Convert decimal degrees, degrees-minutes-seconds, and degrees decimal minutes with DMS, DDM, radians, gradians.
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DMS converter Convert decimal degrees into degrees-minutes-seconds notation, or paste DMS and decimal-minutes coordinates to normalize them into decimal degrees, DDM, radians, gradians, and total arc measures.
Example inputs
Accepted formats
Use signed decimal degrees, DMS symbols, degrees and decimal minutes, spaced values, compact NOAA-style DMS, or a direction letter at either end. Minutes and seconds must stay below 60.
Quick checkpoints
180° = π rad. 90° = 100 gon. One degree equals 60 arcminutes or 3,600 arcseconds.
Enter a value Provide a decimal degree or DMS angle to convert it across common angular formats.
DMS converter: decimal degrees, degrees-minutes-seconds, radians, and gradians explained
A DMS converter translates the same angle between decimal degrees, degrees-minutes-seconds notation, and degrees decimal minutes, then shows matching radians and gradians for surveying, mapping, and coordinate-entry workflows. That matters because geographic tools often accept several coordinate formats, but they do not always expect the same separators, sign rules, hemisphere notation, compact DMS syntax, or decimal-minute layout.
How decimal degrees and DMS relate
Degrees-minutes-seconds notation breaks one degree into 60 arcminutes and each arcminute into 60 arcseconds. Decimal degrees keep the same angle as a single decimal number. The converter moves cleanly between the two by treating the minutes and seconds as fractional parts of one degree.
That means 40° 26′ 46″ is the same angle as about 40.446111°. The representation changes, but the underlying direction does not.
The same value can also be written as degrees and decimal minutes, often abbreviated DDM. In that format, the seconds are folded into the minute field, so 40° 26′ 46″ becomes about 40° 26.7667′. That is why a useful DMS to decimal degrees calculator should make DD, DMS, and DDM visible together rather than forcing users to run separate conversions.
Converts a DMS angle into a single decimal-degree value.
Decimal minutes = minutes + seconds/60
Converts a DMS value into the degrees-and-decimal-minutes format used by many navigation and field workflows.
1° = 60′ = 3,600″
Basic subdivision used by DMS notation. This is the specific relationship the calculator applies when building the result.
Radians = degrees × π/180
Lets the same angle be expressed in radian-based technical work too.
Where DMS still appears in practice
Decimal degrees are common in GIS software, APIs, and spreadsheets because they are easy to store and calculate with. DMS remains common in navigation, field notes, coordinate entry screens, and legacy mapping references because it is familiar and easy to read aloud or verify against paper documents.
The biggest practical trap is format variation. Some tools want symbols such as ° ′ ″, others want space-separated values, and some NOAA workflows accept compact numeric DMS strings instead. Hemisphere letters and sign conventions also matter.
A coordinate printed on a chart, field form, GPS receiver, spreadsheet, or survey note may all describe the same place while using different notation. A copy-friendly degrees minutes seconds calculator is most useful when it helps you spot that difference before pasting a value into a system that expects DD, DDM, or DMS.
DD, DDM, and DMS format choices
Decimal degrees, often written DD, are compact and easy for software to sort, store, and calculate. Degrees decimal minutes, or DDM, keep the whole-degree field but use a decimal minute value. Degrees minutes seconds, or DMS, split that minute value one step further into whole minutes plus seconds.
The best format is the one your receiving system asks for. If a field form expects degrees and decimal minutes, entering full DMS can put the seconds in the wrong column. If a NOAA-style service expects compact DMS with a hemisphere prefix, a spaced or symbol-heavy string may need to be rewritten before submission.
This page therefore treats DMS conversion as a notation problem, not as a map-projection problem. It can convert the angle format, display normalized angle ranges, and show copy-friendly alternatives, but it does not change the underlying coordinate reference frame.
Worked example: DMS to decimal degrees and DDM
Suppose a longitude is written as 73° 59′ 15″ W. The decimal-degree magnitude is 73 + 59/60 + 15/3,600 = 73.9875. Because the hemisphere is west, the signed decimal-degree value is -73.9875°.
The same value in degrees and decimal minutes is 73° 59.25′ W because 15 seconds divided by 60 is 0.25 minutes. Showing both formats helps you copy the right representation into a mapping app, chart note, spreadsheet, or coordinate conversion service without losing the west/south sign.
Sign, hemisphere, and coordinate-entry caveats
Latitude and longitude are not formatted identically in every workflow. Latitude uses two degree digits while longitude often uses three. West and south coordinates are negative in decimal-degree form, but many entry systems let you express that direction with hemisphere letters instead.
This converter handles the formatting math, but it does not choose a datum or coordinate reference frame for you. A position can still differ if the underlying map datum changes, even when the angle format is correct.
Do not combine a negative sign with a north or east hemisphere unless the target system explicitly documents that convention. For most coordinate-entry workflows, north and east are positive while south and west are negative, so a west longitude can be written as either a W suffix or a negative decimal degree, not both.
NOAA Office of Coast Survey — Assist — NOAA help page with practical examples of decimal-degree, degree-minute, and degree-minute-second coordinate entry.
Frequently asked questions
How do I convert DMS to decimal degrees manually?
Take the degree value, add the minutes divided by 60, and add the seconds divided by 3,600. If the coordinate is west or south, apply a negative sign in decimal-degree form.
How do I convert decimal degrees to DMS?
Keep the whole-number part as degrees, multiply the decimal remainder by 60 to get minutes, then multiply the new remainder by 60 to get seconds. For example, 40.446111° becomes 40 degrees, 26 minutes, and about 46 seconds.
What is the difference between DMS and DDM?
DMS uses degrees, whole minutes, and seconds. DDM uses degrees and decimal minutes, so the seconds are folded into the minute field. The two formats can describe the same angle, but they are not interchangeable in a form that expects separate columns.
Can I use this as a DMS coordinate converter?
Yes for one latitude or longitude angle at a time. It converts the notation between decimal degrees, DMS, and degrees decimal minutes. If you need a full latitude-longitude pair, UTM output, a distance, or a datum transformation, use a dedicated coordinate converter instead.
What is compact NOAA-style DMS input?
Some NOAA services accept latitude and longitude as a hemisphere letter followed by fixed-width degrees, minutes, and seconds. For example, N404500.0 means 40 degrees, 45 minutes, and 0 seconds north; W0804500.0 means 80 degrees, 45 minutes, and 0 seconds west.
Why does longitude often use three degree digits?
Because longitude spans 0 to 180 degrees east or west, so the full value often needs three digits while latitude only spans 0 to 90 degrees.
Can the same coordinate be correct in both DMS and decimal form?
Yes. They are just two ways to write the same angle. Problems usually come from missing hemisphere signs, separator mismatches, or entering longitude digits in the wrong format.
Does converting angle format also change the map datum?
No. Format conversion changes only how the angle is written. Datum and reference-frame changes are separate geodetic transformations.
Why are south and west coordinates negative in decimal degrees?
Signed coordinate systems usually treat north latitude and east longitude as positive, while south latitude and west longitude are negative. Hemisphere letters express the same idea in a text-friendly way, so the calculator preserves that sign when converting DMS to decimal degrees.
How precise is a DMS conversion?
The arithmetic relationship is exact, but displayed results are rounded for readability. More decimal places in seconds or decimal degrees preserve more precision, while a rounded value may shift a mapped point slightly if copied into a high-precision GIS workflow.
