Cal11 calculator
Search calculator...

Change Degrees to Minutes and Seconds Calculator

Reviewed by Calculator Editorial Team

This calculator converts decimal degrees to degrees, minutes, and seconds (DMS) format. The conversion is useful in navigation, astronomy, and cartography where precise angular measurements are required.

How to Convert Degrees to Minutes and Seconds

The conversion process involves breaking down the decimal portion of the degree measurement into minutes and seconds. Here's a step-by-step guide:

  1. Identify the whole number of degrees.
  2. Multiply the decimal portion of the degree by 60 to get the minutes.
  3. Multiply the decimal portion of the minutes by 60 to get the seconds.
  4. Combine the degrees, minutes, and seconds in the format: degrees°minutes'seconds".

For example, converting 45.75 degrees:

  • Degrees: 45
  • Minutes: 0.75 × 60 = 45
  • Seconds: 0.75 × 60 = 45 (but since we've already used the decimal, we take the remaining decimal)
  • Final DMS: 45°45'45"

Conversion Formula

Formula

To convert decimal degrees (D) to degrees, minutes, and seconds (DMS):

  1. Degrees = floor(D)
  2. Minutes = floor((D - Degrees) × 60)
  3. Seconds = (D - Degrees - (Minutes / 60)) × 3600

The formula accounts for the fact that each degree is divided into 60 minutes, and each minute is divided into 60 seconds. The floor function ensures we get whole numbers for degrees and minutes.

Worked Examples

Example 1: Converting 30.5 degrees

  1. Degrees = floor(30.5) = 30
  2. Minutes = floor((30.5 - 30) × 60) = floor(3) = 3
  3. Seconds = (30.5 - 30 - (3 / 60)) × 3600 ≈ 0
  4. Result: 30°3'0"

Example 2: Converting 123.75 degrees

  1. Degrees = floor(123.75) = 123
  2. Minutes = floor((123.75 - 123) × 60) = floor(45) = 45
  3. Seconds = (123.75 - 123 - (45 / 60)) × 3600 ≈ 0
  4. Result: 123°45'0"

Example 3: Converting 45.75 degrees

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

Frequently Asked Questions

Why convert degrees to minutes and seconds?

Degrees, minutes, and seconds (DMS) format is commonly used in navigation, astronomy, and cartography for precise angular measurements. It provides a more detailed representation of angles compared to decimal degrees.

How accurate is this conversion?

This calculator provides precise conversions using standard mathematical formulas. The accuracy depends on the precision of the input decimal degrees.

Can I convert minutes and seconds back to decimal degrees?

Yes, you can reverse the process by converting DMS to decimal degrees using the formula: Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600).

What are the practical applications of DMS format?

DMS format is widely used in GPS coordinates, surveying, and navigation systems where precise angular measurements are required. It's also used in astronomy for celestial coordinates.