# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Calculate new coordinates given bearing and distance?
From: Geoffrey Kolbe
Date: 2015 Nov 26, 14:27 +0000
Hello Sam

Here are some direct formulae for you.

Lat1 and Long1 are your start latitude and longitude.
Lat2 and Long2 are the new coordinates at the given bearing and distance
Diff will be the difference between Long1 and Long2
Dist will be the distance in nautical miles. A nautical mile is equivalent to one minute of arc on a Great Circle, so this is converted to degrees in the formulae by dividing by 60

Sin(Lat2) = Cos(Dist/60) Sin(Lat1) + Sin(Dist/60) Cos(Lat1) Cos(Bearing)

Sin(Diff) = Sin(Bearing) Sin(Dist/60) / Cos(Lat2)

Long2 = Long1 + Diff

Caveat

I do not have my scientific calculator with me, so I cannot test these formulae. As General Norman Schwarzkopf once wisely remarked, "If it has not been tested, it does not work."

Geoffey Kolbe

On Thu, Nov 26, 2015 at 1:00 AM, Samuel L wrote:

These things are all fine and well but does anyone have a demonstratable method for solving the problem mathematically and can explain it directly and not abstractly?

Sam

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