Formula
D = floor(|DD|)
M = floor((|DD| − D) × 60)
S = (((|DD| − D) × 60) − M) × 60
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Decimal Degrees to Degrees Minutes Seconds
Convert decimal degrees
DMS result
Formatted coordinate or angle
Signed DMS—
Components—
Decimal degrees—
Worked calculation
Enter decimal degrees to see the degree, minute, and second steps.
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How to convert decimal degrees to DMS
- Degrees: take the whole-number part of the absolute decimal degree value.
- Minutes: multiply the remaining fractional degree by 60, then take its whole-number part.
- Seconds: multiply the remaining fractional minute by 60. Round only at the end, then apply the original sign or coordinate hemisphere.
Example: −73.985656°
D = 73
M = floor(0.985656 × 60) = 59
S = 0.13936 × 60 = 8.3616
Result: 73° 59′ 8.36″ W as longitude.
Symbols: DD is decimal degrees, D is whole degrees, M is whole arcminutes, and S is arcseconds. One degree contains 60 arcminutes; one arcminute contains 60 arcseconds.
Decimal degrees and DMS examples
| Decimal degrees | DMS | Coordinate meaning |
|---|---|---|
| 51.5074 | 51° 30′ 26.64″ | 51° 30′ 26.64″ N as latitude |
| −73.985656 | −73° 59′ 8.3616″ | 73° 59′ 8.3616″ W as longitude |
| 0.5 | 0° 30′ 0″ | Half of one degree |
| 12.345678 | 12° 20′ 44.4408″ | Positive latitude is north; positive longitude is east |
| −0.0002777778 | −0° 0′ 1″ | The sign applies even when whole degrees are zero |
Signs, hemispheres, and rounding
Latitude and longitude ranges
Latitude runs from −90° to +90°; longitude runs from −180° to +180°. Negative latitude is south, and negative longitude is west. At zero, this tool labels latitude as the equator and longitude as the prime meridian.
The sign belongs to the whole angle
In −73° 59′ 8.36″, the minutes and seconds are not added to −73 as positive values. The notation means the negative of the complete magnitude: −(73 + 59/60 + 8.36/3600).
Rounding can carry
If seconds round to 60, the converter shows 0 seconds and increases the minutes. If that produces 60 minutes, it shows 0 minutes and increases the degrees. This keeps every DMS result normalized.
DMS versus decimal minutes
Degrees-minutes-seconds and degrees-decimal-minutes are different formats. For example, 40° 26′ 46″ is DMS, while 40° 26.7667′ uses decimal minutes.
Frequently asked questions
How do I convert decimal degrees to DMS?
Take the whole part as degrees. Multiply the remaining fraction by 60 for minutes, then multiply the remaining minute fraction by 60 for seconds.
What is 1 decimal degree in minutes and seconds?
One degree equals 60 arcminutes or 3,600 arcseconds. The words “minutes” and “seconds” here describe parts of an angle, not time.
How are negative decimal degrees shown?
A minus sign applies to the complete DMS angle. In geographic coordinates, negative latitude becomes S and negative longitude becomes W.
Can DMS seconds equal 60?
Not in normalized DMS. A rounded value of 60 seconds carries into one additional minute, and 60 minutes carries into one additional degree.
How precise should the seconds be?
Match the precision of the original measurement. Extra displayed digits make formatting finer but cannot add accuracy that was absent from the source coordinate.
What do N, S, E, and W mean?
N/S identify latitude relative to the equator. E/W identify longitude relative to the prime meridian.
Is DMS the same as decimal minutes?
No. DMS divides the minute fraction into arcseconds. Degrees and decimal minutes retains that fraction as a decimal number of minutes.