Decimal Degrees to DMS Calculator

How to Convert Decimal Degrees to DMS

Converting decimal degrees to degrees, minutes, and seconds (DMS) is a common task in geography, navigation, and mapping. Here's a comprehensive guide on how to perform this conversion:

Decimal Degrees to DMS Formula

The conversion from decimal degrees to DMS follows these steps:

1. \( \text{Degrees} = \lfloor \text{Decimal Degrees} \rfloor \) (floor function)
2. \( \text{Minutes} = \lfloor (\text{Decimal Degrees} - \text{Degrees}) \times 60 \rfloor \)
3. \( \text{Seconds} = ((\text{Decimal Degrees} - \text{Degrees}) \times 60 - \text{Minutes}) \times 60 \)

Where:

• Degrees is the integer part of the decimal degrees
• Minutes is the integer part of the remaining decimal multiplied by 60
• Seconds is the remaining decimal after minutes, multiplied by 60

Calculation Steps

1. Take the absolute value of the decimal degrees
2. Extract the integer part for degrees
3. Multiply the decimal part by 60 and extract the integer part for minutes
4. Multiply the remaining decimal by 60 for seconds
5. Determine the direction (N/S for latitude, E/W for longitude) based on the original sign

Example: Convert 40.7128° to DMS

1. Degrees: \( \lfloor 40.7128 \rfloor = 40° \)
2. Minutes: \( \lfloor (40.7128 - 40) \times 60 \rfloor = \lfloor 42.768 \rfloor = 42' \)
3. Seconds: \( (42.768 - 42) \times 60 = 46.08" \)
4. Result: 40° 42' 46.08" N

Visual Representation

A visual representation can help understand the concept better. Here's a diagram showing the conversion of 40.7128° to DMS:

This diagram illustrates how 40.7128° is broken down into 40° (blue), 42' (green), and 46.08" (red) in the DMS format.