Formula to Find Bearing or Heading angle between two points. Bearing or heading 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:
- 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
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
So as, β = atan2(X,Y) = atan2(0.05967668696, -0.00681261948)
β = 96.51°
This means, from Kansas City if we move in 96.51° bearing direction, we will reach St Louis.
Tool to find bearing between two lat lon points:
- Check out Advanced Bearing Angle calculator here.
latitude 1 :
longitude 1 :
latitude 2 :
longitude 2 :
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.