DMS to Decimal Degrees Converter

What is DMS and Decimal Degrees?

Degrees, Minutes, Seconds (DMS) and Decimal Degrees are two different ways to express angular measurements, particularly in geography and astronomy. DMS divides a full circle (360°) into degrees (°), minutes ('), and seconds ("), while Decimal Degrees expresses the same angle as a single decimal number.

The Conversion Formula

To convert DMS to decimal degrees, we use this formula:

\[ \text{Decimal Degrees} = D + \frac{M}{60} + \frac{S}{3600} \]

Where:

• \(D\) = Degrees
• \(M\) = Minutes
• \(S\) = Seconds

Step-by-Step Conversion

1. Take the degree value as is.
2. Divide the minutes by 60 (since there are 60 minutes in a degree).
3. Divide the seconds by 3600 (since there are 3600 seconds in a degree).
4. Add these three numbers together.

Example Calculation

Let's convert 40° 26' 46" to decimal degrees:

\[ \begin{align*} \text{Decimal Degrees} &= 40 + \frac{26}{60} + \frac{46}{3600} \\ &= 40 + 0.4333333 + 0.0127778 \\ &\approx 40.4461111° \end{align*} \]

Visual Representation

This diagram shows the angle 40° 26' 46" represented as 40.4461111° on a circle.