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Convert Angles to Degrees Minutes and Seconds Calculator

Reviewed by Calculator Editorial Team

This calculator converts angles between decimal degrees and degrees-minutes-seconds (DMS) format. Whether you're working with geographic coordinates, astronomy, or surveying, understanding how to convert between these formats is essential.

What is Degrees-Minutes-Seconds (DMS) Format?

The degrees-minutes-seconds (DMS) format is an alternative way to represent angles, commonly used in navigation, cartography, and astronomy. It breaks down an angle into three parts:

  • Degrees (°): The whole number part of the angle (0-360°)
  • Minutes ('): The fractional part of the degree (0-59')
  • Seconds ("): The fractional part of the minute (0-59")

For example, 45.75° in decimal degrees would be written as 45°45' in DMS format. The DMS format is particularly useful for precise measurements and historical documents.

Conversion Formulas

Decimal Degrees to DMS

To convert decimal degrees to DMS:

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

DMS to Decimal Degrees

To convert DMS to decimal degrees:

  1. Divide the minutes by 60 and add to the degrees
  2. Divide the seconds by 3600 (60 × 60) and add to the previous result
decimalDegrees = Degrees + (Minutes / 60) + (Seconds / 3600)

Note: These formulas assume positive angles. For negative angles (south or west coordinates), the same formulas apply but the degrees value should be negative.

How to Use This Calculator

Using the calculator is simple:

  1. Enter your angle in either decimal degrees or DMS format
  2. Click the "Convert" button to see the result
  3. Use the "Reset" button to clear the form

The calculator will automatically convert between formats and display the result in the other format. You can also view a visual representation of the angle conversion.

Conversion Examples

Example 1: Decimal Degrees to DMS

Convert 37.45° to DMS:

  1. Degrees = floor(37.45) = 37°
  2. Minutes = floor((37.45 - 37) × 60) = floor(0.45 × 60) = 27'
  3. Seconds = (0.45 × 60 - 27) × 60 = (27 - 27) × 60 = 0"

Result: 37°27'0"

Example 2: DMS to Decimal Degrees

Convert 45°30'15" to decimal degrees:

  1. Degrees = 45
  2. Minutes = 30
  3. Seconds = 15
  4. decimalDegrees = 45 + (30 / 60) + (15 / 3600) = 45 + 0.5 + 0.004166... ≈ 45.504166°

Result: 45.504166°

Decimal Degrees DMS Equivalent
12.3456° 12°20'44.2"
56.789° 56°47'20.4"
90.0° 90°0'0"

FAQ

What is the difference between decimal degrees and DMS?
Decimal degrees represent angles as a single decimal number (e.g., 37.45°), while DMS format breaks the angle into degrees, minutes, and seconds (e.g., 37°27'0"). DMS is often used in navigation and cartography for precise measurements.
When should I use decimal degrees vs. DMS?
Decimal degrees are generally used in scientific calculations and computer systems, while DMS is more common in traditional navigation and surveying. Choose the format that best fits your application.
Can I convert negative angles with this calculator?
Yes, the calculator handles both positive and negative angles. Negative angles are typically used to represent south or west coordinates.
Is there a difference between DMS and DM?
Yes, DMS includes seconds (e.g., 37°27'0"), while DM (degrees-minutes) omits the seconds (e.g., 37°27'). This calculator supports both formats.
How precise are the conversions?
The conversions are precise to six decimal places, which is sufficient for most applications. For extremely precise measurements, additional decimal places may be needed.