Overview: The DMS Coordinate Converter Tool is designed to seamlessly convert between Degrees, Minutes, Seconds (DMS) and decimal degree formats. This is essential for geographic coordinate systems, where DMS notation (using symbols °, ', ") is common. The tool operates on the principle: 1 degree = 60 minutes, and 1 minute = 60 seconds.

Understanding Degrees, Minutes, and Seconds (DMS)

We often describe time in hours and minutes for clarity. The same principle applies to geographic coordinates. While decimal degrees are precise, the DMS format often offers a more intuitive understanding of location. You can distinguish the components by their unique symbols: the degree symbol (°) for degrees, the single quote (') for minutes, and the double quote (") for seconds. This format is the cornerstone of the global geographic coordinate system.

How to Convert DMS to Decimal Degrees

The conversion relies on a simple relationship: one degree contains 60 minutes, and one minute contains 60 seconds. Therefore, one degree is equivalent to 3600 seconds. To convert coordinates from DMS to decimal degrees, apply this formula: 

Decimal degrees = Degrees + (Minutes / 60) + (Seconds / 3600)

Since a minute is 1/60th of a degree and a second is 1/3600th of a degree, you simply add these fractional parts to the whole number of degrees.

Practical Example

Let's convert 67°48'25" to decimal degrees. Plug the values into the formula: 

67 + (48 / 60) + (25 / 3600) = 67 + 0.8 + 0.00694 ≈ 67.80694°

Converting Decimal Degrees Back to DMS

Transforming decimal degrees into the DMS format involves a few steps. Follow this procedure:

  1. The integer part of the decimal degree is the degrees.
  2. Multiply the remaining decimal fraction by 60. The integer part of this result is the minutes.
  3. Multiply the new decimal remainder by 60 again. The result is the seconds.

Practical Example

Let's convert 47.392° to DMS. 

Degrees = 47° (integer part of 47.392)
Minutes = integer part of (0.392 × 60) = integer part of 23.52 = 23'
Seconds = 0.52 × 60 = 31.2"
Result: 47°23'31.2"

This process essentially separates the fractional part of a degree into minutes, and then the fractional part of a minute into seconds.

Summary of Key Formulas

DMS to Decimal:

Decimal = D + (M / 60) + (S / 3600)

Decimal to DMS:

D = integer part of Decimal
M = integer part of ((Decimal - D) × 60)
S = ((Decimal - D) × 60 - M) × 60