Earthwork Calculation: Excavation & Filling Volume (Trapezoidal Formula)

Introduction

Earthwork includes excavation (cutting) and filling (embankment). It is measured in cubic metres as per IS 1200 and forms a major part of foundation and road estimates.

This guide covers:

• Simple excavation (foundations, trenches)
• Trapezoidal and prismoidal formulae for linear earthwork
• Bulking and compaction factors

Units (IS 1200)

Item	Unit	Payment
Earthwork in excavation	cum	per cum
Earthwork in filling (foundation trenches)	cum	per cum
Earthwork in filling (plinth)	cum	per cum

Simple Excavation (Buildings)

For foundation trenches, use:

Volume = Length × Breadth × Depth

• Length, breadth – At bottom of excavation (or average of top and bottom)
• Depth – From ground level to bottom of excavation

For stepped excavation, find volume of each step and add.

Example: Foundation Trench

Single room, centre line 19.2 m, trench width 0.9 m, depth 1.4 m.

Volume = 19.2 × 0.9 × 1.4 = 24.192 cum

See quantity takeoff methods for long wall–short wall and centre line approaches.

Trapezoidal Formula (Mean Area Method)

For roads, canals, or any linear work with cross-sections at regular intervals:

V = (D/2) × (A₁ + 2A₂ + 2A₃ + ... + 2Aₙ₋₁ + Aₙ)

Where:

• A₁, A₂, ... Aₙ = areas of consecutive cross-sections (sq m)
• D = distance between sections (m)
• n = number of sections

Simplified (Two Sections)

V = (D/2) × (A₁ + A₂)

Example

Chainage	Area (sq m)
0	20
10 m	25
20 m	18
30 m	22

D = 10 m
V = (10/2) × (20 + 2×25 + 2×18 + 22) = 5 × 128 = 640 cum

Prismoidal Formula

More accurate when cross-sections change. Use when number of sections is odd (3, 5, 7...):

V = (D/6) × (A₁ + Aₙ + 4×(A₂ + A₄ + A₆ + ...) + 2×(A₃ + A₅ + A₇ + ...))

Odd subscript: multiply by 4
Even (middle): multiply by 2

Example (5 sections)

A₁=20, A₂=25, A₃=18, A₄=22, A₅=19, D=10 m

V = (10/6) × (20 + 19 + 4×(25+22) + 2×18)
= (10/6) × (39 + 188 + 36) = (10/6) × 263 ≈ 438 cum

Bulking and Compaction

Bulking

Excavated soil occupies more volume than in-situ:

• Sand: ~10–15%
• Ordinary soil: ~15–25%
• Clay: ~20–30%

Bulking factor = Volume after excavation / Volume in-situ
e.g., 1.2 means 20% bulking.

Compaction

Fill is compacted to required density. Compaction factor = In-situ volume / Compacted volume
Often 0.9–0.95 (i.e., 1 cum fill needs 1.05–1.1 cum loose soil).

Application

• Excavation to fill:
  Fill volume (compacted) × (1 + bulking) ≈ Excavation required
• Borrow pit:
  Order more excavated material than fill volume if transporting from elsewhere.

Volume from Spot Levels

For irregular terrain (e.g., building site):

1. Take grid of spot levels.
2. Find cut/fill at each grid point (depth below/above formation).
3. Use formula:

V = (A/4) × (Σ h at corners)

Where A = area of one grid cell, h = cut/fill depth.
For prismoid over each cell: V = (A/4) × (h₁ + h₂ + h₃ + h₄).

Side Slopes

For trapezoidal cross-section (road in cutting/filling):

Area = (B + s×h) × h
(approximate for uniform slope)

Where:

• B = bottom width
• h = depth of cut or fill
• s = horizontal distance per 1 m vertical (e.g., 1.5:1 → s = 1.5)

Measurement Rules

1. Linear – to nearest 0.01 m

2. Area – to nearest 0.01 sq m

3. Volume – to nearest 0.01 cum

4. Same work, different conditions – measure separately (e.g., soft soil vs hard rock excavation).

Cost of Earthwork in India (2025-26 Rates)

Earthwork rates vary dramatically based on soil type, depth, and city. Here are typical rates per cubic metre:

Type of Earthwork	Rate per m³ (₹)	Measurement Ref
Ordinary soil excavation (0-1.5m depth)	₹150-250	IS 1200 Part 1
Ordinary soil (1.5-3.0m depth)	₹200-350	IS 1200 Part 1
Hard soil / murrum excavation	₹300-500	IS 1200 Part 1
Soft rock (weathered)	₹600-1,000	Separate item
Hard rock blasting	₹1,200-2,500	Separate item
Filling with excavated earth (within 50m lead)	₹100-180	IS 1200 Part 1
Filling with borrowed earth (including transport)	₹250-500	Lead charges extra
Sand filling (in foundation/plinth)	₹1,800-3,500	Based on sand rate
De-watering (per hour)	₹300-600	Pump + operator

Worked Example: Foundation Excavation Cost

For a residential building, 10m × 10m plan, strip foundation 1.2m deep × 0.9m wide:

• Perimeter trench: (10+10+10+10) × 1.2 × 0.9 = 43.2 m³ of ordinary soil excavation
• At ₹200/m³: Excavation cost = ₹8,640
• Refilling: ~60% of excavated soil used for backfilling = 25.9 m³ × ₹120/m³ = ₹3,108
• Disposal of surplus: 17.3 m³ × ₹180/m³ (including lead) = ₹3,114
• Total earthwork cost: ~₹14,862

Machine vs Manual Excavation

Parameter	Manual	JCB/Excavator
Rate	₹150-300/m³	₹80-150/m³
Speed	2-3 m³ per worker per day	80-120 m³ per day
Best for	Small trenches, tight spaces	Open foundations, large sites
Typical machine hire	—	₹1,500-2,500/hour (JCB)

For small residential projects, manual excavation is common. For anything above 50 m³, machine excavation is more economical.

IS Code References for Earthwork

• IS 1200 Part 1:1992 — Method of measurement of building works: Earthwork
• IS 2720 (various parts) — Methods of test for soils (moisture, density, bearing capacity)
• IS 3764:1992 — Excavation work: Code of safety
• IS 6403:1981 — Code of practice for determination of bearing capacity of shallow foundations

Next Steps

• Quantity Takeoff Methods – Long wall, short wall, centre line for building foundations
• Detailed Estimates – Full estimate including earthwork