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How to Convert Degrees to Degree Minutes Seconds Calculator

Reviewed by Calculator Editorial Team

Converting degrees to degrees, minutes, and seconds (DMS) is a common requirement in navigation, astronomy, and cartography. This guide explains the process step-by-step and provides an interactive calculator to perform the conversion quickly.

What is Degree Minute Second?

The Degree Minute Second (DMS) format is an alternative way to represent angles or geographic coordinates. While decimal degrees are commonly used in digital systems, DMS provides a more precise and traditional representation that's familiar to navigators and surveyors.

In DMS format:

  • Degrees (º) represent the whole number part of the angle
  • Minutes (') represent 1/60th of a degree
  • Seconds (") represent 1/3600th of a degree

For example, 45.75 degrees in DMS would be written as 45º 45' 0".

How to Convert Degrees to DMS

Converting decimal degrees to DMS format involves these steps:

  1. Separate the whole number degrees from the decimal portion
  2. Multiply the decimal portion by 60 to get the minutes
  3. Separate the whole number minutes from the new decimal portion
  4. Multiply the remaining decimal by 60 to get the seconds

This process ensures you maintain the precise value of the original decimal degrees.

Conversion Formula

The mathematical formula for converting decimal degrees to DMS is:

Degrees = floor(decimal degrees)
Minutes = floor((decimal degrees - Degrees) × 60)
Seconds = (decimal degrees - Degrees - (Minutes / 60)) × 3600

Where "floor" means rounding down to the nearest whole number.

Example Conversion

Let's convert 36.875 degrees to DMS:

  1. Degrees = floor(36.875) = 36º
  2. Minutes = floor((36.875 - 36) × 60) = floor(0.875 × 60) = floor(52.5) = 52'
  3. Seconds = (36.875 - 36 - (52/60)) × 3600 ≈ (0.875 - 0.8667) × 3600 ≈ 0.0083 × 3600 ≈ 30"

The result is 36º 52' 30".

Common Uses

Converting degrees to DMS is particularly useful in these fields:

  • Navigation: GPS coordinates are often displayed in DMS format
  • Astronomy: Celestial coordinates use DMS notation
  • Cartography: Traditional maps often use DMS for coordinates
  • Surveying: Precise angle measurements require DMS format

FAQ

Why convert degrees to DMS?
DMS format is often preferred in traditional navigation and surveying because it provides more precise fractional values than decimal degrees.
Can I convert DMS back to decimal degrees?
Yes, you can reverse the process by converting each component back to decimal degrees: Degrees + (Minutes/60) + (Seconds/3600).
What's the difference between DMS and decimal degrees?
Decimal degrees use a single decimal number (e.g., 36.875º), while DMS breaks it into degrees, minutes, and seconds (e.g., 36º 52' 30").
When should I use DMS instead of decimal degrees?
Use DMS when working with traditional navigation tools, surveying equipment, or when a more precise fractional representation is needed.