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Coordinates and distance

In surveying, points are given by coordinates, often north and east in metres. The distance between two points is found with Pythagoras, and the direction with the arctangent. That is how a building is set out precisely on the site.

s = \sqrt{\Delta N^2 + \Delta E^2}

horizontal distance

\alpha = \arctan\frac{\Delta E}{\Delta N}

direction measured from north

Symbols

$\Delta N,\ \Delta E$	coordinate differences north and east	m
$s$	distance	m
$\alpha$	bearing	°

Example

From (N 100, E 200) to (N 130, E 240):

$s = \sqrt{30^2 + 40^2} = 50$ m.

Check which quadrant the direction lies in. The arctangent alone cannot tell opposite directions apart.

Practise surveying for free →

← Levelling · Area from coordinates →

Part of Building and Structures: Surveying.