Hong Life CalculatorsUnderstanding the earthwork volume calculator — concept and principle
Road, railway, canal and site-grading projects move large quantities of soil, and costs are driven by the cut and fill volumes between surveyed cross-sections. This calculator estimates the volume between two cross-sections with the average end area method, optionally with the more accurate prismoidal formula, and converts the in-place (bank) volume into the loose volume that trucks will actually haul.
How it is calculated
- Average end area: V = L·(A₁ + A₂)/2, where A₁ and A₂ are the areas of cut or fill at the two sections (m²) and L the distance between them (m).
- Prismoidal: V = L·(A₁ + 4A_m + A₂)/6, where A_m is the measured area at the midpoint section. Leave A_m = 0 to skip it.
- Loose volume: V_loose = V·(1 + swell/100), using the average end area volume.
The principle
The average end area method treats the earth between sections as a prism with a straight-line change in area, so the volume is just the mean area times the length. It is exact only when area varies linearly. When the shape tapers in a curved way, as with a cone or pyramid, the prismoidal formula is exact for any solid whose area varies as a quadratic in distance; it is Simpson's rule applied to areas, which is why the middle area carries a weight of 4. Soil also changes volume when dug: grains loosen and voids increase, so the same mass occupies more space in a truck. That increase, as a percentage of bank volume, is the swell factor.
Worked example
- Inputs: A₁ = 30 m², A₂ = 40 m², A_m = 0 (skipped), L = 20 m, swell = 25%.
- Average end area: (30 + 40)/2 × 20 = 35 × 20 = 700 m³ (bank volume).
- Prismoidal volume is shown as "—" because no middle area was entered.
- Loose volume: 700 × 1.25 = 875 m³ to be hauled.
| Distance (m) | Average end area (m³) |
|---|---|
| 5 | 175 |
| 10 | 350 |
| 15 | 525 |
| 20 | 700 |
| 25 | 875 |
| 30 | 1,050 |
| 40 | 1,400 |
How to read the result
Total earthwork is the sum of such slices along the alignment, kept separately for cut and fill. The loose volume sets the number of truck loads: at about 10 m³ per load, 875 m³ means roughly 88 trips. Compacted fill usually occupies less than the bank volume, so a shrinkage factor is used for fill quantities.
Common mistakes
- Adding cut and fill areas in the same section instead of computing them separately.
- Using swell to estimate compacted fill volume, which needs shrinkage instead.
- Using the average of A₁ and A₂ as A_m, which simply reproduces the average end area result.
Frequently asked questions
Which method do contracts use?
Many specifications use average end area for its simplicity; some require prismoidal corrections or digital terrain model comparisons.
What is a typical swell factor?
It depends on the material; common earth is often around 25%, with clays and blasted rock higher.
How close should cross-sections be?
Often every 20 m on roads, with extra sections at sharp changes in terrain.
Sources: R. C. Brinker and P. R. Wolf, Elementary Surveying, Harper & Row · C. D. Ghilani and P. R. Wolf, Elementary Surveying: An Introduction to Geomatics, Pearson