Degrees Minutes Seconds Calculator
Instantly convert degrees minutes seconds with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
DD = D + M/60 + S/3600 | Radians = DD x PI/180
Converting DMS to decimal degrees sums the degrees plus minutes/60 plus seconds/3600. Converting to radians multiplies decimal degrees by pi/180. Gradians equal decimal degrees times 10/9. These conversions are reversible and exact.
Worked Examples
Example 1: Navigation Coordinate
Problem:Convert 45 degrees 30 minutes 15.5 seconds to decimal degrees.
Solution:DD = D + M/60 + S/3600\nDD = 45 + 30/60 + 15.5/3600\nDD = 45 + 0.5 + 0.004306\nDD = 45.504306 degrees\nRadians = 45.504306 x PI/180 = 0.794264 rad
Result:45 deg 30 min 15.5 sec = 45.504306 degrees = 0.794264 radians
Example 2: Decimal to DMS
Problem:Convert 73.985833 decimal degrees to DMS format.
Solution:Degrees = 73 (integer part)\nRemaining = 0.985833 x 60 = 59.15 minutes\nMinutes = 59\nSeconds = 0.15 x 60 = 9.0 seconds\nResult: 73 deg 59 min 9.0 sec
Result:73.985833 degrees = 73 deg 59 min 9.0 sec
Frequently Asked Questions
What are degrees, minutes, and seconds in angle measurement?
Degrees, minutes, and seconds (DMS) is a way of expressing angles where one full rotation equals 360 degrees. Each degree is divided into 60 minutes (also called arc-minutes), and each minute is divided into 60 seconds (arc-seconds). This system originated with the ancient Babylonians who used a base-60 number system. DMS is widely used in navigation, astronomy, surveying, and geographic coordinate systems to express latitude and longitude with high precision.
How do I convert DMS to decimal degrees?
To convert DMS to decimal degrees, add the degrees to the minutes divided by 60, plus the seconds divided by 3600. The formula is DD = D + M/60 + S/3600. For negative values (south latitude or west longitude), apply the negative sign to the final result. For example, 45 degrees 30 minutes 15.5 seconds becomes 45 + 30/60 + 15.5/3600 = 45 + 0.5 + 0.004306 = 45.504306 degrees.
What is the difference between radians and degrees?
Degrees divide a full circle into 360 equal parts, while radians use the ratio of arc length to radius. One full rotation equals 2 times pi radians (approximately 6.2832 radians). To convert degrees to radians, multiply by pi/180. Radians are the natural unit for calculus and physics because they simplify many formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. Most programming languages and scientific calculators use radians by default.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy