Distance by triangulation calculator
A baseline of 100 with base angles of 50° and 60° puts the target 92.1604985107 from the first station and 81.5207469096 from the second. Enter your baseline and the two sighted angles to get both distances at once. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Baseline
- 100
- Angle a
- 50
- Angle b
- 60
- Angle c
- 70
- Distance from a
- 92.1604985107
- Distance from b
- 81.5207469096
- Angle unit
- deg
Triangulation is the classic way to find how far a remote landmark sits from a short measured baseline when you can only sight angles at the two ends of that base. Surveyors, orienteering coaches, cadet training, and outdoor STEM labs still use this plane geometry pattern: fix a baseline length, measure the interior angle at each station toward the same target, recover the apex angle as one hundred eighty degrees minus the sum of the base angles, and apply the law of sines so each unknown ray equals the baseline times the sine of the opposite base angle over the sine of the apex. Students who already know a over sin A equals b over sin B need a purpose-built landing that speaks survey language—baseline, base angles, distance to target—rather than a general triangle solver that asks for arbitrary side labels.
What baseline triangulation measures and why the law of sines is enough
Place two observation points A and B a known distance apart—that length is the baseline. From A you measure the interior angle between the baseline and the line of sight to a remote target C; from B you measure the matching interior angle on the other end. Those two base angles and the fixed baseline determine a unique plane triangle as long as their sum is strictly less than one hundred eighty degrees.
The remaining apex angle at C is simply one hundred eighty minus the sum of the base angles. The law of sines then states that each side over the sine of its opposite angle is the same common ratio, so the distance from A to C equals the baseline times sin of the angle at B over sin of the apex, and the distance from B to C equals the baseline times sin of the angle at A over sin of the apex.
Search intent clusters around phrases such as distance by triangulation calculator, triangulation range from baseline, and find distance with two angles and a base. People want a numeric range they can check against a field book, a homework key, or a training exercise, not a full computer-algebra session that asks them to rename sides.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate triangulation distance while checking a survey sketch, a orienteering lesson, or a classroom problem without installing a computer-algebra system. Keep angles in degrees as interior base angles of the triangle, not bearings from true north unless you have already reduced them to the interior angles between the baseline and the lines of sight. Returned lengths share the same unit as the baseline you provided—metres, feet, or any other linear unit—because the law of sines is homogeneous.
There is no language model, no external GIS service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials.
What you can do with it
Field survey and orienteering drills
Convert a paced or taped baseline and two sighted base angles into distances from each station to a remote landmark for training logs and simple maps.
Classroom triangulation labs
Let students check homework that asks for the range to a tower or tree given a baseline and the two base angles, with clear rejection when the angles cannot close a triangle.
FAQ
What if my two base angles sum to 180° or more?
No plane triangle exists in that case, so those calls are not charged.
Is the distance by triangulation calculator free?
The browser tool runs free on your device.
Which unit should I use for the baseline?
Any linear unit you prefer—metres, feet, yards. Returned distances use the same unit as the baseline because the ratios are dimensionless.
How far is the target with a baseline of 100 and angles of 50° and 60°?
The angle at the target is 70°, so the target is 92.1604985107 from the first station and 81.5207469096 from the second, in the same unit as the baseline.
Can I enter compass bearings instead of base angles?
Not directly. Each angle must be the inside angle between the baseline and your line of sight to the target, so convert bearings from north into those inside angles before entering them.
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/triangulation-distance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"baseline":100,"angle_a":50,"angle_b":60}'const res = await fetch("https://api.kit.forhosting.com/trig/triangulation-distance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"baseline": 100,
"angle_a": 50,
"angle_b": 60
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/trig/triangulation-distance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"baseline": 100,
"angle_a": 50,
"angle_b": 60
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/trig/triangulation-distance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"baseline":100,"angle_a":50,"angle_b":60}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"baseline":100,"angle_a":50,"angle_b":60}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/trig/triangulation-distance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"baseline": 100,
"angle_a": 50,
"angle_b": 60
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "trig.triangulation_distance",
"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 baseline triangulation measures and why the law of sines is enough
Returning both rays plus the computed apex angle as structured JSON makes the result easy to paste into notes, pin in automated tests, or feed into a larger mapping pipeline without reimplementing degree-to-radian conversion in every language you teach or deploy.
How this calculator validates input, applies the law of sines, and rejects impossible triangles
The engine checks that each field is a finite number, that the baseline is strictly positive, and that each angle is a positive interior value strictly less than one hundred eighty. When the angles are valid, the apex angle is one hundred eighty minus their sum, the sine of the apex is taken as the common denominator, and the two target distances follow from the law of sines ratios described above. Edge cases are explicit: zero or negative baseline, non-numeric strings, missing fields, angles outside the open interval from zero to one hundred eighty, and pairs whose sum leaves a non-positive apex all fail before a fake range is returned. Send a JSON body with three required fields: baseline as a positive finite length in whatever unit you already use for the field measurement, angle_a as the interior base angle at endpoint A in degrees, and angle_b as the interior base angle at endpoint B in degrees. If the two base angles sum to one hundred eighty or more, no plane triangle exists and the request fails with invalid_input so those failed calls are not charged. Results are rounded to a stable decimal precision so the same input always yields the same JSON. The response echoes the inputs, reports angle_c, distance_from_a (ray AC opposite the angle at B), distance_from_b (ray BC opposite the angle at A), the angle unit, the method tag law_of_sines_triangulation, and a short formula string you can show next to the answer.
Practical use, limits, pricing, and delivery channels
Each successful request is one billable item at $0.002; failed validation does not consume balance. Results are fully deterministic: the same baseline, angle_a, and angle_b always yield the same apex and the same two target distances. Wire the endpoint into survey demos, cadet training sheets, STEM triangulation labs, or preprocessing steps where you already prefer explicit domain errors—especially angle sums that cannot close a triangle—over opaque black-box widgets that cannot show why a measured pair of base angles cannot form a real remote point.
Integration use cases
Deterministic fixtures for geometry tests
Pipelines that seed unit tests or interactive survey demos can call a pure triangulation oracle instead of reimplementing degree trig in every language.
Technical questions
How do I compute distance by triangulation with this API?
Send baseline (positive length) plus angle_a and angle_b in degrees as interior base angles. The response returns angle_c and both distances from the baseline ends to the remote point.
What formula does the triangulation calculator use?
Apex angle_c = 180 − angle_a − angle_b. Then distance_from_a = baseline × sin(angle_b) / sin(angle_c) and distance_from_b = baseline × sin(angle_a) / sin(angle_c) by the law of sines.