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Convert Decimal Degrees to Degrees Minutes Seconds Calculator

Reviewed by Calculator Editorial Team

Converting decimal degrees to degrees, minutes, and seconds (DMS) is essential for navigation, surveying, and geographic coordinate systems. This calculator provides an accurate conversion and explains the process step-by-step.

How to Convert Decimal Degrees to DMS

The conversion process involves separating the decimal part of the coordinate into minutes and seconds. Here's how it works:

  1. Take the decimal part of the coordinate and multiply it by 60 to get the minutes.
  2. Take the decimal part of the minutes and multiply it by 60 to get the seconds.
  3. Combine the whole degrees, minutes, and seconds to form the DMS coordinate.

This method ensures precise conversion between the two coordinate systems used in different applications.

Conversion Formula

Degrees = floor(decimal degrees)
Minutes = floor((decimal degrees - Degrees) × 60)
Seconds = ((decimal degrees - Degrees) × 60 - Minutes) × 60

Where:

  • Degrees is the whole number part of the decimal degrees
  • Minutes is the whole number part of the remaining decimal after calculating degrees
  • Seconds is the remaining decimal after calculating degrees and minutes

Note: The formula assumes positive decimal degrees. For negative values, apply the same process to the absolute value and then reapply the sign.

Worked Examples

Example 1: Converting 45.75° to DMS

  1. Degrees = floor(45.75) = 45°
  2. Minutes = floor((45.75 - 45) × 60) = floor(0.75 × 60) = 45'
  3. Seconds = (0.75 × 60 - 45) × 60 = (45 - 45) × 60 = 0"

Result: 45°45'0"

Example 2: Converting -123.456° to DMS

  1. Degrees = floor(123.456) = 123° (with negative sign)
  2. Minutes = floor((123.456 - 123) × 60) = floor(0.456 × 60) = 27'
  3. Seconds = (0.456 × 60 - 27) × 60 ≈ 21.6"

Result: -123°27'21.6"

FAQ

Why convert decimal degrees to DMS?
DMS format is commonly used in navigation, surveying, and older mapping systems. It provides a more intuitive representation of geographic coordinates.
Is this conversion accurate for all decimal degrees?
Yes, the formula works for any valid decimal degree value, including negative values representing southern latitudes or western longitudes.
Can I convert DMS back to decimal degrees?
Yes, you can reverse the process by dividing minutes by 60, adding to degrees, then dividing seconds by 3600 and adding to the previous result.