Bearing Angle Calculator

Calculator Inputs

Start X Coordinate

Start Y Coordinate

End X Coordinate

End Y Coordinate

Current Heading (Optional)

Magnetic Declination (Optional)

Distance Unit Label

Reset

Coordinate rule used here: X increases eastward and Y increases northward. Bearings are measured clockwise from north.

Example Data Table

Example	Start Point	End Point	Distance	True Bearing	Quadrant Notation
Route A	(0, 0)	(30, 40)	50.000 units	36.870°	N 36° 52' 11.63" E
Route B	(10, 15)	(-5, 45)	33.541 units	333.435°	N 26° 33' 54.18" W
Route C	(4, -3)	(20, -10)	17.464 units	113.629°	S 66° 22' 14.24" E

Formula Used

1) Coordinate differences
Δx = x₂ - x₁
Δy = y₂ - y₁

2) Bearing from north, clockwise
Bearing = (atan2(Δx, Δy) × 180 / π + 360) mod 360

3) Reverse bearing
Reverse Bearing = (Bearing + 180) mod 360

4) Distance between points
Distance = √(Δx² + Δy²)

5) Standard math angle from the positive x-axis
Math Angle = (atan2(Δy, Δx) × 180 / π + 360) mod 360

6) Magnetic bearing, if declination is supplied
Magnetic Bearing = (True Bearing - Declination) mod 360
Use east declination as positive and west declination as negative.

How to Use This Calculator

Enter the start point coordinates in the first two fields.
Enter the end point coordinates in the next two fields.
Add an optional current heading to compare your existing direction with the target bearing.
Add optional magnetic declination if you need magnetic bearing instead of only true bearing.
Choose a distance label such as meters, kilometers, feet, or nautical miles.
Press Calculate Bearing to show the results above the form.
Review the decimal bearing, DMS form, reverse bearing, quadrant notation, and plotted route.
Use the CSV or PDF buttons to export the result summary.

FAQs

1) What is a bearing angle?

A bearing angle shows direction from one point to another, measured clockwise from north. It is widely used in navigation, surveying, mapping, and coordinate geometry.

2) How is a bearing different from a normal math angle?

A normal math angle starts on the positive x-axis and increases counterclockwise. A bearing starts at north and increases clockwise, so the formulas are arranged differently.

3) What is quadrant notation?

Quadrant notation writes direction from north or south toward east or west, such as N 36° 52' 12" E. It is another way to express the same bearing.

4) Can I use negative coordinates?

Yes. Negative coordinates are valid. The calculator uses coordinate differences, so it works in any quadrant as long as both points use the same reference system.

5) Why cannot the two points be identical?

If both points are the same, distance is zero and direction is undefined. A bearing needs movement from a start point to a different end point.

6) What does magnetic declination change?

Declination adjusts true bearing to magnetic bearing. Enter east declination as positive and west declination as negative so the conversion matches your chosen reference.

7) Why is the turn angle helpful?

Turn angle compares your current heading with the target bearing. It helps in navigation, robotics, path correction, and classroom direction problems.

8) Does declination change the distance or graph shape?

No. Declination only changes the directional reference. The distance, coordinate change, and plotted segment remain the same because the actual points do not move.