GEOGRAPHY & CARTOGRAPHY CALCULATOR
Pathdestination Point
A precise tool.
What is the Pathdestination Point & How does it work?
When navigating across the Earth’s surface, the shortest path between two points follows a greatβcircle. Determining the endpoint of a journey that starts at a known latitudeβ―phi_1 and longitudeβ―lambda_1, proceeds along a constant bearingβ―theta for a distanceβ―d, requires converting the linear distance into an angular distance on the sphere.
The calculation first converts all angular quantities to radians, then applies the spherical trigonometry formulas above. After the destination latitudeβ―phi_2 and longitudeβ―lambda_2 are obtained in radians, they are converted back to degrees for presentation.
Because the Earth is not a perfect sphere, the result is an approximation that is accurate enough for most navigation and mapping tasks. Using a more precise ellipsoidal model would require additional corrections beyond the scope of this widget.
phi_2 = arcsinbigl(sinphi_1cosdelta + cosphi_1sindeltacosthetabigr)newline lambda_2 = lambda_1 + operatorname{atan2}bigl(sinthetasindeltacosphi_1, cosdelta – sinphi_1sinphi_2bigr)
Ξ΄ = d / R (angular distance), R = Earth radius, ΞΈ = bearing (rad), Ο, Ξ» = latitude/longitude (rad)
Parameters
Result
β
Frequently Asked Questions
How do I calculate the endpoint of a journey on Earth’s surface?
Use the formula with your starting latitude (Ο1), longitude (Ξ»1), constant bearing (ΞΈ), and distance (d) to find the destination point.
What is a great-circle path in navigation?
A great-circle path is the shortest route between two points on the Earth’s surface, following the curvature of the planet.
How do I convert distance to angular distance for this calculation?
Divide the linear distance by the Earth’s radius to get the angular distance in radians.
What is the formula for calculating Ο2 in this calculator?
Ο2 = arcsin(sin(Ο1)cos(Ξ΄) + cos(Ο1)sin(Ξ΄)cos(ΞΈ)).
How do I calculate Ξ»2 using the atan2 function?
Ξ»2 = Ξ»1 + atan2(sin(ΞΈ)sin(Ξ΄), cos(Ο1)cos(Ξ΄)).
Can this calculator handle different units of measurement?
Yes, ensure all inputs are in consistent units (e.g., degrees for angles and meters or nautical miles for distance).
What is the purpose of the atan2 function in this calculation?
The atan2 function calculates the angle from the positive x-axis to a point, which helps determine the correct longitude (Ξ»2) considering the bearing and angular distance.
Results are for informational purposes only and do not constitute professional advice.