Decimal degrees to DMS converter
A latitude of 40.7128 becomes 40° 42′ 46.08″ N: pick latitude or longitude, and the converter splits the number into degrees, minutes and seconds, takes the hemisphere from the sign and rebuilds the decimal so you can check it. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 40.7128
- Axis
- Latitude
- Degrees
- 40
- Minutes
- 42
- Seconds
- 46.08
- Hemisphere
- N
Decimal degrees are the default coordinate form in GIS layers, GPS logs, web maps, and spreadsheet exports, yet field manuals, nautical charts, survey plats, and many regulatory forms still require sexagesimal degrees-minutes-seconds with an explicit hemisphere letter. This converter takes one signed decimal-degree number and an axis choice—latitude or longitude—and returns integer degrees, integer minutes, fractional seconds, the hemisphere (N, S, E, or W), a printable DMS string, and a reconstructed decimal so you can verify round-trip accuracy. Positive values mean north or east; negative values mean south or west; zero uses the positive hemisphere by convention. Values outside the axis range fail with a clear validation error instead of wrapping silently past the pole or the antimeridian.
How decimal degrees become degrees, minutes, and seconds
Start with a signed decimal-degree value v and an axis that decides both the legal range and the hemisphere alphabet. For latitude the closed interval is negative ninety through positive ninety degrees and the letters are N for non-negative values and S for negative values. For longitude the closed interval is negative one hundred eighty through positive one hundred eighty degrees and the letters are E for non-negative values and W for negative values.
Seconds are rounded to a fixed number of decimal places, and if rounding pushes seconds to sixty they carry into minutes; if minutes then reach sixty they carry into degrees. That carry path prevents ugly results such as sixty seconds or sixty minutes when a value is extremely close to a whole minute or degree boundary. The hemisphere is chosen from the original sign and the axis, never from absolute magnitude alone, so a southern latitude always shows S even when degrees minutes and seconds are positive integers.
Where decimal-to-DMS conversion shows up in real work
Surveyors, navigators, and GIS analysts constantly reformat machine-friendly decimal coordinates into the sexagesimal notation used on plats, Notices to Mariners, aviation charts, and cadastral descriptions; a single trusted converter removes spreadsheet formula drift between teams. Open-data portals often publish WGS eighty-four points as decimal degrees while partner agencies demand DMS strings with hemisphere letters in fixed-width report templates, and ETL jobs need deterministic rounding and carry so batch exports do not flip a parcel by one second.
Educators teaching coordinate systems want students to see both the signed decimal form and the N S E W form side by side without hand-calculating sixty-based remainders under exam time pressure. If you later need the inverse path from DMS parts back to decimal degrees, great-circle destination points, or slippy-map tile indices from lat and lon, treat those as separate search intents and landings rather than overloading this decimal-to-DMS page.
What you can do with it
Survey and cadastral report formatting
Turn signed decimal GPS or GIS points into degrees, minutes, seconds and hemisphere letters for plats, deed exhibits, and regulatory submittals.
Bulk GPS track and open-data ETL
Convert entire columns of decimal latitudes and longitudes to stable DMS strings with deterministic rounding and axis-range validation.
Teaching coordinate systems
Show students the exact sexagesimal split of a signed decimal degree with N/S or E/W so homework answer keys match one ground truth.
FAQ
What is the difference between decimal degrees and DMS?
Decimal degrees store a coordinate as a single signed number (for example 40.7128). DMS splits the absolute value into integer degrees, integer minutes, and seconds of arc, then adds a hemisphere letter (N, S, E, or W) from the sign and axis.
What ranges are accepted?
Latitude must be in [-90, 90] decimal degrees. Longitude must be in [-180, 180].
How are positive and negative values interpreted?
Positive means north for latitude and east for longitude. Negative means south and west. Zero uses the positive hemisphere (N or E) by convention.
Can I pass lat or lon instead of latitude or longitude?
The response always normalizes axis to latitude or longitude.
What does it cost?
The browser tool is free and runs locally.
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/geo/decimal-to-dms \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":40.7128,"axis":"latitude"}'const res = await fetch("https://api.kit.forhosting.com/geo/decimal-to-dms", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 40.7128,
"axis": "latitude"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/decimal-to-dms",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 40.7128,
"axis": "latitude"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/decimal-to-dms", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":40.7128,"axis":"latitude"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":40.7128,"axis":"latitude"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/decimal-to-dms", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"value": 40.7128,
"axis": "latitude"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.decimal_to_dms",
"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
How decimal degrees become degrees, minutes, and seconds
The conversion works on the absolute value: take the integer floor of the absolute decimal as the degree component, multiply the fractional remainder by sixty to obtain minutes of arc, take the integer floor of that product as the minute component, then multiply the leftover fractional minute by sixty again to obtain seconds of arc. The pipeline is pure deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network geocoding, and no model drift, so the same value and axis always yield the same JSON. Inputs that are missing, non-numeric, NaN, or Infinity are rejected, and values that exceed the axis range fail with invalid_input so callers can correct coordinates instead of publishing impossible positions.
What you send and what you get back
Send two fields: value as a finite number of signed decimal degrees, and axis as the string latitude or longitude. Both fields are required. Classic checks include forty point seven one two eight latitude for New York City mapping samples, negative seventy-four point zero zero six longitude for the same city on the west side of Greenwich, zero on either axis for the equator or prime meridian edge cases, and deliberately out-of-range values such as ninety-one latitude or one hundred eighty-one longitude to exercise the error path. Wire the free browser form for homework and quick sanity checks, then call the identical contract from scripts when you need bulk conversion of GPS tracks or answer keys. Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. When value is outside negative ninety to ninety for latitude, or outside negative one hundred eighty to one hundred eighty for longitude, the request fails with a message that names the axis range so automated clients can surface a precise fix. On success the response echoes the cleaned value and normalized axis, integer degrees, integer minutes, fractional seconds, hemisphere as a single letter, sign as plus or minus one, absolute_decimal as the magnitude used in the sexagesimal split, a human-readable dms string with degree minute and second symbols plus the letter, a compact dms_compact form without spaces, reconstructed decimal degrees for quick verification, the numeric range object for the axis, method decimal_to_dms, and a short formula string. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where decimal-to-DMS conversion shows up in real work
Curriculum authors building interactive lessons need the same JSON shape offline and online so auto-graders and worksheets stay aligned. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.