Angle Measure Converter
Conversion of decimal degrees into degrees, minutes and seconds (DMS format)
Angle Calculator (DMS)
Decimal Degree Converter
Select the unit of measurement that you know and enter its value. The calculator converts decimal degrees into DMS format (degrees° minutes' seconds").
DMS Format - Overview
Degrees-Minutes-Seconds System
1° = 60' = 3,600"
What is DMS Format?
The DMS format (Degrees, Minutes, Seconds) is a traditional way to represent angles. It divides a degree into 60 arcminutes and each arcminute into 60 arcseconds.
- Degree (°): Main unit of the angle
- Arcminute ('): 1/60 of a degree
- Arcsecond ("): 1/60 of an arcminute = 1/3600 of a degree
Applications
- Navigation: GPS coordinates (e.g., 48° 8' 35" N)
- Astronomy: Positions of stars and planets
- Cartography: Latitude and longitude
- Surveying: Precise angle measurements
- Geodesy: Land surveying
Example: Munich
Decimal degree: 48.1351° N, 11.5820° E
DMS format: 48° 8' 6" N, 11° 34' 55" E
Important Conversions
- 1° = 60' (arcminutes)
- 1° = 3,600" (arcseconds)
- 1' = 60" (arcseconds)
- 1' = 0.01667° (approx. 1/60 degree)
- 1" = 0.000278° (approx. 1/3600 degree)
Formulas for Angle Conversion
Basic Relationships
Degree, Arcminute, Arcsecond
\(\displaystyle 1° = 60' = 3600''\)
Radian and Degree
\(\displaystyle degree = radian \cdot \frac{180}{\pi}\)
\(\displaystyle radian = degree \cdot \frac{\pi}{180}\)
Gradian
\(\displaystyle degree = gradian \cdot \frac{90}{100}\)
\(\displaystyle radian = gradian \cdot \frac{\pi}{200}\)
Mil
\(\displaystyle mil = degree \cdot \frac{3200}{180}\)
\(\displaystyle mil = gradian \cdot 16\)
Conversion Decimal Degree → DMS
Example: Convert 45.515° to DMS
\(\displaystyle deg_{dec} = 45.515°\)
\(\displaystyle deg = int(deg_{dec})\)
\(\displaystyle = int(45.515) = 45\)
\(\displaystyle min_{dec} = (deg_{dec} - deg) \cdot 60\)
\(\displaystyle = (45.515 - 45) \cdot 60 = 30.9\)
\(\displaystyle min = int(min_{dec})\)
\(\displaystyle = int(30.9) = 30\)
\(\displaystyle sec = (min_{dec} - min) \cdot 60\)
\(\displaystyle = (30.9 - 30) \cdot 60 = 54\)
Result
45° 30' 54"
Practical Tips
Decimal degree → DMS:
- Degree: Integer part
- Minutes: Decimal part × 60 (integer)
- Seconds: Remainder × 60
DMS → Decimal degree:
- Formula: deg + min/60 + sec/3600
- Example: 45° 30' 54" = 45 + 30/60 + 54/3600
- Result: 45.515°
Comparison Table Decimal Degree ↔ DMS
| Decimal Degree | DMS Format | Description |
|---|---|---|
| 0° | 0° 0' 0" | Zero angle |
| 30° | 30° 0' 0" | 30-degree angle |
| 45.515° | 45° 30' 54" | Example with decimal places |
| 48.1351° | 48° 8' 6" | Latitude Munich |
| 90° | 90° 0' 0" | Right angle |
| 180° | 180° 0' 0" | Straight angle |
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