Degrees to Degrees, Minutes, Seconds (DMS) Converter

What is DMS?

Degrees, Minutes, Seconds (DMS) is a sexagesimal system used to express angular measurements, particularly in geography and astronomy. It divides a full circle (360°) into degrees (°), minutes ('), and seconds (").

The Conversion Formula

To convert decimal degrees to DMS, we use these formulas:

\[ \begin{align} D &= \lfloor \text{decimal degrees} \rfloor \\ M &= \lfloor (\text{decimal degrees} - D) \times 60 \rfloor \\ S &= ((\text{decimal degrees} - D - M/60) \times 3600) \end{align} \]

Where:

• \(D\) = Degrees
• \(M\) = Minutes
• \(S\) = Seconds
• \(\lfloor \rfloor\) represents the floor function (rounding down to the nearest integer)

Step-by-Step Conversion

1. Extract the whole number part for degrees: \[D = \lfloor \text{decimal degrees} \rfloor\]
2. Multiply the fractional part by 60 and extract the whole number for minutes: \[M = \lfloor (\text{decimal degrees} - D) \times 60 \rfloor\]
3. Multiply the remaining fractional part by 60 for seconds: \[S = ((\text{decimal degrees} - D - M/60) \times 3600)\]

Example Calculation

Let's convert 12.32° to DMS:

1. \(D = \lfloor 12.32 \rfloor = 12°\)
2. \(M = \lfloor (12.32 - 12) \times 60 \rfloor = \lfloor 19.2 \rfloor = 19'\)
3. \(S = ((12.32 - 12 - 19/60) \times 3600) = 12"\)

Therefore, 12.32° = 12° 19' 12"

Visual Representation

This diagram shows the angle 12.32° represented as 12° 19' 12" on a circle.