Distance & Bearing Calculator - GPS Coordinates

Point 1 (Start)

Latitude

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Longitude

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Point 2 (End)

Latitude

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Longitude

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Results

What is Distance & Bearing Calculation?

Distance and bearing calculations determine the shortest path and direction between two points on Earth's surface. The distance is calculated using the haversine formula (great-circle distance), which accounts for Earth's spherical shape. Bearing indicates the direction from one point to another, measured in degrees clockwise from north.

These calculations are essential for navigation, aviation, maritime operations, hiking, and any application involving movement between geographic locations. The results provide comprehensive information for route planning and navigation.

Key concepts:

• Great-Circle Distance: The shortest distance between two points on a sphere's surface, following a great circle arc.
• Initial Bearing (Forward Azimuth): The compass direction at the starting point toward the destination.
• Final Bearing (Back Azimuth): The compass direction when arriving at the destination.
• Midpoint: The geographic center point along the great-circle path between the two locations.

Understanding these measurements is crucial for navigation planning, whether you're piloting an aircraft, sailing a boat, planning a road trip, or analyzing geographic data.

How to Calculate Distance and Bearing

Distance and bearing calculations use spherical trigonometry formulas. The haversine formula calculates distance, while bearing is calculated using arctangent of the coordinate differences.

Distance Formula (Haversine):

Initial Bearing Formula:

Where:

• d = great-circle distance
• r = Earth's radius (6,371 km or 3,959 miles)
• φ₁, φ₂ = latitude of point 1 and point 2 (in radians)
• Δφ = difference in latitude
• Δλ = difference in longitude
• θ = bearing angle (converted from radians to degrees)

The initial bearing differs from the final bearing due to Earth's curvature. On a sphere, a straight path (great circle) continuously changes direction relative to north, except when traveling due north/south or along the equator.

Understanding Bearing Measurements

Bearing is measured in degrees clockwise from true north:

• 0° / 360° = North
• 90° = East
• 180° = South
• 270° = West

For example, a bearing of 45° means northeast, while 225° means southwest. Initial and final bearings differ because the shortest path on a sphere is not a straight line on a flat map—it's a curve on a globe.

Practical Applications

Distance and bearing calculations are used in:

• Aviation: Flight planning, navigation, fuel calculations
• Maritime: Ship routing, coastal navigation, offshore operations
• Land Navigation: Hiking, orienteering, search and rescue
• Logistics: Delivery route optimization, transportation planning
• GIS & Mapping: Spatial analysis, proximity calculations, geographic research
• Mobile Apps: Location-based services, navigation apps, geocaching

Distance Conversion Examples

Common distance conversions:

• 1 kilometer = 0.621371 miles = 0.539957 nautical miles
• 1 mile = 1.60934 kilometers = 5,280 feet
• 1 nautical mile = 1.852 kilometers = 1.15078 miles

Nautical miles are commonly used in aviation and maritime navigation because one nautical mile equals one minute of latitude, making chart navigation simpler.