Degrees to Minutes, Seconds Converter
Convert between decimal degrees and degrees, minutes, seconds (DMS) format or Degree Converter.
Decimal Degrees → DMS
DMS → Decimal Degrees
How Degrees, Minutes, Seconds (DMS) Work
Degrees, minutes, and seconds (DMS) is a system for expressing angles and geographic coordinates. One full circle is 360 degrees. Each degree is divided into 60 minutes (denoted by ′), and each minute is divided into 60 seconds (denoted by ″). This gives 3,600 seconds per degree. DMS notation is widely used in navigation, surveying, cartography, and astronomy. For example, the coordinates of the Statue of Liberty are approximately 40° 41′ 21″ N, 74° 2′ 40″ W.
DMS Conversion Formulas
Decimal Degrees to DMS: Degrees = integer part of the decimal. Minutes = integer part of (fractional part × 60). Seconds = remainder × 60. In formula form: d = floor(DD), m = floor((DD − d) × 60), s = ((DD − d) × 60 − m) × 60. DMS to Decimal Degrees: DD = d + m/60 + s/3600. For negative angles (south latitude or west longitude), apply the sign to the entire result.
Worked Example: Convert 45.5125° to DMS
Step 1: The whole number part is the degrees: 45°. Step 2: Take the decimal part: 0.5125. Multiply by 60: 0.5125 × 60 = 30.75. The whole number part is the minutes: 30′. Step 3: Take the remaining decimal: 0.75. Multiply by 60: 0.75 × 60 = 45. The seconds: 45″. Result: 45.5125° = 45° 30′ 45″. Reverse check: 45 + 30/60 + 45/3600 = 45 + 0.5 + 0.0125 = 45.5125° ✓.
Common Angle Conversions
0° = 0° 0′ 0″ · 30° = 30° 0′ 0″ · 45° = 45° 0′ 0″ · 45.5° = 45° 30′ 0″ · 60° = 60° 0′ 0″ · 90° = 90° 0′ 0″ · 120° = 120° 0′ 0″ · 180° = 180° 0′ 0″ · 270° = 270° 0′ 0″ · 360° = 360° 0′ 0″. GPS examples: 40.7128° N = 40° 42′ 46.08″ N (New York City) · 51.5074° N = 51° 30′ 26.64″ N (London) · 35.6762° N = 35° 40′ 34.32″ N (Tokyo).
Technical Details
DMS is a sexagesimal (base-60) subdivision system inherited from Babylonian mathematics. Minutes and seconds in angle measurement are distinct from minutes and seconds of time, though they share the same base-60 structure. Precision: 1 second of latitude equals approximately 30.87 meters on Earth's surface. 1 second of longitude varies with latitude — at the equator it is about 30.87 meters, decreasing to 0 at the poles. This converter handles negative angles for south latitudes and west longitudes, and displays seconds to 4 decimal places for sub-meter GPS accuracy.
Frequently Asked Questions
What is 90.5 degrees in DMS? 90° 30′ 0″. The 0.5 degree equals 30 minutes (0.5 × 60 = 30). How accurate is DMS notation? With seconds expressed to two decimal places, DMS can represent positions to within about 0.3 meters — sufficient for most surveying and navigation. Why are there 60 minutes in a degree? This convention comes from the ancient Babylonian base-60 (sexagesimal) number system, which was adopted by Greek astronomers and has been used ever since. What is the difference between decimal degrees and DMS? They represent the same angle in different formats. Decimal degrees (45.5125°) are easier for calculations, while DMS (45° 30′ 45″) is traditional in navigation and map reading. Can DMS values be negative? Yes. Negative values indicate south latitude or west longitude in geographic coordinates, or clockwise rotation in some engineering contexts.