Formula to Find Bearing or Heading angle between two points: Latitude Longitude

Formula to Find Bearing or Heading angle between two points. Bearing or heading angle is used to define navigation generally in the field of aircraft or marine or Vehicle navigation or while working for land surveying. So what’s the heading or bearing? How we can find bearing between the two points on earth, with the formula? Or How we can find the other point, when one point, actual traveled distance and bearing is given? Let us discuss all this points, followed with the example and experiment with the tool for calculating bearing provided in the post.

Bearing can be defined as direction or an angle, between the north-south line of earth or meridian and the line connecting the target and the reference point. While Heading is an angle or direction where you are currently navigating in.  This means to reach a particular destination you need to adjust your heading direction with the bearing. Generally a ‘compass’ is an instrument, which gives you the direction information for navigation. You must refer Haversine distance formula before going through this post.

Calculating Bearing or Heading angle between two points:

So if you are from GIS field or dealing with GIS application, you should know bearing and how to calculate bearing with formula. Let us look on formula and tool for bearing:

• Let ‘R’ be the radius of Earth,
• L’ be the longitude,
• ‘θ’ be latitude,
• β‘ be Bearing.

Denote point A and B as two different points, where ‘La’ is point A longitude and ‘θa’ is point A latitude, similarly assume for point B. Bearing would be measured from North direction i.e 0° bearing means North, 90° bearing is East, 180° bearing is measured to be South, and 270° to be West.

Note: If bearing is denoted with +ve or –ve initials whose values lies between 0° to 180°, then –ve is denoted for South and West sides.

Formula to find Bearing, when two different points latitude, longitude is given:

Bearing from point A to B, can be calculated as,

β = atan2(X,Y),

where, X and Y are two quantities and can be calculated as:

X = cos θb * sin ∆L

Y = cos θa * sin θb – sin θa * cos θb * cos ∆L

Lets us take an example to calculate bearing between the two different points with the formula:

• Kansas City: 39.099912, -94.581213
• St Louis: 38.627089, -90.200203

So X and Y can be calculated as,

X =  cos(38.627089) * sin(4.38101)

X  = 0.05967668696

And

Y = cos(39.099912) * sin(38.627089) – sin(39.099912) * cos(38.627089) * cos(4.38101)

Y = 0.77604737571 * 0.62424902378 – 0.6306746155 * 0.78122541965 * 0.99707812506

Y = -0.00681261948

***Convert θ into radians***

So as, β = atan2(X,Y) = atan2(0.05967668696, -0.00681261948) = 1.684463062558 radians

convert it into degree

β = 96.51°

This means, from Kansas City if we move in 96.51° bearing direction, we will reach St Louis.

You can also check video explanation of bearing angle.

Tool to find bearing angle between two lat lon points:

Check out the following IGISMap tools to work with Bearing Angle

IGISMap Bearing Angle Tool

IGISMap is a GIS based web platform providing multiple GIS applications that are most important in the field of geospatial analytics. The peculiarity of IGISMAP in the GIS Industry is its UI/UX that helps the user to perform effortless geospatial operations.

Bearing Angle tool of IGISMap can be used to create geospatial path based on bearing angle, distance and location. A path will be one or more straight lines connected between points plotted in order. User can plot required locations by simply clicking on the map or by entering address or coordinates. The path created in Bearing Angle will be available as GIS layer in the IGISMap. This GIS layer can be downloaded as GIS data in any format such as Shapefile, GeoJSON, CSV or KML.

Check https://map.igismap.com/bearing-angle to open Bearing Angle

Formula to find a lat lon point, when bearing, distance and another lat lon is given

Let us assume a condition, where you want to find out the where will an Airplane will land up, if you have following details of that Airplane, i.e actual distance it will travel, the bearing and the starting point (lat,lon)?

• Let first point latitude be la1,
• longitude as lo1,
• d be distance,
• R as radius of Earth,
• Ad be the angular distance i.e d/R and
• θ be the bearing,

Here is the formula to find the second point, when first point, bearing and distance is known:

• latitude of second point = la2 =  asin(sin la1 * cos Ad  + cos la1 * sin Ad * cos θ), and
• longitude  of second point = lo2 = lo1 + atan2(sin θ * sin Ad * cos la1 , cos Ad – sin la1 * sin la2)

You may find both the tool on separate page, with Google map working on it: (It will be update in 2 days, please visit us again)

• Tool to Find Bearing, when two points are given
• Tool to find other point, when bearing, distance and one of the point is given.

I hope this article will definitely help you, to find the bearing or heading. You are free to share more data related to bearing or any thing that you uses to calculate bearing and how you use navigation with bearing.

If you find anything difficulty to understand the bearing calculation, you may comment below, so that we will discuss further on finding bearing or heading angle.

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