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Earthwork quantities

Intermediate Estimation and Quantity Surveying Reviewed 24 Oct 2026 2 min read

Roads, railways, canals and embankments move huge volumes of earth, and earthwork is often the largest single item in their cost. Quantities come from cross sections taken at regular chainages along the centre line.

At each chainage, the area of cut or fill is worked out from the formation width, side slopes and the depth at the centre line, or by coordinates for irregular ground. Volumes between sections are then found by the average end area method, simple but slightly over-estimating for tapering shapes, or by the prismoidal formula, which is exact for prismoids and needs an odd number of sections at equal spacing.

Diagram: Indiacon original, not to scale.

A mass-haul diagram plots cumulative volume along the route. It shows where cut can be used as fill, the haul distances, and where borrow or disposal is needed. Bulking and shrinkage factors convert between bank, loose and compacted volumes.

Our earthwork calculator applies both methods so you can compare them.

Key formulas
  • Area of a level section: A = (b + s h) h, with b formation width, s side slope (H:V), h depth
  • Average end area: V = d [ (A₁ + A_n)/2 + A₂ + … + A_(n−1) ]
  • Prismoidal: V = (d/3) [A₁ + A_n + 4 (A₂ + A₄ + …) + 2 (A₃ + A₅ + …)], n odd
Solved example

Problem. Three sections 20 m apart have areas 12, 18 and 26 m². Find the volume by both methods.

  1. Average end area: 20 × [(12 + 26)/2 + 18] = 20 × 37 = 740 m³.
  2. Prismoidal: (20/3) × [12 + 26 + 4 × 18] = 6.667 × 110 = 733.3 m³.

Answer. 740 m³ (end area) versus 733 m³ (prismoidal)

Quick quiz

1Which method needs an odd number of sections?

Prismoidal.

2What does a mass-haul diagram show?

Cumulative cut and fill along the route and haul distances.

3Does average end area tend to over- or under-estimate?

Over-estimate for tapering shapes.

Code note
  • IS 1200 (series) (India): Method of measurement of building and civil engineering works, one part per trade.

Clauses and documents to read

  • IS 1200 (Part 1): earthwork measurement

Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.

References and further reading

Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.

  • B. N. Dutta, Estimating and Costing in Civil Engineering, UBS Publishers, latest edition.

Free and official sources

All references for this subject →

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