Bearing Calculator
This bearing calculator works out a compass bearing from the east and north components of a direction or displacement. A bearing is measured in degrees clockwise from north, from 0 up to 360, so due north is 0, east is 90, south is 180 and west is 270. Enter how far east (positive) or west (negative) and how far north (positive) or south (negative) you are heading, and the calculator returns the bearing and the straight line distance. Because bearings start from north and go clockwise, the formula uses atan2 of the east component over the north component, adjusted into the 0 to 360 range. Bearings are essential in navigation, tramping, marine and aviation work, and surveying. The formula, a worked example and the assumptions are set out below.
The formula
The bearing is atan2(east, north), converted to degrees and shifted into the 0 to 360 range (add 360 to any negative result). Note that bearings use east over north, and run clockwise from north, unlike a standard maths angle. The distance is sqrt(east^2 + north^2).
Worked example
Heading 1 unit east and 1 unit north gives a bearing of atan2(1, 1) = 45 degrees, north-east, over a distance of sqrt(2), about 1.414214. Enter 1 and 1 above to confirm.
Frequently asked questions
How is a bearing measured?
In degrees clockwise from north, from 0 to 360. North is 0, east 90, south 180, west 270.
Why east over north, not north over east?
Bearings are measured from north, clockwise, so the formula is atan2(east, north). That differs from a standard maths angle, which is measured from the east axis anticlockwise.
What if my bearing comes out negative?
Add 360 degrees. The calculator already shifts the result into the 0 to 360 range for you.
Who this calculator is for
This calculator is for trampers, sailors, pilots, surveyors and students learning navigation.
What this calculator assumes
- You enter east and north components with the right signs.
- The bearing is a true bearing, clockwise from north.
- Results are rounded for display.
Formula and sources
Related calculators
- Trig Calculator: all six trig functions at once.
- Degrees to Radians Calculator: convert angle units.
- Right Angle Triangle Calculator: solve a right triangle.
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