B splits that segment into two smaller pieces AB and BC. The segment addition postulate asserts that those pieces are not independent decorations on the diagram: their lengths add, with no leftover and no overlap, to the length of the whole.
In symbols the claim is AB + BC = AC, and that single equation is enough to recover whichever of the three numbers a problem statement left blank. If the two parts are known, the whole is their sum. If the whole and one part are known, the other part is the difference, provided the difference is not negative — a negative remainder would mean the labelled “part” is already longer than the segment it is supposed to sit inside, which cannot happen for ordinary Euclidean length.
The postulate does not require a coordinate system, a unit conversion, or an angle. It is a statement about betweenness and measure only, which is why a three-field calculator can implement it with one addition or one subtraction and a handful of sign checks. Classroom language sometimes restates the same fact as “the whole is equal to the sum of its parts” or writes the three letters in a different order (BA + AC = BC when A is the interior point).
Input contract, how the missing length is found, and errors
Leave the unknown field out entirely; do not send null. When the omitted field is ac the answer is ab plus bc. When the omitted field is bc the answer is ac minus ab.
When the omitted field is ab the answer is ac minus bc. If that difference is negative the pair violates the postulate and the task fails instead of returning a signed length. On success the body echoes the completed triple ab, bc, and ac; names the reconstructed field in missing; reports the reconstructed measure in length; and repeats the identity in formula as AB + BC = AC.
Numbers are rounded to twelve decimal places so goldens compare byte-for-byte across runtimes. Example: ab equals five and bc equals eight yields ac thirteen, missing ac, and length thirteen. Example: ab equals five and ac equals thirteen yields bc eight.
Units travel through unchanged: centimetres in, centimetres out.
Where a segment-addition calculator earns its keep
Geometry classrooms and tutoring platforms use a segment addition postulate calculator so learners can check a missing length without flipping an addition or subtraction by hand, then see the completed AB, BC, AC triple next to the formula they are supposed to write in the margin. Exam-prep generators and LMS plugins need a deterministic oracle that marks a negative length as wrong instead of silently returning NaN that a buggy grader might treat as success.
Drafting, CAD, and construction-layout scripts often know two taped distances on a wall or a cut list and need the third collinear measure before they can place a stud, a weld, or a dimension string. Game and map pipelines that store waypoints as a chain of segment lengths recover a missing span the same way, without pulling a full computer-algebra system for one addition. Failed validation does not consume balance.
Keep requests small, pin the rounded length in tests, and you get reproducible missing lengths for homework, batch graders, and edge workers without standing up symbolic geometry infrastructure of your own.
What you can do with it
Classroom and homework checks
Let students enter any two of AB, BC, and AC and verify the missing length against the textbook identity AB + BC = AC.
Exam and LMS auto-grading
Mark segment-addition items with a deterministic oracle that rejects negative lengths and pairs that cannot sit on one segment.
Layout and collinear dimensions
Recover the third taped distance on a wall, cut list, or waypoint chain from the two lengths already measured.
FAQ
How do I find a missing length with the segment addition postulate?
Send exactly two of ab, bc, and ac as non-negative finite numbers.
What if a length is negative?
A Euclidean segment cannot have a negative measure, and a whole shorter than one of its parts is equally impossible.
Can I send all three lengths?
No. Provide exactly two known lengths and omit the unknown.
Is a zero length allowed?
Yes. Zero means two labelled points coincide. Only strictly negative values, non-finite values, and postulate-breaking pairs are rejected.
What if the whole is shorter than one of the parts?
The calculator refuses the pair. A whole AC of 5 with a part of 8 would leave the other part with a negative length, which cannot happen on a straight line, so you get an error instead of a signed distance.
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/math/segment-addition-postulate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"ab":5,"part_a":0}'const res = await fetch("https://api.kit.forhosting.com/math/segment-addition-postulate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"ab": 5,
"part_a": 0
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/segment-addition-postulate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"ab": 5,
"part_a": 0
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/segment-addition-postulate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"ab":5,"part_a":0}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"ab":5,"part_a":0}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/segment-addition-postulate", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"ab": 5,
"part_a": 0
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.segment_addition_postulate",
"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
Negative measures are rejected with invalid_input, because a Euclidean segment cannot have a negative length. When the two given numbers would force the unknown part to be negative — a purported whole shorter than one of its parts — the same typed error is raised instead of inventing a signed distance.
Input contract, how the missing length is found, and errors
POST a JSON body that contains exactly two of the three finite numbers ab, bc, and ac — the lengths of AB, BC, and AC in any consistent unit. Each field may arrive as a JSON number or as a numeric string. Aliases part_a, part, and AB are accepted for ab; part_b and BC for bc; whole and AC for ac, so scripts can reuse the names printed in a textbook. Zero is a legal degenerate length (A and B coincide, or the interior point sits on an endpoint). Sending one field, all three, or none is also invalid_input, because the postulate then has either no unique solution or nothing to solve.
Technical questions
What does the segment addition postulate calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.