Degrees Minutes Seconds Calculator

Degrees, minutes, and seconds, commonly shortened to DMS, divide an angle into progressively smaller parts. One degree contains 60 minutes, and one minute contains 60 seconds. Decimal degrees express the same angle as a single decimal number. Both formats are widely used for geographic coordinates, surveying observations, navigation, astronomy, and mapping, but different devices and documents may prefer one format over the other. To convert DMS to decimal degrees, divide the minutes by 60 and the seconds by 3,600, then add both values to the whole degrees. A coordinate of 40 degrees, 42 minutes, and 51 seconds becomes 40.7141666667 decimal degrees before rounding. South and west coordinates are conventionally negative, while north and east coordinates are positive. The selected direction therefore determines the sign of the decimal result. To convert decimal degrees to DMS, begin with the absolute decimal magnitude. The whole-number portion supplies the degrees. Multiply the remaining fraction by 60; its whole-number portion supplies the minutes. Multiply the new remaining fraction by 60 to obtain seconds. The direction records the hemisphere and avoids ambiguity, especially when the input coordinate is displayed without a sign. Small floating-point differences may produce long seconds values, so the calculator presents seconds with practical precision. Latitude and longitude have different natural limits. Latitude ranges from 90 degrees south to 90 degrees north, while longitude ranges from 180 degrees west to 180 degrees east. This general angle converter accepts magnitudes through 180 degrees, so users should separately confirm that a latitude does not exceed 90 degrees. Minutes and seconds must each be at least zero and below 60; reaching 60 means that value should carry into the next larger unit. DMS is common on historical maps, land surveys, nautical references, and some GPS displays. Decimal degrees are convenient for geographic information systems, spreadsheets, web maps, and numerical calculations. Converting correctly is important because treating minutes or seconds as ordinary decimal fractions can move a location substantially. For instance, 30 minutes is half a degree, not 0.30 degree. Use enough precision for the intended task. A few decimal places may be adequate for a broad map, while surveying or field data may require more digits. The conversion itself is deterministic, but the accuracy of the location still depends on the original measurement. Retaining the direction and avoiding premature rounding helps preserve that source precision when coordinates move between systems.