Cut and fill calculator: average end area between cross-sections
Calculate cut and fill volumes between cross-sections with the average end area method: enter the stations and the cut and fill areas at each, and get the volumes in metric or US units.
Published · 4 min read · By Malya, the makers of Clarity
The classic earthwork calculation for a road, a channel or a pad: cross-sections along the work, the area of cut and fill on each, and the volume between them. Enter your stations and areas below; the totals update as you type. It starts with four sections 20 m apart so you can see the arithmetic work.
Cut and fill calculator
One row per cross-section, in order along the line: its station, and the area of cut and of fill measured on that section.
- Cut
- 632 m³
- Fill
- 321 m³
- Net (surplus to haul off)
- 311 m³
Section by section
| Between | Length | Cut | Fill |
|---|---|---|---|
| 0 → 20 | 20 m | 313 m³ | 12 m³ |
| 20 → 40 | 20 m | 254 m³ | 90 m³ |
| 40 → 60 | 20 m | 65 m³ | 219 m³ |
Average end area: V = (A₁ + A₂) ÷ 2 × L for each pair of neighbouring sections, cut and fill kept separate. US volumes are cubic feet ÷ 27. These are bank volumes: apply swell and shrinkage for your material when you turn them into truckloads.
How the calculation works
Between each pair of neighbouring sections the calculator takes the mean of the two cut areas and multiplies by the distance between the stations; the same for fill. With the starting numbers, the first 20 m carries (12.4 + 18.9) ÷ 2 × 20 = 313 m³ of cut and (0 + 1.2) ÷ 2 × 20 = 12 m³ of fill. Over all three gaps that comes to 632 m³ of cut and 321 m³ of fill: a surplus of 311 m³ to haul off site or to place elsewhere.
| What | Rule |
|---|---|
| Volume between two sections | (A₁ + A₂) ÷ 2 × L |
| Cut and fill | Calculated separately, never netted section by section |
| Assumes | The ground changes evenly between sections |
| Overstates | Where the section tapers to a point between stations (a cut running out to grade) |
| US units | Areas in ft², stations in ft, volume in ft³ ÷ 27 = yd³ |
Where it goes wrong
- Sections too far apart. A hump or hollow between two sections is invisible to the method. Halving the spacing near changes of grade is the cheap fix.
- Netting on the section. A section that is half cut and half fill should be entered as both areas, not their difference; the contractor moves both.
- Areas from a coarse survey. The volume is only as good as the ground the sections were drawn on. Spot heights every 20 m give smooth, wrong sections.
- Bank, loose, compacted. The answer is bank volume. Swell and shrinkage come after.
Surface to surface instead of sections
A drone survey gives the existing ground as a height every few centimetres. Subtracted from the design surface, it gives cut and fill at every point of the site rather than at every 20 m, with nothing missed between sections and the gross figures complete. The three methods (grid, cross-section and surface-to-surface) are compared, with a worked example, in the cut and fill calculation guide. Clarity does the surface comparison against a LandXML or DXF design, or against an earlier flight, inside any boundary you draw, and draws cross-sections off the same surfaces when the job is paid by chainage.
Questions people ask
How do you calculate cut and fill volumes?
Draw cross-sections across the work at regular intervals and measure the area of cut and the area of fill on each. The volume between two neighbouring sections is the average of their two areas times the distance between them. Add the pieces, keeping cut and fill separate. That is the average end area method, and it is what this calculator does.
What is the average end area method?
A way of turning cross-section areas into a volume: the volume between two sections equals the sum of their end areas divided by two, times the distance between them. It is exact for a prism and slightly overstates volumes where the shape tapers between sections, which the prismoidal formula corrects. Closer sections reduce the error.
How far apart should cross-sections be?
Typically every 20 to 50 feet, or 10 to 25 metres, on roads and channels, and closer where the ground or the design changes quickly: at the start and end of a cut, at culverts, at changes of grade. The method assumes the ground changes evenly between sections, so anything between them that does not is missed.
Are cut and fill the same as the truckloads I will haul?
No. Cut and fill are bank volumes, the earth as it sits in the ground. Excavated material swells, typically by 10 to 30 percent for most soils and more for blasted rock, and fill shrinks when it is compacted. Apply your material's swell and shrinkage factors to the bank volumes when you turn them into loads and hours.
Do it in Clarity.
Explore is free, with no card and no expiry: a real quarry, already flown, to try every tool on. Studio is $50 a month for up to five sites of your own ground, from the orthomosaic and terrain model you already have. Enterprise processes your photos.
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