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Degrees to Degree Minutes Seconds Calculator

Reviewed by Calculator Editorial Team

Convert decimal degrees to degrees, minutes, and seconds with our precise calculator. This tool is essential for astronomy, navigation, and cartography where angular measurements are critical. Learn how to perform the conversion manually and understand the practical applications of this format.

How to Use This Calculator

Enter the decimal degree value you want to convert in the input field. The calculator will automatically display the equivalent degrees, minutes, and seconds. You can also choose to display the result with or without direction indicators (N, S, E, W).

Tip

For precise measurements, ensure your decimal degree input has at least 4 decimal places. This provides enough precision for most applications.

Conversion Formula

The conversion from decimal degrees to degrees, minutes, and seconds follows these steps:

  1. Take the integer part of the decimal degree as the degree value.
  2. Multiply the remaining decimal by 60 to get the minutes.
  3. Take the integer part of the minutes as the minute value.
  4. Multiply the remaining decimal by 60 to get the seconds.
Degrees = floor(decimal degrees) Minutes = floor((decimal degrees - Degrees) × 60) Seconds = (decimal degrees - Degrees - (Minutes / 60)) × 3600

Example Calculation

Let's convert 45.7654° to degrees, minutes, and seconds:

  1. Degrees = floor(45.7654) = 45°
  2. Minutes = floor((45.7654 - 45) × 60) = floor(0.7654 × 60) = 45.924 minutes
  3. Take the integer part: 45'
  4. Seconds = (0.924 × 60) ≈ 55.44 seconds

The final result is 45° 45' 55.44".

Decimal Degrees Degrees Minutes Seconds
45.7654° 45° 45' 55.44"

Common Uses

Degrees, minutes, and seconds format is commonly used in:

  • Astronomy for celestial coordinates
  • Navigation and cartography
  • Surveying and land measurement
  • Historical documents and maps

Note

In modern applications, decimal degrees are often preferred for calculations, but the DMS format remains important for precise documentation and historical records.

FAQ

Why convert decimal degrees to DMS?

DMS format is more intuitive for human reading and is required for many traditional maps, charts, and documentation standards.

How accurate is this conversion?

The calculator provides results accurate to the millisecond level, which is sufficient for most practical applications.

Can I convert DMS back to decimal degrees?

Yes, our sister calculator performs the reverse conversion with equal precision.