Cut and fill calculator: grid or cross sections

1. At each grid point, the depth is existing minus proposed: positive is cut, negative is fill.
2. A cell all in cut (or all in fill) is its area × the average of its four corners. Summed over a whole grid, a point counts once, twice, three or four times by how many cells share it: V = A ÷ 4 × (Σh₁ + 2Σh₂ + 3Σh₃ + 4Σh₄).
3. A cell with corners on both sides of grade is split by what the USDA calls the four-point method: cut = A ÷ 4 × (Σcut)² ÷ (Σcut + Σfill), with the depths taken as positive, and fill the same with Σfill on top. USDA's worked example, a 100-ft square with 0.4 ft of cut and 0.3 ft of fill at its corners, gives 21.2 cubic yards of cut and 11.9 of fill; averaging the signed depths would call it 9.3 of cut.

1. Between two stations, volume = length × (A₁ + A₂) ÷ 2, for the cut and the fill areas separately.
2. Where an area runs out to nothing at one end, the solid is a pyramid, length × A ÷ 3, and averaging overstates it by half. The correction is on unless you turn it off.

The example sections below come to 311 cubic yards of cut with the correction and 317 without.

A pad 200 by 150 feet on a 50-ft grid, cut at the high corner and fill at the low one (the calculator's starting values): 831 cubic yards of cut and 357 of fill, with 6 of the 12 cells crossing grade.

The sections example runs from 0+00 to 2+00: 311 cubic yards of cut and 93 of fill.

Fill is placed compacted and cut is dug in the bank, so the balance runs the fill back to bank yards through the soil's shrink; what's left goes to the haul calculator. Site Bid works the same out from the existing and proposed surfaces, by area or by cross section.

• Grid method: US Army FM 5-430-00-1, Road Design, Ch. 3.
• Transition cells: USDA SCS National Engineering Handbook, Section 15, Ch. 12, Land Leveling (the four-point method), and FAO Irrigation and Drainage Paper 45, Land levelling.
• Average end area and the pyramid: Wyoming DOT Survey Manual, Appendix F, Volume (rev. July 2024).
• All checked October 4, 2026.

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