Bearing Calculator
About Bearing Calculator
Understanding Bearings
Bearings, a fundamental concept in navigation, originated in ancient civilizations and evolved through maritime exploration. From celestial navigation using the North Star to modern GPS systems, bearing calculations remain crucial for human exploration and navigation. Persian mathematician Al-Biruni's 11th-century work on spherical trigonometry revolutionized geographical coordinate determination and bearing calculations across Earth's curved surface.
During the Age of Exploration (15th-17th centuries), Portuguese navigators refined maritime bearing calculations, leading to more accurate ocean navigation. These methods evolved with improved instruments and understanding of magnetic variation.
Mathematical Foundation
θ = atan2(sin(Δλ)×cos(φ₂), cos(φ₁)×sin(φ₂) - sin(φ₁)×cos(φ₂)×cos(Δλ))
d = acos(sin(φ₁)×sin(φ₂) + cos(φ₁)×cos(φ₂)×cos(Δλ))×R
Δσ = atan2(√[(cos(φ₂)×sin(Δλ))² + (cos(φ₁)×sin(φ₂) - sin(φ₁)×cos(φ₂)×cos(Δλ))²], sin(φ₁)×sin(φ₂) + cos(φ₁)×cos(φ₂)×cos(Δλ))
Key Variables
- θ (theta): Initial bearing angle
- φ (phi): Latitude in radians
- λ (lambda): Longitude difference
- R: Earth's mean radius (6,371 km)
- d: Great circle distance
- Δσ: Angular distance on sphere
Important Notes
- All angles must be in radians
- Accounts for Earth's spherical shape
- Uses Haversine formula principles
- Considers great circle paths
Reference Systems
True Bearings
- References true north
- Uses 000° to 359° notation
- Essential for GPS systems
- Standard in aviation
Magnetic Bearings
- References magnetic north
- Includes declination
- Changes annually
- Used in basic navigation
Grid Bearings
- Based on map grid
- Uses grid north
- Varies by projection
- Used in land surveys
Cardinal Directions
Primary Points
- North (N): 000°
- East (E): 090°
- South (S): 180°
- West (W): 270°
Intercardinal Points
- Northeast (NE): 045°
- Southeast (SE): 135°
- Southwest (SW): 225°
- Northwest (NW): 315°
Tell us more, and we'll get back to you.
Contact Us