Worked problem

Earthwork Cut and Fill by the Average-End-Area Method

Calculate cut and fill between four 50 ft cross sections, then apply swell and shrinkage factors while keeping bank, loose and compacted volumes separate.

Civil & Structural · Last reviewed October 17, 2026

Given

Four cross sections are 50 ft apart. Surveyed areas in square feet:

Station	0+00	0+50	1+00	1+50
Cut area (ft²)	160	90	20	0
Fill area (ft²)	0	10	70	130

For this exercise, excavated soil swells by 25% (loose volume = 1.25 × bank volume) and the compacted fill has a shrinkage factor of 0.90, which means 1 bank cubic yard (BCY) of soil makes 0.90 compacted cubic yard (CCY).

Find

The cut volume, the fill volume, the bank volume of soil needed to make the fill, the net balance and the loose volume to haul.

Solution

V = (A1 + A2) ÷ 2 × L ÷ 27   (yd³, areas in ft², L in ft)

Segment	Cut (BCY)	Fill (CCY)
0+00 to 0+50	(160 + 90) ÷ 2 × 50 ÷ 27 = 231.5	(0 + 10) ÷ 2 × 50 ÷ 27 = 9.3
0+50 to 1+00	(90 + 20) ÷ 2 × 50 ÷ 27 = 101.9	(10 + 70) ÷ 2 × 50 ÷ 27 = 74.1
1+00 to 1+50	(20 + 0) ÷ 2 × 50 ÷ 27 = 18.5	(70 + 130) ÷ 2 × 50 ÷ 27 = 185.2
Total	351.9	268.5

Cut is measured in the ground, so it is 351.9 bank cubic yards.
The fill is measured compacted: 268.5 CCY. The bank soil needed to make it = 268.5 ÷ 0.90 = 298.4 BCY.
Net balance = 351.9 − 298.4 = 53.5 BCY of surplus soil.
Surplus to haul away, as loose soil in the truck: 53.5 × 1.25 = 66.9 LCY. (All the cut, once dug, is 351.9 × 1.25 = 439.8 LCY.)

Answer

cut 351.9 BCY  |  fill 268.5 CCY (needs 298.4 BCY)  |  surplus 53.5 BCY = about 67 LCY to export

Three volumes, three states

Bank: in the ground. Cut volumes from cross sections are bank volumes.
Loose: after digging, which swells. Trucks and hauling are counted in loose volume.
Compacted: after placement and compaction. Fill from the cross sections is compacted volume.

Do not add cut and fill directly. Convert one to the state of the other first, here fill to bank volume.

Common mistakes

Subtracting fill from cut with no conversion for swell or shrinkage.
Applying the swell factor to the fill instead of the cut, or the shrinkage factor the wrong way (dividing instead of multiplying).
Using the average-end-area method on sections where the ground changes shape sharply or where cut turns to fill inside the interval. It then over- or under-estimates, and a finer section spacing helps.
Using the factors for a different soil. Swell and shrinkage depend on the soil type and compaction specification.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

Are 25% swell and 0.90 shrinkage typical?

They are exercise values. Real values come from the geotechnical report and the compaction specification and vary widely with soil type.

Why is the average-end-area method approximate?

It treats the volume between two sections as a prism with a linear change of area. A prismoidal formula is more accurate when the sections differ a lot.

What do software tools do differently?

They calculate volumes between a design surface and an existing surface on a fine grid or a triangulated surface, which avoids the sampling error of widely spaced sections.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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