DMS to Decimal Degrees Calculator

How to Convert DMS to Decimal Degrees

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

DMS to Decimal Degrees Formula

The formula to convert DMS to decimal degrees is:

\[ \text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600} \]

Where:

• Degrees is the whole number of degrees
• Minutes is the whole number of arc-minutes
• Seconds is the number of arc-seconds (can include decimals)

Calculation Steps

1. Start with the degrees value
2. Divide the minutes by 60 and add to the degrees
3. Divide the seconds by 3600 and add to the result
4. If the direction is South (S) or West (W), make the final result negative

Example: Convert 40° 42' 46.08" N to Decimal Degrees

1. Start with 40°
2. Add 42' ÷ 60 = 0.7°
3. Add 46.08" ÷ 3600 = 0.0128°
4. Sum up: 40 + 0.7 + 0.0128 = 40.7128°
5. Direction is N (positive), so the final result is 40.7128°

Visual Representation

A visual representation can help understand the concept better. Here's a diagram showing the conversion of 40° 42' 46.08" N to decimal degrees:

This diagram illustrates how 40° 42' 46.08" N is represented as 40.7128° in decimal degrees format.