### How to Calculate Scale Factor (in Land Surveying)

A map projection provides a means of representing the curved surface of the earth on a plane surface so that coordinate grids can be defined and maps drawn. The relative positions of points on the grid are altered slightly from their ground positions as a result of using Transverse Mercator Projection to account for the curvature of the earth. The formula for the scale factor is

Scale Factor=Grid Distance/Measured Distance (at MSL)

For example take these two coordinates

- A=1882281.927 , 182474.093
- B=1882314.193 , 182458.059
- The grid distance (calculated distance) on the map is given as 36.03
- That is √((1882281.927 -1882314.193)²+(182474.093-182458.059)²)=36.030
- If you measured the horizontal distance between A&B in ground with tape or Total station and got 36.000 m. Then the scale factor is calculated as
- Scale Factor=Grid Distance/Measured Distance (at MSL)
- Scale Factor=36.030/36.000
- Scale Factor=1.000833
- Alternatively we can calculate the ground distance from the above plan
- The ground distance between point
- 1 to 2 =36.03/1.0008428=36.00

The Simple way to calculate the scale factor is

to take the two coordinates and calculate the distance between them in calculator. Then measure the actual distance between the points with with tape or Total station. Then divide calculated distance by measured distance. For road works scale factor can be included in the job settings.

Thank you for this article and it’s calculations. Helped me a lot!