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Convert between decimal degrees and DMS format. Essential for GPS coordinates, navigation, and geographic applications.
DMS to Decimal:
decimal = degrees + (minutes / 60) + (seconds / 3600)
Decimal to DMS:
Degrees = integer part, Minutes = (decimal part × 60) integer, Seconds = (minutes decimal × 60)
Example: 45.5° = 45° 30' 0" (45 + 30/60 = 45.5)
| Decimal Degrees | DMS Format | Example |
|---|---|---|
| 0° | 0° 0' 0" | |
| 30.5° | 30° 30' 0" | |
| 45.75° | 45° 45' 0" | |
| 51.5074° | 51° 30' 26.64" | London, UK (lat) |
| 40.7128° | 40° 42' 46.08" | New York, USA (lat) |
| 35.6762° | 35° 40' 34.32" | Tokyo, Japan (lat) |
| -33.8688° | -33° 52' 7.68" | Sydney, Australia (lat) |
| 48.8566° | 48° 51' 23.76" | Paris, France (lat) |
| 55.7558° | 55° 45' 20.88" | Moscow, Russia (lat) |
| -23.5505° | -23° 33' 1.8" | São Paulo, Brazil (lat) |
| 90° | 90° 0' 0" |
DMS (Degrees, Minutes, Seconds) is a geographic coordinate system that expresses latitude and longitude using three components: degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. This system has been used for centuries in navigation and cartography, originating from the Babylonian base-60 number system.
Decimal degrees express coordinates as a single number (e.g., 45.5°), while DMS breaks it into three parts (45° 30' 0"). Decimal degrees are easier for calculations and computer processing, making them standard in GPS devices and mapping software. DMS is more traditional and still commonly used in navigation, surveying, and when communicating coordinates verbally.
Modern GPS systems can display coordinates in both formats. Aviation and maritime navigation often prefer DMS format for precision and tradition. Land surveying uses DMS for property boundaries and legal descriptions. Smartphone apps and online maps typically use decimal degrees for simplicity, but can convert to DMS when needed for compatibility with traditional navigation tools.
Take the integer part as degrees. Multiply the decimal part by 60 to get minutes. Take the integer minutes, then multiply the remaining decimal by 60 to get seconds. For example: 45.5° = 45° + (0.5 × 60)' = 45° 30' 0".
Use the formula: decimal = degrees + (minutes ÷ 60) + (seconds ÷ 3600). For example: 45° 30' 0" = 45 + (30 ÷ 60) + (0 ÷ 3600) = 45.5°. Remember to keep the negative sign for southern latitudes or western longitudes.
Use decimal degrees for most modern applications, including programming, data analysis, and online maps. Use DMS when working with traditional navigation tools, aviation charts, nautical charts, or when coordinates need to be communicated verbally. Most GPS devices can display both formats.
Latitude ranges from -90° to +90° (south to north of the equator). Longitude ranges from -180° to +180° (west to east of the prime meridian). In DMS format: latitude is 90° 0' 0" S to 90° 0' 0" N, and longitude is 180° 0' 0" W to 180° 0' 0" E.