Introduction:
Calculating the area of a piece of land is an essential step in land surveying, urban planning, and many other fields. One of the commonly used methods for calculating land area is by using the Northing and Easting coordinates. Northing and Easting are two of the coordinates used in the Universal Transverse Mercator (UTM) coordinate system. In this article, we will discuss how to calculate the area of a piece of land using Northing and Easting coordinates.
Understanding Northing and Easting Coordinates
The UTM coordinate system divides the Earth’s surface into 60 zones, each 6 degrees wide in longitude. These zones are numbered from 1 to 60, starting at the International Date Line and moving eastward. Each zone is further divided into grid squares, with a size of 100,000 meters by 100,000 meters.
The Northing coordinate is a measure of distance in meters north of the equator. It is measured in meters from the equator to the point of interest. The Easting coordinate is a measure of distance in meters east of the central meridian of the UTM zone. The central meridian is the longitude line that passes through the middle of the UTM zone.
Calculating the Area Using Northing and Easting Coordinates
To calculate the area of a piece of land using Northing and Easting coordinates, you need to follow the steps below:
Step 1: Collect Data Collect the Northing and Easting coordinates of the corners of the piece of land you want to calculate the area for. The more corners you have, the more accurate your calculation will be. You can get this data from a surveyor or from maps that show Northing and Easting coordinates.
Step 2: Arrange Data Arrange the Northing and Easting coordinates in a table. The table should have three columns: Point ID, Northing, and Easting. The Point ID is a unique identifier for each corner of the land.
Step 3: Calculate the Area To calculate the area, you need to use the formula:
Area = (A + B + C + D + … + N) x F
Where: A, B, C, D, …, N are the distances between the adjacent corners of the land F is a constant factor that depends on the units used for the coordinates. If the coordinates are in meters, F is 0.5. If the coordinates are in feet, F is 0.04166667.
To calculate the distance between two adjacent corners, you can use the Pythagorean theorem:
Distance = √((Easting₂ – Easting₁)² + (Northing₂ – Northing₁)²)
Where: Easting₁ and Easting₂ are the Easting coordinates of the two adjacent corners Northing₁ and Northing₂ are the Northing coordinates of the two adjacent corners
After calculating the distances between all adjacent corners, you can add them up and multiply the sum by the constant factor F to get the area of the land in square meters or square feet, depending on the units used.
How do you find area with coordinates?
In order to find the area with coordinates, you need to have the coordinates of the vertices of the polygon. Once you have the coordinates, you can use the coordinate geometry formula to calculate the area of the polygon.
How do you calculate northing and easting?
Northing and easting are the measurements of a point’s position relative to a reference point, typically a survey marker. To calculate northing and easting, you need to measure the distance and direction from the reference point to the point in question.
How do you calculate area in surveying?
To calculate area in surveying, you need to know the length of the sides of the polygon and the angles between the sides. Once you have this information, you can use the surveying formula to calculate the area of the polygon.
What is area by coordinates method surveying?
Area by coordinates method surveying is a method used to calculate the area of a polygon based on the coordinates of its vertices.
Area by coordinates method surveying examples
An example of area by coordinates method surveying would be to calculate the area of a rectangular property with the coordinates of its four corners.
Northing and easting coordinates
Northing and easting coordinates are the measurements of a point’s position relative to a reference point, typically a survey marker, in the north-south and east-west directions respectively.
Area by coordinates method surveying calculator
An area by coordinates method surveying calculator is a tool that uses the coordinates of a polygon’s vertices to calculate the area of the polygon.
How to calculate northing and easting coordinates in excel
To calculate northing and easting coordinates in Excel, you can use the trigonometry functions to calculate the distances and angles between the reference point and the point in question.
How to calculate land area using coordinates
To calculate land area using coordinates, you need to have the coordinates of the vertices of the polygon that represents the land area. Once you have the coordinates, you can use the coordinate geometry formula to calculate the area of the polygon.
Northing and easting in total station
Northing and easting are the measurements of a point’s position relative to a reference point, typically a survey marker, in the north-south and east-west directions respectively. Total stations are surveying instruments that measure angles and distances to determine the coordinates of points on the earth’s surface. The coordinates measured by a total station include northing and easting.
Area by coordinates method surveying pdf
Area by coordinates method surveying pdf is a document that explains the method used to calculate the area of a polygon based on the coordinates of its vertices. It typically includes examples and illustrations to help explain the method.
Area by coordinates formula
The area by coordinates formula is a formula used to calculate the area of a polygon based on the coordinates of its vertices. The formula typically involves using the coordinate geometry formula to calculate the area of each triangle formed by the polygon’s vertices and then summing the areas of the triangles.
What is calculating area using northing and easting?
Calculating area using northing and easting involves using the coordinate system to determine the area of a given land or property.
What is a northing and easting coordinate system?
A northing and easting coordinate system is a geographic coordinate system used to identify a specific location on the Earth’s surface. Northing refers to the distance from the equator and easting refers to the distance from the prime meridian.
How does calculating area using northing and easting work?
Calculating area using northing and easting works by breaking down the given land or property into small sections using a grid system of northing and easting coordinates. The area of each section is then calculated by multiplying the distance between the northing and easting coordinates. The sum of all these sections gives the total area of the land or property.
What are the benefits of using northing and easting coordinates to calculate area?
Using northing and easting coordinates to calculate area is beneficial because it provides a precise measurement of the area of a given land or property. It also enables easy and accurate calculation of irregularly shaped areas and is used by land surveyors and cartographers.
What tools are used to calculate area using northing and easting?
To calculate area using northing and easting, one needs a map or survey plan with northing and easting coordinates, a calculator or computer program to calculate the area of each section, and a tool to sum up all the areas.
Are there any limitations to using northing and easting coordinates to calculate area?
Yes, there are limitations to using northing and easting coordinates to calculate area. This method only works well for areas with regular shapes, and for irregular shapes, it may require more detailed measurements, which can be time-consuming and tedious. Additionally, errors in measurement or calculation can result in inaccurate area calculations.
Conclusion:
Calculating the area of a piece of land using Northing and Easting coordinates is a straightforward process. It involves collecting the Northing and Easting coordinates of the corners of the land, arranging the data in a table, and using a formula to calculate the area. The accuracy of the calculation depends on the number of corners used and the precision of the Northing and Easting coordinates. Land surveyors, urban planners, and others who work with land area calculations can benefit from knowing how to calculate the area of a piece of land using Northing and Easting coordinates.
