Latitude Longitude

Overview

Engineering reference data for Latitude Longitude in mathematics.

Key Formulas

Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Roots of ax² + bx + c = 0.

Pythagorean Theorem

$c^2 = a^2 + b^2$

Right triangle relationship.

Circle Area

$A = \pi r^2$

Area of a circle.

Logarithm

$\log_b(x) = \frac{\ln(x)}{\ln(b)}$

Change of base formula.

Variables

Definitions

• Latitude is the angle formed between the equatorial plane and a line drawn from the point to the center of the Earth. Its values range from -90° (South Pole) to +90° (North Pole), with 0° at the Equator.
• Longitude is the angle between the half-plane passing through the axis of the Earth and the Prime Meridian (Greenwich) and the half-plane passing through the axis and the point. Its values range from -180° (West) to +180° (East).

Conversion Formula

The formula to convert a coordinate given in Degrees (°), Minutes ('), and Seconds (") to Decimal Degrees (DD) is:

$$\text{DD} = \text{Degrees} + \left(\frac{\text{Minutes}}{60}\right) + \left(\frac{\text{Seconds}}{3600}\right)$$

Note: For coordinates in the Southern (S) or Western (W) hemispheres, the decimal degree value is negative.

Practical Examples

The following examples demonstrate the conversion process:

1. DMS to Decimal Degrees:

   • Input: Latitude 63° 30' 22.1178" N, Longitude 9° 12' 3.276" E
   • Calculation: 63 + (30/60) + (22.1178/3600) ≈ 63.506144
   • Result: *Latitude: 63.506144, Longitude: 9.20091

2. Decimal Degrees to DMS:

   • Input: Latitude 63.506144, Longitude 9.20091
   • Process:
     • Degrees: floor(63.506144) = 63°
     • Remaining minutes: (63.506144 - 63) * 60 = 30.36864
     • Minutes: floor(30.36864) = 30'
     • Remaining seconds: (30.36864 - 30) * 3600 ≈ 132.71" (or 22.1178" as per the precise input)
   • Result: Latitude: 63° 30' 22.1178" N, Longitude: 9° 12' 3.276" E

References

• Original Source