Tech Chat | Coordinate Forward & Inverse Calculations in Surveying and Mapping

In the field of surveying and mapping, coordinate inverse and forward calculation are very common methods, which help us determine azimuth angle, distance, point coordinates, etc. based on known information. In this blog, we will introduce these concepts and simplify their practical application with time-saving solutions of SingularPad software.


  • Coordinates Forward Calculation: This method finds the coordinates of point B, given point A's coordinates, a horizontal distance, and an azimuth.
  • Coordinates Inverse Calculation: This method involves calculating azimuth, plane and spatial distances, elevation difference, and slope ratio between two known points, A and B.
  • Azimuth: Azimuth represents the direction of a straight line, measured clockwise from the north direction as the reference.

Traditional Calculation Process:

Coordinates Forward Calculation:

Given coordinates (XA, YA), azimuth α between A and B, and the need to find coordinates for point B, use these formulas:

  •   XB = XA + L * cos(α)
  •   YB = YA + L * sin(α)

Coordinate Inverse Calculation:

When you have coordinates for both point A (XA, YA) and point B (XB, YB), follow these steps:

  • Calculate L^2 = (XB - XA)^2 + (YB - YA)^2

To find the coordinate azimuth α, first determine the quadrant angle R of line AB:

  1. Calculate the tangent of R: tan R = |ΔyAB| / |ΔxAB| = |yB - yA| / |xB - xA|
  2. Find R: R = arctan(|yB - yA| / |xB - xA|)
  3. Calculate L: L = √(ΔxAB^2 + ΔyAB^2) = |ΔyAB| / sin(α) = |ΔxAB| / cos(α)
  4. Determine α based on R and the quadrant:
  • If R falls in the first quadrant (0° to 90°), α = R
  • In the second quadrant (90° to 180°), α = 180° - R
  • In the third quadrant (180° to 270°), α = 180° + R
  • In the fourth quadrant (270° to 360°), α = 360° - R

SingularPad Fast Calculation

These traditional calculations can be time-consuming and prone to errors. Luckily, modern surveying software like SingularPad streamlines these processes. Users can input coordinates, and the software handles the complex calculations swiftly and accurately, improving efficiency in surveying and mapping work.

SingularPad software offers a range of surveying and mapping functions, making it a powerful and versatile tool for professionals in the field. It's a game-changer that saves time and ensures precision in coordinate calculations.

In conclusion, mastering coordinate inverse and positive calculations is essential for accurate surveying and mapping work. With the aid of software like SingularPad, these tasks become more efficient and reliable, ultimately enhancing the quality of your work.

Learn more about SingularPad field software,

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