Road Quantity and Cost Estimation: Earthwork to Abstract

To estimate the quantity and cost of a road, you split the work into items, measure each item from the longitudinal section and cross-sections, multiply by rates from a rate analysis, and add everything in an abstract of cost. Earthwork comes from cross-section areas, pavement layers from width × thickness × length, and spray coats from area. In Nepal the rates come from government norms combined with the district rates published for each fiscal year.

This post walks through road quantity and cost estimation step by step with numbers you can check.

What you need before you start

• Plan and longitudinal section (L-section) with chainages, ground levels and formation levels
• Cross-sections at regular intervals, often every 20 m, and closer at curves and sudden ground changes
• Typical cross-section showing carriageway, shoulders, layer thickness and drains
• Drawings of culverts, retaining walls and other structures
• Specifications, norms for rate analysis, and the current district rates

Typical fill section used in the worked example. Layers are drawn thicker than scale so they can be read.

Step 1: Earthwork from cross-sections

For a fill on level ground with formation width b, height h and side slope s horizontal to 1 vertical, the cross-section area is:

A = b h + s h²

On hill roads the sections are part cut and part fill on sloping ground. Their areas are worked out by the coordinate method or read from CAD, but the volume formulas below stay the same. Keep cut volumes separate by soil class (ordinary soil, hard soil, soft rock, hard rock) because each class has a different rate.

Worked example

b = 10 m, s = 1.5, sections every 20 m from chainage 0+000 to 0+080.

Chainage	Fill height h (m)	Area A (m²)	Segment volume by average end area (m³)
0+000	0.80	8.96
0+020	1.20	14.16	(8.96 + 14.16) / 2 × 20 = 231.20
0+040	1.60	19.84	(14.16 + 19.84) / 2 × 20 = 340.00
0+060	1.40	16.94	(19.84 + 16.94) / 2 × 20 = 367.80
0+080	1.00	11.50	(16.94 + 11.50) / 2 × 20 = 284.40
Total by average end area			1,223.40

Average end area (trapezoidal) formula: V = d × [(A₁ + Aₙ) / 2 + A₂ + A₃ + ... + Aₙ₋₁]

V = 20 × [(8.96 + 11.50) / 2 + 14.16 + 19.84 + 16.94] = 20 × 61.17 = 1,223.40 m³

Prismoidal (Simpson's) formula: V = d / 3 × [A₁ + Aₙ + 4 × (even sections) + 2 × (remaining odd sections)]. It needs an odd number of sections, which we have (five).

V = 20 / 3 × [8.96 + 11.50 + 4 × (14.16 + 16.94) + 2 × 19.84] = 20 / 3 × 184.54 = 1,230.27 m³

The two answers differ by 6.87 m³, about 0.6 percent. The prismoidal result is closer to the true volume when the area changes in a curved way between sections, as it does here because A has an h² term. For checking site quantities quickly, try the excavation and earthwork calculator.

Step 2: Sub-base, base and surfacing quantities

Pavement layers are measured as compacted volume in place, or as area for thin surfacing. Take a 1 km road with a 5.5 m carriageway:

• Granular sub-base, 7.5 m wide × 0.20 m thick: 1,000 × 7.5 × 0.20 = 1,500 m³
• Crushed stone base, 6.5 m wide × 0.15 m thick: 1,000 × 6.5 × 0.15 = 975 m³
• Bituminous surfacing over the carriageway: 1,000 × 5.5 = 5,500 m²

If a layer has sloped edges, use its average width. When ordering material, remember that loose material shrinks on compaction, so the quantity to bring to site is more than the compacted volume. The norms give the factor to use.

Step 3: Prime coat and tack coat area

Prime coat is measured as the area of granular base that receives bituminous surfacing. In the example that is 5,500 m², plus any sealed shoulders. Tack coat is measured for each bituminous layer laid on another bituminous layer. If asphalt concrete is laid in two layers, there is one tack coat of 5,500 m².

Bitumen quantity = area × spray rate in the specification. For example, if the specification says 0.9 kg/m², then 5,500 × 0.9 = 4,950 kg, or about 4.95 tonnes. Use the rate written in your own specification; the figure here is only for the arithmetic.

Step 4: Drains

An unlined trapezoidal side drain with 0.3 m bottom, 0.9 m top and 0.5 m depth has an area of (0.3 + 0.9) / 2 × 0.5 = 0.30 m². Over 1 km on one side, excavation is 0.30 × 1,000 = 300 m³. For a lined drain, add the masonry or concrete volume as lining section area × length, plus pointing or plaster area. Culverts, causeways and retaining walls are estimated separately, one structure at a time, and their totals are carried into the road abstract.

Step 5: Rate analysis with norms and district rates

Each item's rate is built up from government norms, which give the labour, material and equipment needed per unit of work. These quantities are priced using the district rates for labour, construction materials and equipment hire that each district publishes for the fiscal year. Add transport of materials from the source to site, then overheads and contractor's profit as allowed in the norms. Since district rates change every year and differ between districts, always use the current list for the district where the road lies.

Step 6: Abstract of cost

The abstract collects every item with its quantity and rate. Below is a sample for 1 km of the example road. Suppose the full cross-section sheet for the kilometre gives 14,800 m³ of embankment fill. Rates are left out because they must come from your own rate analysis.

S.N.	Item	Unit	Quantity	Rate (Rs)	Amount (Rs)
1	Site clearance, 12 m width	m²	12,000	From rate analysis	Qty × rate
2	Earthwork in embankment, compacted	m³	14,800	From rate analysis	Qty × rate
3	Side drain excavation	m³	300	From rate analysis	Qty × rate
4	Granular sub-base, 200 mm	m³	1,500	From rate analysis	Qty × rate
5	Crushed stone base, 150 mm	m³	975	From rate analysis	Qty × rate
6	Prime coat	m²	5,500	From rate analysis	Qty × rate
7	DBST surfacing	m²	5,500	From rate analysis	Qty × rate
Sub-total					Sum of items
VAT 13% on sub-total					0.13 × sub-total
Contingencies as per client practice					Percentage of total
Grand total					Sum

The percentage and VAT calculator is handy for the last lines. Once approved, these items and quantities become the bill of quantities for the tender. See our post on the bill of quantities (BOQ) for how that works, and the flexible vs rigid pavement post for the layers themselves.

Common mistakes in road estimates

• Using cross-sections too far apart on rolling or hilly ground, which misses peaks and dips
• Mixing cut in rock with cut in soil under one rate
• Forgetting that some cut material can be reused as fill, which changes the borrow quantity
• Measuring surfacing over the full formation width instead of the sealed width
• Using last year's district rates

Grades on the L-section can be checked with the slope and gradient calculator.

Frequently asked questions

Which is more accurate, average end area or prismoidal formula?

The prismoidal formula is generally more accurate when areas vary smoothly, but it needs an odd number of equally spaced sections. Average end area is simpler and widely accepted for payment, so check which one the contract specifies.

At what interval should road cross-sections be taken?

Every 20 m is common, with extra sections at curves, culverts, and wherever the ground changes sharply. On steep hill roads closer spacing gives a better estimate.

Where do rates for road estimates in Nepal come from?

From a rate analysis that applies government norms to the district rates for labour, materials and equipment. Each district publishes its rates for every fiscal year, so confirm you are using the current list.