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Convert Decimal Degrees to Dms Calculator

Reviewed by Calculator Editorial Team

Converting decimal degrees to degrees, minutes, and seconds (DMS) is essential for precise geographic coordinates, navigation, and mapping applications. This calculator provides an accurate conversion and explains the process in detail.

What is DMS format?

Degrees, minutes, and seconds (DMS) is an alternative format for representing geographic coordinates and angles. Unlike decimal degrees, which express values as a single decimal number, DMS breaks coordinates into three components:

  • Degrees (º) - The whole number part of the coordinate (0-360 for longitude, 0-90 for latitude)
  • Minutes (') - The fractional part of the degree, divided into 60 equal parts (0-59)
  • Seconds (") - The fractional part of the minute, divided into 60 equal parts (0-59.999...)

DMS format is commonly used in older navigation systems, surveying, and some mapping applications. It provides a more precise representation of small angular differences compared to decimal degrees.

How to convert decimal degrees to DMS

The conversion process involves separating the whole number degrees from the decimal portion, then converting the remaining decimal to minutes and seconds. Here's the step-by-step method:

  1. Identify the whole number degrees (the integer part of the decimal degree)
  2. Multiply the decimal portion by 60 to get the minutes
  3. Take the decimal portion of the minutes and multiply by 60 to get the seconds
  4. Round the seconds to an appropriate number of decimal places

Note: The direction (N/S for latitude, E/W for longitude) is not part of the conversion process and must be handled separately.

Conversion formula

Degrees: degrees = floor(decimal_degrees)

Minutes: minutes = floor((decimal_degrees - degrees) × 60)

Seconds: seconds = (decimal_degrees - degrees - minutes/60) × 3600

The formula works for both positive and negative decimal degree values. For latitude, positive values are north and negative are south. For longitude, positive values are east and negative are west.

Examples

Example 1: Converting 45.75° to DMS

  1. Degrees: floor(45.75) = 45°
  2. Minutes: (45.75 - 45) × 60 = 45'
  3. Seconds: (45.75 - 45 - 45/60) × 3600 = 0"
  4. Result: 45°45'0"

Example 2: Converting -123.456° to DMS

  1. Degrees: floor(-123.456) = -123°
  2. Minutes: (-123.456 + 123) × 60 = 27'
  3. Seconds: (-123.456 + 123 + 27/60) × 3600 ≈ 21.6"
  4. Result: -123°27'21.6"

FAQ

Why would I need to convert decimal degrees to DMS?

DMS format is often required for older navigation systems, surveying equipment, and some mapping applications that don't support decimal degrees. It provides a more precise representation of small angular differences.

How accurate is this conversion?

The calculator uses standard mathematical conversion formulas and provides results accurate to the number of decimal places you specify. For most practical purposes, this is more than sufficient.

Can I convert DMS back to decimal degrees?

Yes, the reverse conversion is straightforward. The formula is: decimal_degrees = degrees + (minutes/60) + (seconds/3600).

What's the difference between DMS and decimal degrees?

Decimal degrees express coordinates as a single decimal number (e.g., 45.75°), while DMS breaks them into degrees, minutes, and seconds (e.g., 45°45'0"). DMS is often used in older systems and provides more precision for small angles.