Degrees Minutes Seconds Calculator
Instantly convert degrees minutes seconds with our free converter. See conversion tables, formulas, and step-by-step explanations.
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.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Is Degrees Minutes Seconds Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.