How this calculator works
Two directed bearing rays determine a location where they meet. A north-based bearing has direction (sin bearing, cos bearing) in east-north coordinates. To locate a landmark, rays start at the stations. To locate the observer, rays start at the known landmarks with reversed directions because the measured bearings point from the observer toward the landmarks. Offsets are added independently before solving. The model is planar, with no Earth curvature, refraction or measurement-error estimate.
Formula
For P+tU=Q+sV, det=Ux Vy-Uy Vx and t=((Qx-Px)Vy-(Qy-Py)Vx)/det. North bearing direction U=(sin(alpha), cos(alpha)).
Worked example
From stations (0,0) and (10,0), bearings 45 and 315 degrees meet at (5,5). Both station-to-landmark distances are sqrt(50), about 7.071067812 units.
Advertisement
Frequently asked questions
Can I enter latitude and longitude?
No. Project nearby positions into a suitable local east-north grid first. Raw geographic degrees are not equally scaled Cartesian distances.
Why reverse rays when locating myself?
Your measured bearings point toward the known landmarks. Looking back from each landmark toward you requires the opposite direction.
Why are almost parallel bearings unreliable?
Their intersection moves greatly under small angle changes. Determinants within 1e-12 of zero are rejected, and nearby cases can still be sensitive.