**What Are Coordinates (Northing and Easting)?**

The geographic **Cartesian Coordinates** of a point on earth are referred to as **Easting** (the **x **value), and **Northing** (the **Y** value). The distance (**L**) is known as the **Orthogonal Coordinate** measured from a horizontal datum. We use the method of **Latitude** and **Departure** to determine the Northing and Easting, thus calculating the Coordinates.

To calculate coordinates, you need to have the source data such as the bearing and distance of lines connecting two or multiple points. As Excel only takes bearings in **Radians**, you should first convert the bearing readings into radians.

For illustration, we have a sample dataset with a reference point (i.e., New York City coordinate). From the reference point, we have multiple points maintaining intervals of certain distances. We will calculate the coordinates of those points using the **Latitude **and **Departure** methods.

**Step 1 – Setting Up Bearings and Distances**

Arrange the given bearing (i.e., *Degrees, Minutes, Seconds*) and distance readings in an organized manner in Excel Worksheet. Provide clear labels for the data, along with their units (i.e., *Meter or Degree, Minute, Second*), as shown in the image below.

**Step 2 – Bearing Conversion in Radian**

âž¤ Use the formula below to convert **Degrees**, **Minutes**, and **Seconds** into **Radians**.

`=RADIANS(E7+(G7/60)+(I7/3600))`

In the formula, **G7/60** converts the **Minutes** into **Degrees**,** I7/3600** the **Seconds** into **Degrees**, and the **RADIANS** function converts the **Degree** values into **Radians**.

âž¤ Drag the **Fill Handle **to apply the formula to other cells.

**Step 3 – Finding Latitude and Departure**

**Additional LatitudeÂ **

The Latitude is the product of the **Cosine** value of the Bearing and the Distance (L).

âž¤ Add the following **COS function** in cell **L7**.

`=D7*COS(K7)`

âž¤ Drag the **Fill Handle** to execute the formula in the other cells.

You will get the additional **Latitude** from the reference point (i.e., New York City).

**Additional Departure**

**Departure** is the horizontal distance from a reference point.

**Departure** is the product of the **Sine** value and **Distance**.

âž¤ Add the following formula in any blank cell (i.e., **M7**)

`=D7*SIN(K7)`

âž¤ Apply the **Fill Handle** to display the *Departure* values in all the other cells.

**Step 4 – Calculating Coordinates from Bearing and Distance**

Users need a reference point (i.e., *New York* City Coordinates) to measure the coordinates of regular intervals and bearings. There is a reference *Coordinates* in the dataset and users have to add each additional **Latitude** and **Departure** to find the respective **Northing** and **Easting**.

**Point Northing**

âž¤ Add the additional** Latitude** to the reference **Northing** to find the final **Northing** of any point.

`=L7+N6`

âž¤ Drag the **Fill Handle** to display the **Northing** **Coordinate** values in all cells.

**Point Easting**

âž¤ Use the **Addition Operator** to find the final **Easting** of any point.

`=M7+O6`

âž¤ Drag the **Fill Handle **to execute the addition operator in other cells.

You’ll get the *Coordinates* from bearing and distance.

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Thanks! Very helpful

Welcome @Janice

How do you factor in the East or West of the bearing – does this need to be accounted for? For example, should 19 degrees East be positive radians whereas if it were West, it would be negative Radians – or am I not understanding something. I am trying to use this process on a set of legal descriptions, and so far, it’s not aligning with a known map.

Hello Hannah!

Thanks for reaching out! You are correct. The direction (East or West) of the bearing is crucial, and it needs to be accounted for in the calculation of radians.

In navigation and mapping, the convention is usually to measure bearings clockwise from north, meaning that eastward directions are considered positive, and westward directions are considered negative. Bearings can be given in degrees, minutes, and seconds or in radians. To account for this, you should modify the formula for converting bearings to radians as follows:

For East Bearings: Simply convert degrees, minutes, and seconds to radians as previously described, and the result will be positive.

=RADIANS(Degrees + (Minutes / 60) + (Seconds / 3600))

For West Bearings: Convert degrees, minutes, and seconds to radians as previously described, but make the result negative.

=-RADIANS(Degrees + (Minutes / 60) + (Seconds / 3600))

By introducing the negative sign for West bearings, you account for the direction correctly. Positive radians represent East bearings, and negative radians represent West bearings.

Please keep in mind,

Bearings measured clockwise from true north: East is positive. West is negative.

Bearings measured in radians: Counterclockwise is positive. Clockwise is negative.

If you have any further queries, please inform us in the reply section. Thanks.

Best Regards,

ExcelDemy Team

hello, can you explain how to modify formula if have southerly direcctions in the bearings. thank you

Dear, Thanks for visiting our blog and sharing your questions. You want to modify the existing formula to deal with the southerly direction of the bearings. The provided formulas in the article work for any bearing, regardless of direction. This is because the

SINandCOSfunctions account for the direction within their calculations.Southerly bearingstypically range from180to270 degrees. The formulas will handle these values fine and automatically calculate the appropriate change inNorthingandEastingbased on the southerly direction. The cosine value for bearings in this range will be negative, meaning there will be a decrease in Northing because the reference point is likely north of the new point. Likewise, the sine value will be positive, meaning an increase in Easting because a southerly direction moves the point eastward.So, you don’t need to modify the formulas for southerly directions. They will work as intended.

Regards

Lutfor Rahman ShimantoExcelDemy