Great Circle Calculator
Calculate shortest distance and bearing between two points on a sphere
Calculate Great Circle Distance
Point 1 Coordinates
Range: -90° to +90° (S to N)
Range: -180° to +180° (W to E)
Point 2 Coordinates
Range: -90° to +90° (S to N)
Range: -180° to +180° (W to E)
Calculation Settings
Great Circle Results
Haversine Formula: d = 2r × arcsin(√(sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2)))
Coordinates: Point 1: (33.9425°, -118.4081°), Point 2: (51.47°, -0.4543°)
Radius: 6371.0 km
Distance Analysis
Example Calculation
LAX to LHR Flight Route
Los Angeles (LAX): 33.9425°N, 118.4081°W
London Heathrow (LHR): 51.4700°N, 0.4543°W
Great Circle Distance: ~8,760 km (5,440 miles)
Initial Bearing: ~38° (NE)
Why Great Circles Matter
• Airlines use great circle routes to minimize fuel consumption
• Flight paths appear curved on flat maps but are straight in 3D
• Can save hundreds of kilometers compared to straight-line map routes
• Essential for navigation, GPS systems, and satellite communications
Major City Coordinates
Distance Formulas
Haversine Formula
Most accurate for all distances
Law of Cosines
Good for short distances
Vincenty's Formula
Most accurate for ellipsoids
Bearing
Direction from point to point
Understanding Great Circles
What is a Great Circle?
A great circle is the shortest distance between two points on the surface of a sphere. It's formed by the intersection of the sphere with a plane that passes through the center of the sphere. This creates the largest possible circle that can be drawn on the sphere.
Why Do Flight Paths Look Curved?
- •Maps project 3D Earth onto 2D surfaces, causing distortion
- •Great circle routes appear curved on flat maps
- •These "curved" paths are actually straight in 3D space
- •Airlines save fuel by following great circle routes
Mathematical Formulas
Haversine Formula:
d = 2r × arcsin(√(sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2)))
Initial Bearing:
θ = atan2(sin(Δλ) × cos(φ₂), cos(φ₁) × sin(φ₂) - sin(φ₁) × cos(φ₂) × cos(Δλ))
- d: Distance between points
- r: Radius of the sphere
- φ₁, φ₂: Latitude of point 1 and 2
- Δφ, Δλ: Difference in latitude and longitude
- θ: Bearing angle