Azimuth Calculator
Calculate bearing and distance between two geographical coordinates
📍 Starting Point
London, UK
Greenwich Mean Time origin
51.507°, -0.128°
Rio de Janeiro, Brazil
Christ the Redeemer statue
-22.907°, -43.173°
New York City, USA
The Big Apple
40.713°, -74.006°
Tokyo, Japan
Land of the Rising Sun
35.676°, 139.650°
Custom Starting Point
Enter your own coordinates
North: positive (+), South: negative (-)
East: positive (+), West: negative (-)
🎯 End Point
Sydney, Australia
Opera House and Harbor Bridge
-33.869°, 151.209°
Cape Town, South Africa
Table Mountain
-33.925°, 18.424°
Paris, France
City of Light
48.857°, 2.352°
Moscow, Russia
Red Square and Kremlin
55.756°, 37.618°
Custom End Point
Enter your own coordinates
North: positive (+), South: negative (-)
East: positive (+), West: negative (-)
📊 Calculation Results
Compass Direction
Point compass to Southwest
📍 Starting Point
Decimal: 51.507400°, -0.127800°
DMS: 51°30'26.6"N, 0°7'40.1"W
🎯 End Point
Decimal: -22.906800°, -43.172900°
DMS: 22°54'24.5"S, 43°10'22.4"W
Navigation Information
Great Circle Distance: 9277.42 km
Nautical Miles: 5009.41 nm
Initial Bearing: 219.26° from North
Travel Time (plane): ~10.3 hours
📐 Azimuth Formula
Azimuth Calculation
θ = atan2(x, y)
Where:
x = sin(Δλ) × cos(φ₂)
y = cos(φ₁) × sin(φ₂) - sin(φ₁) × cos(φ₂) × cos(Δλ)
Distance (Haversine)
d = 2R × arctan2(√a, √(1-a))
Where:
a = sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2)
Variables
φ = latitude, λ = longitude
R = Earth's radius (6,371 km)
θ = azimuth angle (0-360°)
🧭 Compass Directions
Azimuth: Angle measured clockwise from North
Bearing: Direction from one point to another
🎯 Applications
Satellite Dishes
Point antennas toward satellites for optimal signal
Navigation
Marine and aviation navigation systems
Astronomy
Locate celestial objects in the sky
Surveying
Land surveying and mapping applications
Understanding Azimuth and Bearing
What is Azimuth?
Azimuth is the angular measurement in a spherical coordinate system that represents the angle between a reference direction (usually North) and a line from the observer to a point of interest, projected onto a horizontal plane. It's always measured clockwise from North.
Key Characteristics
- 📐Range: 0° to 360° (or 0° to 359.999...°)
- ⬆️Reference: True North (0°/360°)
- 🔄Direction: Always measured clockwise
- 🌍Projection: Onto horizontal plane
Mathematical Foundation
Spherical Trigonometry
The azimuth calculation uses spherical trigonometry to account for Earth's curvature. The atan2 function ensures the result is in the correct quadrant.
Haversine Formula
Used to calculate the great-circle distance between two points on a sphere. This gives the shortest distance "as the crow flies."
Real-world Example: London to Rio de Janeiro has an azimuth of about 219°, meaning you'd head southwest from London. The great-circle distance is approximately 9,289 km.