Bearing Calculator

This bearing calculator turns an east and north displacement into a compass bearing and a straight-line distance, the two numbers you need whenever you are navigating by dead reckoning, plotting a course on a map, or checking a survey direction. You enter two values: how far you have moved east, using a negative number for west, and how far north, using a negative number for south. From these the calculator works out the bearing in degrees, measured clockwise from north through 0 to 360, so due north reads as 0, east as 90, south as 180 and west as 270. It also shows the same bearing converted to radians, and the straight-line distance between your start and end points, found with Pythagoras from the east and north components. Behind the scenes it uses the atan2 function on the east and north values, which places the bearing in the correct quadrant and then shifts any negative result into the 0 to 360 range automatically, so you never need to adjust for a negative angle yourself. This makes it useful for trampers and sailors working out a heading, pilots and surveyors converting coordinate offsets into a true bearing, and students checking navigation or trigonometry homework. Enter your east and north components, which update live, and read off the bearing, the distance and the radian equivalent below.

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East component (+E / -W)

North component (+N / -S)

Distance

Bearing (radians)

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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