Degrees minutes seconds
45.51° becomes 45° 30′ 36″: enter a decimal angle and get whole degrees, minutes and seconds on the sixty-to-one scale, plus a DMS string ready to paste. Built for plane angles in drawings and exercises, not map coordinates. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 45.51
- Degrees
- 45
- Minutes
- 30
- Seconds
- 36
- Sign
- 1
Sexagesimal notation still appears wherever an angle is printed for a human even though software stores that angle as a single decimal-degree number. A rotation in a CAD file, a heading on a worksheet, a bearing in a surveying notebook, or a textbook exercise often arrives as forty-seven point five degrees, while the printed report still wants forty-seven degrees thirty minutes zero seconds. This converter takes one finite decimal-degree angle, splits it into whole degrees, minutes, and seconds on the exact sixty-to-one ladder, and returns those three values plus a compact DMS string you can paste into a form or a test.
What degrees, minutes and seconds mean on a full circle
A degree is one three-hundred-sixtieth of a full turn. Each degree divides into sixty minutes of arc, and each minute divides into sixty seconds of arc, so one degree equals three thousand six hundred seconds. That sexagesimal ladder is older than decimal degrees and still dominates printed bearings, construction call-outs, astronomy logs, and exam questions that ask for an angle as D, M, and S rather than a single floating number.
Converting from decimal degrees is a short sequence of floors: whole degrees are the integer part of the absolute value; leftover fraction times sixty yields minutes; leftover fraction of those minutes times sixty yields seconds. The algebraic sign of the original angle is applied to the degrees component so minutes and seconds stay non-negative, which matches the usual classroom writing of minus forty-five degrees thirty minutes rather than minus forty-five minus thirty.
This capability treats the input as a general plane angle on a full circle, not as a geographic coordinate: there is no hemisphere letter, no latitude versus longitude axis, and no wrapping past a turn. An absolute value greater than three hundred sixty degrees is rejected, because a reported angle that large is almost always a unit mix-up or a missing modulo rather than a value this landing is meant to typeset. Zero maps to zero degrees zero minutes zero seconds.
A positive full turn of exactly three hundred sixty degrees is kept as three hundred sixty degrees rather than folded to zero, so callers who asked for a closed interval can round-trip the bound they sent.
Where a decimal-to-DMS angle split earns its keep
Teachers and exam-prep sites use a degrees-minutes-seconds converter so learners can check a hand split of a decimal heading without mixing the sixty-to-one scale with a ten-to-one decimal. CAD and CNC notes still print rotational offsets as D M S on drawings even when the CAM file stores a float; a tiny parse call turns the float into the three integers a checker can stamp next to the dimension.
Surveying office software that is not yet in geographic mode—traverse angles, interior angles, deflection angles—needs a full-circle bound rather than a latitude range of plus or minus ninety, which is why this landing refuses values that exceed 360 degrees instead of attaching N or S. Astronomy worksheets that quote altitude or azimuth as sexagesimal numbers can feed a decimal from a spreadsheet and get minutes and seconds back without a GIS hemisphere.
Prefer this capability when the search is degrees minutes seconds or decimal degrees to DMS for a general angle; use a dedicated latitude-longitude converter when you need a hemisphere letter, and a bidirectional DMS tool when you must go from printed D M S back to a decimal. Stay inside the published range, pin reconstructed against the input in tests, and you get a reproducible sexagesimal triple for homework, drawing notes, and edge workers without standing up a computer-algebra system.
What you can do with it
Classroom heading checks
Let students submit a decimal heading and verify the degrees, minutes and seconds split against the textbook sixty-to-one method without wrapping past a full turn.
CAD and drawing call-outs
Turn a stored decimal rotation into a printable DMS triple for a dimension note, checker stamp, or CNC comment block.
Survey traverse angles
Split interior or deflection angles that live on a 360-degree circle, not on a latitude axis, so out-of-range values fail instead of growing a silent hemisphere.
FAQ
What happens if the angle exceeds 360 degrees?
Absolute values greater than 360 are rejected so a missing modulo or a unit mix-up cannot wrap silently around a full turn. Exactly 360 is accepted as 360° 0' 0".
Are negative angles allowed?
Yes, down to minus 360 degrees. The sign is applied to the degrees component; minutes and seconds stay non-negative. Example: minus 45.5 becomes minus 45 degrees 30 minutes 0 seconds.
Is this a GPS or latitude-longitude converter?
No. This landing splits a general plane angle and does not attach a hemisphere letter or an axis. Use a dedicated geographic DMS tool when you need N, S, E, or W from a latitude or longitude.
How is 45.51 degrees split into minutes and seconds?
Keep the 45 whole degrees, multiply the leftover 0.51 by 60 to get 30 full minutes, then multiply what remains of the last minute by 60 to get 36 seconds. The result is 45° 30′ 36″.
How many seconds are in one degree?
A degree has 60 minutes of arc and each minute has 60 seconds, so one degree holds three thousand six hundred seconds. Mixing this sixty-to-one ladder with a ten-to-one decimal is the classic slip.
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/conv/degrees-minutes-seconds \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":45.51}'const res = await fetch("https://api.kit.forhosting.com/conv/degrees-minutes-seconds", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 45.51
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/conv/degrees-minutes-seconds",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 45.51
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/conv/degrees-minutes-seconds", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":45.51}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":45.51}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/conv/degrees-minutes-seconds", 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": 45.51
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "conv.degrees_minutes_seconds",
"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_abs_degrees | 360 |
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
Input that is not a finite number, or whose absolute magnitude exceeds three hundred sixty degrees, fails with invalid_input instead of wrapping silently around a full turn.
Input contract, response shape, and the 360-degree bound
Missing fields, empty strings, bare plus or minus signs, non-numeric text, NaN, and infinities fail the same way and are never billed. Example: value forty-five point five one yields forty-five degrees, thirty minutes, and thirty-six seconds, because the fractional zero point five one times sixty is thirty point six minutes and the leftover zero point six minutes times sixty is thirty-six seconds. Pair the numeric fields with your own typesetting if you need Unicode primes; the dms string is the stable copy-paste form. POST a JSON body with one required finite number named value: the angle in decimal degrees. Aliases degrees, angle, decimal, decimal_degrees, and deg are accepted so forms and SDK clients can use the name that fits the product. Absolute magnitude must stay inside three hundred sixty degrees inclusive; a value such as four hundred fails with invalid_input naming value and stating that it exceeds 360 degrees. On success the body echoes rounded value, sets degrees to the signed whole-degree component, minutes to an integer in zero through fifty-nine, seconds to a non-negative remainder that may be fractional, sign to one or minus one, dms to a compact ASCII string with degree, prime, and double-prime marks, reconstructed to the decimal rebuilt from those three parts, formula to the floor-and-scale identity, and method to decimal_to_dms. Seconds that round onto sixty carry into minutes, and minutes that reach sixty carry into degrees, so IEEE noise never publishes sixty seconds or sixty minutes.
Where a decimal-to-DMS angle split earns its keep
Failed validation does not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately omit value or pass text.
Technical questions
How do I convert decimal degrees to degrees, minutes and seconds?
Send a finite number in value (aliases degrees, angle, decimal, decimal_degrees, deg). The API returns signed degrees, non-negative minutes and seconds, a compact dms string, and a reconstructed decimal from those parts.
What does the degrees-minutes-seconds converter cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.