The Decimal Degrees to DMS Calculator converts decimal degree angles into degrees, minutes, and seconds (DMS), and converts DMS strings back into decimal degrees. Enter a decimal such as 40.446 or a DMS set such as 40° 26′ 46″ and read the paired form with each arithmetic step shown.
Maps, survey notes, and older navigation tools still print DMS. Modern GPS APIs often return decimal degrees. The Decimal Degrees to DMS Calculator bridges those formats for the same geographic angle without changing the underlying direction on the globe.
Convert decimal degrees to degrees minutes seconds
Decimal degrees store the whole angle as one real number. DMS splits that angle into whole degrees, whole minutes (each 1/60 of a degree), and seconds (each 1/60 of a minute). The Decimal Degrees to DMS Calculator extracts those three parts in order so a single decimal field becomes a readable sexagesimal triple.
The conversion does not change the size of the angle. It only changes how the angle is written. Forty and a half degrees is 40.5 in decimal form and 40° 30′ 0″ in DMS. Both describe the same direction or coordinate component.
Latitude and longitude pairs often mix the two styles in the same project. Keeping one converter for both directions reduces transcription errors when copying between a GIS layer and a printed deed description.
Apply the DMS conversion
The DMS conversion uses three fixed steps from a positive decimal degree value. The Decimal Degrees to DMS Calculator applies them automatically and prints the intermediate values. 1. Degrees. Take the whole-number part of the decimal degrees as the degree field.
2. Minutes. Multiply the fractional part by 60. The whole-number part of that product is minutes.
3. Seconds. Multiply the remaining fractional part of the minutes by 60 to get seconds.
Worked example: convert 40.446° to DMS.
1. Whole degrees = 40.
2. Fractional part 0.446 × 60 = 26.76, so minutes = 26.
3. Fractional part 0.76 × 60 = 45.6, so seconds ≈ 45.6″.
Result: 40° 26′ 45.6″ (display may round seconds to a chosen precision). The Decimal Degrees to DMS Calculator keeps full precision internally before rounding seconds for the panel.
Another check case: 12.5° becomes 12° 30′ 0″, because 0.5 × 60 = 30 minutes exactly with no leftover seconds.
Convert DMS to decimal degrees
DMS converts to decimal degrees by adding the parts as fractions of a degree. Degrees contribute their full value. Minutes divide by 60. Seconds divide by 3600, because there are 60 × 60 = 3600 seconds in one degree.
decimal degrees = degrees + (minutes / 60) + (seconds / 3600)Worked example: convert 40° 26′ 46″ to decimal degrees.
40 + 26/60 + 46/3600 = 40 + 0.433333... + 0.012777... ≈ 40.44611°.
The Decimal Degrees to DMS Calculator substitutes the entered DMS fields into that formula and shows each term. Reverse converting the decimal result should recover the original DMS within display rounding, which confirms the factors of 60 and 3600 were applied correctly.
Handle latitude and longitude signs
Latitude runs from −90° to +90°. Longitude runs from −180° to +180° in many digital systems, or 0° to 360° in some marine contexts. Positive latitude is north; negative latitude is south. Positive longitude is east; negative longitude is west in the signed decimal convention used by most GPS libraries.
The Decimal Degrees to DMS Calculator preserves the sign on the degree component, or attaches N/S and E/W labels when the interface uses hemisphere letters instead of a leading minus. Mixing a south label with a negative number double-applies the direction and flips the point. Enter either a signed decimal or an unsigned magnitude plus one hemisphere marker, not both conflicting cues.
| Hemisphere | Signed decimal | DMS style |
|---|---|---|
| North | +40.446 | 40° 26′ 45.6″ N |
| South | −40.446 | 40° 26′ 45.6″ S |
| East | +74.006 | 74° 0′ 21.6″ E |
| West | −74.006 | 74° 0′ 21.6″ W |
Seconds of longitude near the equator span a different ground distance than seconds of latitude, but the DMS arithmetic itself is identical for both coordinates. Ground distance needs a separate geodesic calculation; this page only reformats the angle.
FAQ
How do I convert decimal degrees to DMS?
To convert decimal degrees to DMS, take the whole degrees, multiply the fractional part by 60 for minutes, then multiply the leftover fraction by 60 for seconds. The Decimal Degrees to DMS Calculator performs those three steps and shows each intermediate value.
How do I convert DMS to decimal degrees?
To convert DMS to decimal degrees, compute degrees + minutes/60 + seconds/3600. For example, 40° 26′ 46″ becomes about 40.44611°. The Decimal Degrees to DMS Calculator substitutes the DMS fields into that formula.
What does DMS stand for?
DMS stands for degrees, minutes, and seconds. It is a sexagesimal way to write an angle that many maps and survey records still use. The Decimal Degrees to DMS Calculator converts between that form and a single decimal degree number.
How many minutes are in one degree?
One degree contains 60 minutes of arc, and each minute contains 60 seconds of arc. Those factors of 60 are why the Decimal Degrees to DMS Calculator multiplies and divides by 60 and 3600.
How do negative latitudes work in DMS?
Negative latitudes represent south in the signed decimal system. The Decimal Degrees to DMS Calculator keeps the south sense either as a minus on the degrees or as an S suffix, so the plotted point stays in the southern hemisphere.
Is DMS the same as converting degrees to radians?
No. DMS reformats degrees into minutes and seconds. Radians are a different unit of angle. Use the Angle Converter for degree-radian changes, and use the Decimal Degrees to DMS Calculator for decimal versus sexagesimal degree formatting.
Why do GPS apps show decimal degrees?
Digital mapping stacks store floating-point decimal degrees because they add and interpolate cleanly. Printed deeds and older charts often keep DMS for readability. The Decimal Degrees to DMS Calculator translates between those conventions for the same coordinate.
What precision should seconds use?
Survey work may keep tenths or hundredths of a second; casual map reading often rounds to whole seconds. The Decimal Degrees to DMS Calculator can show extra fractional seconds so you choose the rounding that matches the source document.
Summary
The Decimal Degrees to DMS Calculator converts decimal degrees into degrees, minutes, and seconds by splitting the fractional part with factors of 60, and converts DMS back with degrees + minutes/60 + seconds/3600. Worked cases such as 40.446° illustrate each step, and reverse conversion recovers the decimal form within display rounding.
Latitude and longitude signs or N/S and E/W labels must stay consistent so the hemisphere is not flipped. The page formats angular coordinates; it does not convert to radians or compute ground distance between points.