Point of Intersection from Two Bearings

Given two bearings of points X and Y whose locations are known, this form calculates the latitude and longitude of the point of intersection Z where both bearings were measured from.

Rule #1: Remember to convert from magnetic bearings to true bearings, i.e., add any eastern deviation or subtract any western deviation before inputting the bearings.

Rule #2: All arguments are in decimal degrees, with north latitude and west longitude being positive.

       Bearing of X: 
Latitude of X:
Longitude of X:
Bearing of Y:
Latitude of Y:
Longitude of Y:

Latitude of Z:
Longitude of Z:
Distance from Z->X:
Distance from Z->Y:

The example button inputs values from the original case that caused me to consider this problem. I was in my boat in Rosario Strait (San Juan Islands of Washington State) and took two bearings moments apart of Mount Baker (10785') and Mount Rainier (14441'). I wanted to know where I was from the known location of these two magnificient mountains.

So, in this example, point X is Mt. Baker (latitude N48°46'39", longitude W121°48'43") and I measured it at 50° from magnetic north. The deviation here is 18°47' East, so I added this to 50° to get my first bearing. Point Y is Mt. Rainier (latitude N46°51'10", longitude W121°45'31") and I measured it at 140° from north. I added the same correction for magnetic deviation to obtain its true bearing.

My best guess at the position where I took these measurements is N48°30.647' and W122°45.082'. This program calculates N48°32.0' and W122°44.8', for an error of 1.37 nmi, not too bad. I measured my bearings with the compass that is built into a pair of Fujinon 7x50 binoculars. I wonder if the elevation of these mountains should be included in this calculation for better accuracy?

The formulas for this are from Ed Williams' Aviation Formulary, to whom many thanks!

View the HTML source code to this page to see the embedded JavaScript code for the formulas used.

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Created:   5 Aug 2003  
Modified:  5 Aug 2003