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How to Convert Bearings And Distances to Coordinates
In This Article I will explain how to convert bearings and distance to coordinates.
Let’s Start,
Given a known Bearing (θ) & Horizontal Distance (Hz Distance) from a known point (Eo , No), the
coordinates (Ep , Np) may be calculated as follows:
This works for ALL bearings 0°<360°
Hand Calculating
(1) It is important to carry out the above calculation in the correct sequence:
Sin(θ) x Hz Distance is not the same as Sin(θ x Hz Distance)
(2) Typing the above formulae into the Scientific Calculator, it may be necessary to enter the
bearing before the SIN/COS functions.
Eg, θ [SIN] [x] Hz Distance etc.
Microsoft Excel
The calculation may also be done using an Excel spreadsheet.
Note, that Excel assumes angles are measured in the “radians” & so the Bearing (measured in the
Degrees) must be converted using the “RADIANS(x)” function.
=(SIN(RADIANS(Bearing)) x Hz Distance)+East 0
=(COS(RADIANS(Bearing)) x Hz Distance)+North 0
Where “Bearing” is the known bearing in the degrees (or decimal degrees) and Hz Distance is the known
Horizontal Distance.
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Example
Q: Calculate the coordinates of an unknown point measured from the Survey Station at known
coordinates (123.456mE, 456.789mN), given a measured Bearing of 127.5 degrees and the measured
Horizontal Distance of 34.567m?
A=
Easting=
Sin (127.5) = 0.79335334 Hint: U may need to enter 127.5 SIN on the calculator
x 34.567 = 27.42384491
+ 123.456 = 150.880m = East
B=
Northing=
Cos(127.5) = -0.608761429 Hint: Take care to note the “negative” sign
x 34.567 = –21.04305632
+ 456.789 = 435.746m = North
Note: The figures in RED show the “differences” in the position between the Survey Station & the
Unknown point. In this case, the point lies 27.424m to the EAST & 21.043m to the SOUTH of
Survey Station. As a check, this is where would expect the bearing 127.5 degrees to the point to.
