Triangle perimeter calculator
Sides of 3, 4 and 5 give a perimeter of 12. Enter the three lengths and the calculator first confirms they can close into a triangle, then adds them, so an impossible set never yields a misleading total. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Side a
- 3
- Side b
- 4
- Side c
- 5
- Perimeter
- 12
The perimeter of a triangle is the total distance around its boundary: add the three side lengths and you have the closed path length. Before that sum is meaningful, the three lengths must be able to form a triangle at all — each pair of sides must be strictly longer than the third, the classical triangle inequality. Students checking homework after measuring a sketch, surveyors and DIY planners converting three edge measurements into fence or trim length, exam generators that need a deterministic oracle for perimeter items, and automation pipelines that already hold side lengths all reach for the same validated sum.
What triangle perimeter means and why the inequality comes first
A triangle is a three-sided polygon. The classical triangle inequality states that the sum of any two sides must be strictly greater than the third side. If a + b is not greater than c, the segments collapse into a line segment or cannot meet at a vertex, so there is no triangular region and reporting a “perimeter” would be misleading for geometry work.
In classroom language the perimeter is the distance around the figure. In construction and layout the same number is the total linear material for a closed triangular frame, the cut length of trim around a triangular panel, or the fence length enclosing a triangular bed when you already have all three edge measurements from a tape. Keeping the contract to three inputs and one primary output makes the calculator ideal as a fast check beside a diagram, a three-field form, or a one-line step in a larger geometry pipeline.
When sides are positive and satisfy the inequality, the result scales linearly with each contribution, so scaling every side by the same positive factor scales the perimeter by that factor with no hidden constants beyond ordinary addition of the three lengths that define the closed path.
Where a triangle perimeter calculator earns its keep
Geometry homework and entrance exams often ask for the perimeter of a triangle given all three side lengths, sometimes after students have already found a missing side from Pythagoras or the law of cosines. Learners flip sign errors, omit a side, or add lengths that cannot form a triangle; a deterministic oracle that always sums three valid sides and rejects invalid triples catches those slips before a tutor spends a session on arithmetic.
Craft, roofing, and CNC workflows that cut triangular panels or frames need the total edge length for material estimates once the design freezes the three edge sizes. Landscape and event planners who lay triangular stages, garden beds, or traffic islands convert measured edges into total border or rope length without opening a full CAD suite. Exam-prep generators and LMS auto-graders need a tiny closed-form checker that rejects inequality failures and non-positive sides as invalid rather than silently returning a sum that a buggy grader might accept for a non-triangle.
What you can do with it
Classroom and homework checks
Students enter three side lengths and verify that the perimeter is exactly their sum, while invalid triples that fail the triangle inequality are rejected instead of silently graded wrong.
Craft, fencing, and material estimates
Convert three measured or design edge lengths into total border length for frames, trim, laser paths, or stock cut lists around a triangular panel, bed, or stage.
LMS and exam auto-grading
Mark triangle perimeter items with a deterministic oracle that rejects non-positive sides and inequality failures and never invents area or angles when only the three-side sum is required.
FAQ
What is the triangle inequality and why does this calculator enforce it?
Each pair of sides must sum to more than the third side.
What happens if any side length is zero or negative?
A triangle cannot have a non-positive side length, and invalid input is not billed.
Does this calculator also return area or angles?
Use other geometry or trigonometry capabilities (for example Heron’s formula for area) if you need area, height, or angles.
What is the perimeter of a triangle with sides 3, 4 and 5?
The perimeter is 12, the sum of the three sides. Each pair of sides is longer than the third, for example 3 plus 4 is more than 5, so the lengths form a real triangle.
Can I use it to work out fence or trim length?
Yes. The perimeter is the total length around the triangle, so it gives the border needed for a triangular garden bed, frame or panel once you have measured all three edges.
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/trig/triangle-perimeter-from-sides \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"side_a":3,"side_b":4,"side_c":5}'const res = await fetch("https://api.kit.forhosting.com/trig/triangle-perimeter-from-sides", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"side_a": 3,
"side_b": 4,
"side_c": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/trig/triangle-perimeter-from-sides",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"side_a": 3,
"side_b": 4,
"side_c": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/trig/triangle-perimeter-from-sides", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"side_a":3,"side_b":4,"side_c":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"side_a":3,"side_b":4,"side_c":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/trig/triangle-perimeter-from-sides", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"side_a": 3,
"side_b": 4,
"side_c": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "trig.triangle_perimeter_from_sides",
"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
This triangle perimeter from sides calculator accepts three finite positive lengths, rejects triples that violate the inequality or carry non-positive sides, and returns the perimeter together with the echoed sides and a short formula string so classroom demos and paid API callers never disagree on a three-side total.
What triangle perimeter means and why the inequality comes first
Its perimeter is the length of the entire boundary: walk once along side_a, side_b, and side_c and you have travelled the sum of those three lengths. That identity is exact for any three positive finite side lengths that can actually form a closed triangle in the plane. This endpoint intentionally answers only that boundary question after a geometric validity check. It does not compute area (use a Heron-style tool for that), angles, height, or special-case classifications such as right, isosceles, or equilateral beyond what the three lengths already imply.
Input contract, response shape, and error behaviour
Each must be a finite positive number greater than zero. Example: sides three, four, and five yield perimeter twelve, because three plus four plus five is twelve and the triple is a classic right triangle that clearly satisfies the inequality. Units are caller-defined: if you send centimetres you get centimetres of perimeter; if you send metres you get metres. The calculator does not convert units, draw the figure, or estimate waste factors for cutting stock. Pair the numeric result with your own unit labels and drawings. Keep requests small, pin the rounded perimeter in tests, and you get reproducible three-side sums for homework, LMS plugins, and edge workers without standing up a computer-algebra system. POST a JSON body with three required fields: side_a, side_b, and side_c. Fields may arrive as JSON numbers or as numeric strings; empty strings, missing fields, Infinity, and NaN fail with invalid_input naming the problem. Aliases a and side1 map to side_a; b and side2 map to side_b; c and side3 map to side_c so clients that already use short geometry names do not need a rename layer. If the three lengths fail the strict triangle inequality — for example 1, 2, and 10 — the task fails with invalid_input explaining that each pair of sides must sum to more than the third; those failures are not billed. On success the body includes the echoed side_a, side_b, and side_c (each rounded to twelve decimal places for stable goldens), perimeter equal to their sum with the same rounding, formula equal to the string P = side_a + side_b + side_c, and method equal to triangle_perimeter_from_sides for logging and multi-solver UIs.
Where a triangle perimeter calculator earns its keep
Engineering notebooks and spreadsheet replacements can call this endpoint as a three-field step when a larger script already holds side lengths for several polygons and only the triangle perimeter case needs a dedicated, SEO-clear name distinct from area or angle tools. In all of those settings the value is not exotic mathematics: it is a stable contract, clear triangle-inequality errors, and a search intent that matches how people actually query for triangle perimeter from three sides at $0.002 per successful API call.
Technical questions
How do I calculate the perimeter of a triangle from three sides?
Send three finite positive lengths: side_a, side_b, and side_c that satisfy the triangle inequality. The API returns perimeter = side_a + side_b + side_c, plus the echoed sides and the formula string.
What does the triangle perimeter calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.