How to Calculate Earthwork Quantities?

Step 1 - Take cross-sections

The site or road is surveyed along its centreline, with cross-sections taken at regular intervals - commonly every 20 m or 50 m, and closer at changes in grade. Each cross-section shows the existing ground and the design level; the area between them is the cut (above design) or fill (below design) at that section.

Step 2 - Compute each section area

The cross-section is split into trapezoids or triangles and the area of cut and of fill is computed for each section, usually in m². Typical road sections give a central fill with side drains in cut - so cut and fill are often computed separately per section.

The average end area formula

V = L × (A₁ + A₂) / 2

where L is the distance between two sections, and A₁, A₂ are the areas of cut (or fill) at the two sections. The more precise prismoidal formula is used for accuracy on large or expensive works:

V = L/6 × (A₁ + 4Aḓ + A₂)

where Aḓ is the area at the mid-section.

Worked example

You are measuring a 100 m length of embankment. At the start section the fill area is 12 m²; at the end section it is 16 m²:

V = 100 × (12 + 16) / 2 = 100 × 14 = 1,400 m³

So 1,400 m³ of compacted fill over this 100 m length. Repeat section by section and sum - that is the contract quantity.

Compaction and shrinkage - the part everyone forgets

The volume computed from sections is usually the compacted (in-place) volume. Loose soil brought in shrinks roughly 10-15% when compacted, so to place 1,400 m³ of compacted fill you must import about 1,550-1,650 m³ of loose material. Rock swell can run 30% or more. Contracts measure earthwork in the ground; the import quantity is a different, commercial number.

Common mistakes

• Applying the average of a single section pair over a very long chainage - take sections close enough that the ground does not change shape between them.
• Netting cut and fill against each other when the contract requires them measured separately.
• Ignoring shrinkage/swell when ordering material.
• Mixing m² (area) and m³ (volume) in the bill.

Standards that apply

Earthwork is measured under the contract method of measurement (FIDIC-based, PEC forms or highway department specifications) - always state cut and fill separately and exclude topsoil stripping where the spec requires it. Try the built-in earthwork calculator on the tools page to check a run of sections quickly.