**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.

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Land Surveying & Architects

Land Surveying & Architects