Area by double meridian distance
Courses with latitudes 0, 30 and −30 and departures 40, 0 and −40 enclose an area of 600, laid out row by row like a surveying computation sheet. You also get closures, misclosure and perimeter. Free in your browser.
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Run — free
The double meridian distance method is the classical surveying way to turn a closed traverse into an enclosed area once every course already has a latitude and a departure. Surveyors, civil-engineering students, and land-records clerks still compute lot and parcel areas this way: take the northing and easting of each side, build a running double meridian distance from the first departure, multiply each DMD by that course's latitude, sum the products, and take half the absolute value.
What double meridian distance means and how the area is formed
A plane traverse is a chain of measured courses. After you resolve each course into a latitude (the north or south component, north positive) and a departure (the east or west component, east positive), those two numbers are all the double meridian distance method needs. Place a reference meridian through the starting station of the first course.
The double meridian distance of that first course is simply its departure. Every later course adds the previous DMD, the previous departure, and its own departure, so the running value is twice the meridian distance of the course midpoint relative to that first meridian. Multiply each DMD by the latitude of the same course; the product is twice the signed area of the trapezoid that the course sweeps against the reference meridian.
Sum those products and take half the absolute value: that is the enclosed area of the figure, in the square of whatever linear unit you used for the latitudes and departures. For a mathematically closed traverse the latitudes sum to zero, the departures sum to zero, and the last DMD equals the negative of the last departure — a useful arithmetic check before you trust the total.
Where a DMD area calculator is used, priced, and kept distinct
Boundary surveys still publish lot area from a balanced traverse, and the office check that the crew's latitudes and departures enclose the area written on the plat is this exact sum. Civil-engineering and geomatics courses set homework that asks for a full DMD table, not only a final square-metre figure, so a deterministic table with one row per course is what a grader or a student notebook actually needs.
Land-development and cadastral scripts that already store northings and eastings of each side can call the same contract instead of re-implementing the running-meridian recurrence and risking an off-by-one on the first course. Compute or balance the latitudes and departures first, keep one linear unit throughout, and you get a machine-readable enclosed area that matches the double meridian distance column of a plane-surveying computation sheet.
What you can do with it
Office check of a balanced lot traverse
After latitudes and departures have been adjusted, compute the enclosed parcel area and confirm that the last DMD equals the negative of the last departure.
Surveying homework and LMS grading
Return the full per-course DMD table and the area so a student sheet or an auto-grader can check every column, not only the final square units.
Cadastral and civil notebooks
Feed stored course latitudes and departures from a records pipeline and receive a stable enclosed area plus latitude and departure closures.
FAQ
How is traverse area computed by the double meridian distance method?
DMD of the first course is its departure. Each later DMD is the previous DMD plus the previous departure plus the current departure. Area is the absolute value of the sum of (DMD times latitude) divided by two.
What sign convention do latitude and departure use?
Latitude is the northing of the course (north positive, south negative). Departure is the easting (east positive, west negative). Both must share one linear unit so the area is in that unit squared.
How can I check that my traverse closes?
For a closed traverse the latitudes and the departures each add up to zero, and the last DMD equals minus the last departure. The calculator also reports both closures, the linear misclosure and the perimeter.
What area does a 3-4-5 triangle traverse give?
With latitudes 0, 30 and −30 and departures 40, 0 and −40, the DMD column reads 40, 80 and 40 and the enclosed area is 600, half of base 40 times height 30.
Can I enter bearings and distances instead?
No. Resolve each course into its latitude and departure first, and balance them if the area is for a legal description. The calculator does not convert bearings, adjust the traverse or change units.
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/eng/area-dmd \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"sides":[{"latitude":0,"departure":40},{"latitude":30,"departure":0},{"latitude":-30,"departure":-40}]}'const res = await fetch("https://api.kit.forhosting.com/eng/area-dmd", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"sides": [
{
"latitude": 0,
"departure": 40
},
{
"latitude": 30,
"departure": 0
},
{
"latitude": -30,
"departure": -40
}
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/area-dmd",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"sides": [
{
"latitude": 0,
"departure": 40
},
{
"latitude": 30,
"departure": 0
},
{
"latitude": -30,
"departure": -40
}
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/area-dmd", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"sides":[{"latitude":0,"departure":40},{"latitude":30,"departure":0},{"latitude":-30,"departure":-40}]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"sides":[{"latitude":0,"departure":40},{"latitude":30,"departure":0},{"latitude":-30,"departure":-40}]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/area-dmd", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"sides": [
{
"latitude": 0,
"departure": 40
},
{
"latitude": 30,
"departure": 0
},
{
"latitude": -30,
"departure": -40
}
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.area_dmd",
"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.
Limits
max_items | 500 |
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 calculator accepts the ordered latitudes and departures, returns the enclosed area together with the per-course DMD table, the latitude and departure closures, the linear misclosure, and the perimeter, and uses the same pure arithmetic in the free browser tool and on the API. Successful API calls are billed at $0.002; invalid input is not charged.
What double meridian distance means and how the area is formed
The method is algebraically equivalent to the shoelace formula on the stations you would recover by accumulating those latitudes and departures, but the bookkeeping matches the column layout printed in every plane-surveying textbook, so a field book, a homework sheet, and this endpoint can be compared line by line.
Input contract, response shape, and how closure is reported
Optional precision is an integer from 0 to 15 and defaults to ten decimal places on every numeric field. Each table row carries a one-based index, the echoed latitude and departure, the course length from the Pythagorean combination of those two components, the DMD of the course, and that course's contribution to the double-area sum. The engine does not balance the traverse, does not convert bearings and distances into latitudes and departures, and does not change units: send already-computed (and, for a legal area, already-adjusted) L and D values. A 3-4-5 right triangle with latitudes 0, 30, −30 and departures 40, 0, −40 yields area 600, which is half of base 40 times height 30, and a last DMD of 40 that matches the negative of the last departure. POST a JSON body whose required field sides is an ordered array of at least three objects, each with a finite latitude and a finite departure in the same linear unit (metres, feet, or any other consistent pair). The array also accepts the aliases courses, legs, and traverse; each row accepts lat for latitude and dep for departure. Missing sides, a non-array, fewer than three courses, more than five hundred courses, or a non-finite latitude or departure fail with invalid_input that names the field, and those failures are not billed. On success the body returns side_count, the positive enclosed area, the signed double_area sum, latitude_sum, departure_sum, linear_misclosure as the hypotenuse of those two closures, perimeter as the sum of course lengths, a boolean closed flag, the precision used, a formula string, and a sides table. When the traverse does not close, closed is false and an extra closure_ratio equal to perimeter divided by linear misclosure is included so you can quote a 1-in-N figure of merit; when the figure is closed that optional field is omitted.
Where a DMD area calculator is used, priced, and kept distinct
Each successful request is one billable item at $0.002; failed validation does not consume balance.
Technical questions
Does the traverse have to close?
A legal enclosed area expects Σ latitude = 0 and Σ departure = 0. The calculator still returns the DMD sum for an open figure, sets closed to false, and reports linear_misclosure and closure_ratio so you can see the gap.
Do I send bearings and distances or already-computed latitudes and departures?
Send latitudes and departures. Resolve each course (and, if you need a legal area, balance the traverse) before calling this endpoint. It does not apply the compass rule or convert bearings.
What does the double meridian distance area calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.