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Cross Section Area Calculator

Work out cross section area instantly with clear inputs, formula shown and shareable results.

About Cross Section Area Calculator

A two-level cross-section on flat ground is a trapezium: the rectangle of formation width times depth, plus two triangles whose combined area is the side slope ratio times the depth squared. Because the slope term is squared, side slopes dominate the volume on deep cuttings and embankments.

Formulas

Trapezoidal section area

A = b h + s h², where s is the horizontal run per unit of vertical rise

Top width

Top width = b + 2 s h

Worked example

With the default values below, Cross Section Area Calculator returns Cross-sectional area of 26.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Formation widthminimum 0.1 m
10 m
Depth of cut or height of fillminimum 0.01 m
2 m
Side slope, horizontal to one verticalminimum 0
1.5

Results

Cross-sectional area
26.000 m²
Width at the top of the section
16.000 m
Rectangular component
20.000 m²
Side slope component
6.000 m²

Step by step

  1. 1Values used
  2. 2Trapezoidal section area
  3. 3Top width
  4. 4Cross-sectional area= 26.000 m²
  5. 5Width at the top of the section= 16.000 m
  6. 6Rectangular component= 20.000 m²
  7. 7Side slope component= 6.000 m²

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Cross Section Area figure worked out?

A = b h + s h², where s is the horizontal run per unit of vertical rise. A two-level cross-section on flat ground is a trapezium: the rectangle of formation width times depth, plus two triangles whose combined area is the side slope ratio times the depth squared.

What if the ground is sloping across the section?

Then it becomes a three-level section and the two side areas differ. The section must be computed from the actual ground levels at each offset rather than from a symmetrical formula.

What values do I need to enter?

This calculator takes 3 inputs: Formation width, Depth of cut or height of fill, Side slope, horizontal to one vertical. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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