Calculate Latitude and Longitude

Navigation Formulas:

\[ \Delta\varphi = \arcsin(\sin\Delta\sigma \sin\varphi_1 + \cos\Delta\sigma \cos\varphi_1 \cos\varphi_2) \] \[ \lambda = \lambda_1 + \arctan2(\sin\Delta\lambda \cos\varphi_2, \cos\Delta\sigma \sin\varphi_1 - \sin\Delta\sigma \cos\varphi_1 \cos\varphi_2) \]

Start Latitude (φ1):

degrees

Start Longitude (λ1):

degrees

Bearing:

degrees

Distance:

New Latitude:

New Longitude:

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1. What is Latitude and Longitude Calculation?

The latitude and longitude calculation uses spherical trigonometry and the haversine formula to determine new coordinates based on starting position, bearing, and distance. This is essential for navigation, GPS systems, and geographic applications.

2. How Does the Calculator Work?

The calculator uses navigation formulas:

Where:

\( \varphi_1 \) — Starting latitude in radians
\( \lambda_1 \) — Starting longitude in radians
\( \Delta\sigma \) — Central angle (angular distance)
\( \Delta\lambda \) — Longitude difference in radians
Earth radius = 6371 km

Explanation: The formulas calculate new coordinates by projecting a point along a great circle path defined by bearing and distance from the starting position.

3. Importance of Navigation Formulas

Details: Accurate coordinate calculation is crucial for navigation systems, mapping applications, GPS technology, aviation, maritime navigation, and geographic information systems (GIS).

4. Using the Calculator

Tips: Enter starting latitude (-90 to 90°), starting longitude (-180 to 180°), bearing (0-360°), and distance in kilometers. All values must be valid and within specified ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is the haversine formula?
A: The haversine formula calculates great-circle distances between two points on a sphere given their longitudes and latitudes.

Q2: How accurate is this calculation?
A: Very accurate for most practical purposes, assuming a spherical Earth model. For higher precision, ellipsoidal models like WGS84 are used.

Q3: What is bearing in navigation?
A: Bearing is the horizontal angle between the direction of an object and another object, or between it and true north, measured clockwise from north.

Q4: Can I use different distance units?
A: The calculator uses kilometers. For other units, convert to kilometers first (1 mile = 1.60934 km, 1 nautical mile = 1.852 km).

Q5: What applications use these calculations?
A: GPS navigation, aviation, maritime navigation, surveying, mapping software, and location-based services all rely on these fundamental geographic calculations.