Equilateral triangle area calculator
A side of 10 gives an equilateral triangle an area of about 43.301270, and a side of 2 gives √3, about 1.732051. Type one side length and get the area, rounded half-up to six decimals unless you pick another number. Free in your browser.
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Worked example
- Side
- 2
- Area
- 1.732051
Enter the side length of an equilateral triangle and get its exact area, computed with the closed form A = (√3/4)·s² and rounded half-up to the number of decimals you choose (six by default). Because all three sides and all three angles of an equilateral triangle are equal, the side alone determines the area completely: no other measurement, approximation, or lookup table is involved.
Where the √3/4 comes from
An equilateral triangle has three equal sides and three angles of exactly sixty degrees, so one side fixes it completely. Draw the height from one corner to the middle of the opposite side and the triangle splits into two right triangles with angles of 30, 60 and 90 degrees. That height is √3/2 times the side. The area of any triangle is half the base times the height, so half of the side times √3/2 times the side gives √3/4 times the side squared. With a side of 2 that is exactly √3, about 1.732051.
Using the result without surprises
Because the side is squared, the area grows much faster than the side. A side of 10 gives about 43.301270, while a side of 0.5 gives about 0.108253. The side must be a positive number; zero is refused because a flat triangle has no area, and so is a side so large that its square cannot be represented. The area is computed in full precision and only rounded at the end, half-up, to six decimals by default or anywhere from zero to ten. Zero decimals give a whole number, useful for a rough estimate of panels, tiles or gussets.
One side is all you need
An equilateral triangle has three equal sides and three equal angles of exactly sixty degrees, so its whole geometry is fixed the moment you know a single side length. There is no ambiguity to resolve, no second measurement to supply, and no case analysis to perform: every positive finite number describes one real equilateral triangle and one unique area.
The formula behind the result is the classical closed form A = (√3/4)·s², which comes from splitting the triangle into two 30-60-90 right triangles of height (√3/2)·s and applying one half base times height.
What you can do with it
Fabrication and materials
Estimate the sheet area of equilateral panels, tiles, or gussets from a single edge measurement before quoting or cutting stock.
Geometry teaching
Demonstrate that one side fully determines an equilateral triangle's area, with adjustable decimals for step-by-step classroom work.
Layout and graphics
Compute the exact footprint of equilateral shapes for grid layouts, SVG generation, or game and map tile systems.
FAQ
Which formula is used?
The closed form A = (√3/4)·s², derived from the height (√3/2)·s via one half base times height. No iteration or approximation is involved.
What exactly is returned?
An object with the echoed side and the computed area, both rounded half-up to the decimals you chose (six by default).
Can I control the precision?
Yes. The optional decimals field accepts an integer from 0 to 10 and applies a deterministic half-up rounding to the full-precision result.
What is the area of an equilateral triangle with a side of 10?
About 43.301270 with the default six decimals. For comparison, a side of 2 gives √3, about 1.732051, and a side of 0.5 gives about 0.108253, because the area follows the square of the side.
Can I get a whole number for a rough estimate?
Yes. Choose zero decimals and the area is rounded half-up to a whole number, which is handy for a quick material estimate before quoting or cutting panels and tiles.
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/equilateral-triangle-area \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"side":2}'const res = await fetch("https://api.kit.forhosting.com/math/equilateral-triangle-area", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"side": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/equilateral-triangle-area",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"side": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/equilateral-triangle-area", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"side":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"side":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/equilateral-triangle-area", 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": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.equilateral_triangle_area",
"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
The side must be a positive finite number; anything else — zero, a negative value, a string, NaN, or a missing field — is rejected with a typed invalid_input error that tells you exactly what went wrong.
One side is all you need
That is why this endpoint asks for exactly one input, side, and returns exactly one result, area. For example, side = 2 gives A = √3 ≈ 1.732051, side = 10 gives A ≈ 43.301270, and side = 0.5 gives A ≈ 0.108253. Supplying the side as the only required field keeps the contract minimal and makes the call trivial to automate from any script, spreadsheet, or form.
Precision and rounding rules
Rounding to zero decimals is allowed and returns a whole number, which is handy for coarse material estimates. The echoed side field in the response is rounded with the same rule, so the pair you receive is always internally consistent. The area is first computed in full IEEE-754 double precision and only then rounded, so the rounding step never feeds back into the computation and cannot compound. If the side is so large that the squared value overflows to infinity, the result is rejected as a typed error instead of silently returning Infinity, because a non-finite area is never a useful answer.
Validation and error behavior
Zero is rejected too, since a degenerate triangle has no meaningful area to report. The decimals field is optional, but when present it must be an integer from 0 to 10; fractional or out-of-range values are rejected for the same reason — the contract is explicit rather than forgiving, which keeps client bugs visible during development instead of hiding them as silently coerced values. Every call is validated before any arithmetic happens, and every rejection is a typed invalid_input error that names the offending field, so a bad request never costs anything and never returns a half-computed result. The side field is required and must be a JSON number: strings like "2", booleans, null, arrays, and objects are all rejected, as are NaN, Infinity, and negative numbers, because none of them describes a physical length.
Technical questions
What input does it need?
A single number, side: the length of any edge of the equilateral triangle. It must be positive and finite; strings, zero, negatives, and NaN are rejected.
Is it free?
The tier A browser widget is free and runs the same isomorphic module as the API, which is billed from $0.002 per call.