degrees minutes seconds — Definition, Formula & Examples
Degrees minutes seconds (DMS) is a way of writing angle measurements where each degree is divided into 60 minutes and each minute is divided into 60 seconds. For example, 45°30'15" means 45 degrees, 30 minutes, and 15 seconds.
DMS notation expresses an angle as an integer number of degrees (°), an integer number of arcminutes (′), and a real number of arcseconds (″), where 1° = 60′ and 1′ = 60″. This subdivides one degree into 3,600 equal parts.
Key Formula
Where:
- = Whole degrees
- = Arcminutes (0–59)
- = Arcseconds (0–59.99…)
- = Angle expressed in decimal degrees
How It Works
Read a DMS value from left to right: degrees first, then minutes, then seconds. To convert DMS to decimal degrees, keep the degrees whole, divide the minutes by 60, and divide the seconds by 3,600, then add all three. To go the other direction, take the decimal part of a degree, multiply by 60 to get minutes, then take the decimal part of the minutes and multiply by 60 to get seconds. The symbols used are ° for degrees, ′ (or ') for minutes, and ″ (or ") for seconds.
Worked Example
Problem: Convert 37°45'36" to decimal degrees.
Step 1: Keep the whole degrees as they are.
Step 2: Divide the minutes by 60 and the seconds by 3,600.
Step 3: Add all three values together.
Answer: 37°45'36" = 37.76°
Why It Matters
Navigation, surveying, and GPS coordinates all use DMS notation to pinpoint locations on Earth. In trigonometry and astronomy courses, you will frequently need to convert between DMS and decimal degrees to use your calculator or apply formulas correctly.
Common Mistakes
Mistake: Dividing seconds by 60 instead of 3,600 when converting to decimal degrees.
Correction: Seconds are sixtieths of a minute, which are themselves sixtieths of a degree. So seconds must be divided by 60 × 60 = 3,600 to convert directly to degrees.