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Earthwork Cross Sectional Area Calculator

This calculator determines the cross-sectional area of land used for earthwork by inputting the X and Y coordinates of each point outlining the cross-section. It is useful for surveyors and civil engineers working on excavation, road construction, or grading.

Calculate Land Cross Section Area from Coordinates

Input Fields
n
x
Horizontal axis of point 1
y
Vertical axis of point 1
x
Horizontal axis of point 2
y
Vertical axis of point 2
x
Horizontal axis of point 3
y
Vertical axis of point 3
If enabled, the result will update automatically when you change any value.

Polygon Area from Coordinates Formula

Formula
$$A = \frac{1}{2} \left| \sum_{i=1}^{n} (x_i \cdot y_{i+1} – x_{i+1} \cdot y_i) \right|$$

Where:

  • $$(xi​,yi​)$$ — coordinates of the vertices
  • $$xn+1=x1​$$, $$yn+1=y1​$$ (polygon must be closed)


This method uses the shoelace formula (also known as Gauss’s area formula) to compute the area of any irregular polygon defined by a sequence of coordinates. It’s ideal for determining the cross-sectional area of natural ground or designed earthwork profiles before calculating volume.

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