← Estimating & Costing · MP Vyapam Sub Engineer Civil

Chapter 7 of 12

Building, Road and Canal Estimates

In the MP Vyapam Sub Engineer Civil syllabus under Estimating & Costing · 2 parts

Building Estimates — Long Wall-Short Wall & Centre Line Methods · Earthwork, Road & Canal Estimates

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📑 Contents (9 sections)

Part 1 of 2

Building Estimates — Long Wall-Short Wall & Centre Line Methods

Last reviewed 16 Sept 2026 · 7 min read

Methods of estimating walls

In a building, walls and their foundations have the same cross-section along their length, so quantities are found by multiplying length × cross-sectional dimensions for each layer (excavation, concrete bed, footings, plinth and superstructure). The difficulty lies in corners and junctions, where quantities could be double counted or omitted.

1. Long wall–short wall method

Walls in one direction are treated as long walls and those at right angles as short walls.

FormulaLong wall–short wall lengths (for each layer of width b)

Long wall length (out-to-out) $=$ centre-to-centre length $+$ one breadth $b$
Short wall length (in-to-in) $=$ centre-to-centre length $-$ one breadth $b$

The breadth $b$ is the width of that particular layer (trench width, footing width, wall thickness), so the lengths change from layer to layer.

Quantities for each layer are computed separately for long walls and short walls.
Simple and less error-prone for rectangular buildings; laborious for buildings with many walls.

2. Centre line method

The total length of the centre lines of all walls is multiplied by the cross-sectional dimensions of each layer.

FormulaCentre line method

Quantity of a layer = (total centre line length - junction deduction) \times b \times h

At each T-junction (where a cross wall meets a main wall), deduct half the breadth of that layer ( $b /2$ ) from the total centre line length for each junction — because the overlap would otherwise be counted twice.
At corners (L-junctions), no deduction is needed — the extra length on the outer side balances the shortage on the inner side.
At a cross (+) junction of walls, deduct one full breadth (two halves).

Quick and suitable for buildings with walls of uniform section and many junctions (after applying deductions carefully).

3. Partly centre line and partly cross-wall method

Main walls are computed by the centre line method, and cross walls by in-to-in lengths — used where walls have different sections.

Sequence of items in a building estimate

No.	Item	Unit
1	Earthwork in excavation in foundation trenches	m³
2	Lean concrete (e.g. 1 : 4 : 8 PCC) in foundation bed	m³
3	Brick/stone masonry in foundation and plinth (footing steps)	m³
4	Damp-proof course at plinth level	m²
5	Filling in plinth (sand/earth) and floor base	m³
6	Masonry in superstructure (with deductions for openings, lintels, embedded RCC)	m³
7	RCC work — lintels, chajjas, beams, columns, slabs	m³
8	Formwork for RCC items	m²
9	Reinforcement (from BBS)	kg
10	Flooring — base concrete and floor finish; skirting	m², m³
11	Plastering — internal walls, external walls, ceiling	m²
12	Doors, windows, ventilators — frames and shutters, fittings	m², no.
13	Roof treatment / waterproofing, parapet, coping	m²
14	Whitewashing, distempering, painting	m²
15	Steps, sunshades, rainwater pipes, miscellaneous	as applicable
16	Water supply, sanitary and electrical installations	lump sum/%
17	Contingencies, work-charged establishment	%

Worked estimate — single-room building

Worked ExampleEstimate of a single-room building

Data:

Internal room size 5.0 m × 4.0 m; walls 300 mm thick in superstructure; height of superstructure (floor to roof slab bottom) 3.0 m.
Foundation: trench 0.9 m wide, 1.0 m deep below ground level; PCC 1 : 4 : 8 bed 0.9 m wide × 0.2 m thick.
Brick masonry footings: first step 0.6 m wide × 0.3 m; second step 0.45 m wide × 0.3 m; plinth wall 0.3 m wide × 0.6 m (up to plinth level).
Openings: one door 1.0 m × 2.1 m; two windows 1.2 m × 1.2 m; RCC lintels 0.3 m wide × 0.15 m deep with 150 mm bearing on each side.

Centre line lengths: long walls c/c $= 5.0 + 0.3 = 5.3$ m; short walls c/c $= 4.0 + 0.3 = 4.3$ m Total centre line length $= 2 (5.3 + 4.3) = 19.2 m$ (four L-corners, no T-junctions → no deduction)

1. Earthwork in excavation $19.2 \times 0.9 \times 1.0 = 17.28 m^{3}$ Check by long wall–short wall: long walls out-to-out $= 5.3 + 0.9 = 6.2$ m (×2 = 12.4 m); short walls in-to-in $= 4.3 - 0.9 = 3.4$ m (×2 = 6.8 m); total 19.2 m ✓

2. PCC 1 : 4 : 8 in foundation $19.2 \times 0.9 \times 0.2 = 3.46 m^{3}$

3. Brick masonry in foundation and plinth

First step: $19.2 \times 0.6 \times 0.3 = 3.456$ m³
Second step: $19.2 \times 0.45 \times 0.3 = 2.592$ m³
Plinth wall: $19.2 \times 0.3 \times 0.6 = 3.456$ m³ Total $= 9.50 m^{3}$

4. Damp-proof course (at plinth level) $19.2 \times 0.3 = 5.76$ m², less door opening $0.3 \times 1.0 = 0.30$ m² → 5.46 m²

5. Brick masonry in superstructure

Gross: $19.2 \times 0.3 \times 3.0 = 17.28$ m³
Deduct door: $1.0 \times 2.1 \times 0.3 = 0.630$ m³
Deduct windows: $2 \times 1.2 \times 1.2 \times 0.3 = 0.864$ m³
Deduct lintels: length $= (1.0 + 0.3) + 2 (1.2 + 0.3) = 4.3$ m → $4.3 \times 0.3 \times 0.15 = 0.194$ m³ Net $= 17.28 - 0.630 - 0.864 - 0.194 = 15.59 m^{3}$

6. RCC lintels $4.3 \times 0.3 \times 0.15 = 0.194 m^{3}$

7. RCC roof slab (120 mm thick, resting over walls, no projection) $(5.0 + 0.6) \times (4.0 + 0.6) \times 0.12 = 5.6 \times 4.6 \times 0.12 = 3.09 m^{3}$

8. Internal plaster (12 mm) on walls Internal perimeter $= 2 (5.0 + 4.0) = 18.0$ m → gross $= 18.0 \times 3.0 = 54.0$ m² Door (2.1 m²) and windows (1.44 m² each) are between 0.5 and 3 m² → deduct on one face (taken on the inside face here): $2.1 + 2.88 = 4.98$ m² Net internal plaster $= 49.02 m^{2}$

9. External plaster (on superstructure) External perimeter $= 2 (5.6 + 4.6) = 20.4$ m → $20.4 \times 3.0 = 61.20 m^{2}$ (no deductions on this face under the one-face rule for these openings)

10. Ceiling plaster $5.0 \times 4.0 = 20.00 m^{2}$

11. Flooring Floor area $= 5.0 \times 4.0 = 20.00 m^{2}$ (base concrete and finish computed from thicknesses)

The abstract of cost then multiplies each quantity by its rate (from the schedule of rates) and adds contingencies and other provisions.

Worked ExampleDeduction at T-junctions (centre line method)

If an internal cross wall (same foundation section) is added across the room of the example (c/c length 4.3 m), find the centre line length for the excavation layer.

Solution. The cross wall meets the long walls at two T-junctions. For the 0.9 m wide trench, deduct $2 \times \frac{0.9}{2} = 0.9$ m. Centre line length $= 19.2 + 4.3 - 0.9 = 22.6 m$ (a different deduction applies to each layer according to its breadth)

Part 2 of 2

Earthwork, Road & Canal Estimates

Last reviewed 16 Sept 2026 · 7 min read

Earthwork computation

Data

Longitudinal section (L-section) — ground levels (RL) at regular chainages (e.g. every 20 m or 30 m) along the centre line, with the proposed formation level (road/canal bed) fixed by gradient.
Cross-sections — ground levels across the centre line at each chainage.
Formation width, side slopes (cutting and filling), road/canal typical sections.

Depth at a section:

Embankment (filling): height $=$ formation level $-$ ground level (positive).
Cutting: depth $=$ ground level $-$ formation level.

Sectional area of a level section

FormulaLevel section (ground level across the section)

A = B d + s d^{2}

$B$ = formation width (top width of embankment or bottom width of cutting); $d$ = depth of fill or cut at the centre line; $s$ = side slope (horizontal : 1 vertical).

Volume between sections

FormulaEarthwork volume formulas (sections at distance L apart)

1. Mid-section (mean depth) method:

d_{m} = \frac{d _{1} + d _{2}}{2}, V = (B d_{m} + s d_{m}^{2}) L

2. Mean sectional area (trapezoidal / average end area) method:

V = \frac{A _{1} + A _{2}}{2} L

For a series of equally spaced sections: $V = L [\frac{A _{1} + A _{n}}{2} + A_{2} + \dots + A_{n - 1}]$

3. Prismoidal formula:

V = \frac{L}{6} (A_{1} + 4 A_{m} + A_{2})

( $A_{m}$ = area at the mid-section.) For a series with an odd number of equally spaced sections: $V = \frac{L}{3} [A_{1} + A_{n} + 4 \sum A_{e v e n} + 2 \sum A_{o dd}]$

For level sections, the mean area method gives a slightly larger volume than the prismoidal formula (difference = prismoidal correction $\frac{s L}{6} (d_{1} - d_{2})^{2}$ ); the mid-section method gives a slightly smaller volume.
The prismoidal formula is the most accurate for regular sections.

Mixed sections and transitions

Where the formation changes from embankment to cutting, the section at the transition point has zero depth; the chainage of the transition point is found by interpolation between adjoining sections of fill and cut.
Side-long (partly cut, partly fill) sections on sloping ground are computed as triangles/trapezoids for the cut and fill portions separately.

Lead and lift

Lead — horizontal distance over which excavated earth is carried, measured between the centres of gravity of excavation and deposit (or as specified).
Lift — vertical height through which earth is raised.
Schedule rates commonly include an initial lead of 50 m and lift of 1.5 m; extra lead and lift are paid additionally. Lifts may be converted to equivalent leads as per departmental rules.

Mass haul diagram

A plot of cumulative volume of earthwork (cuts positive, fills negative, corrected for shrinkage/bulking) along chainage, used to decide economic haul, borrow pits and spoil, free haul and overhaul (see Computation of Areas & Volumes).

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