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Land & plots

Grid cut and fill volume calculator

Compare supplied elevation grids using explicit triangular interpolation and separate positive cut and fill regions.

Your numbers

2–11 rows with the same 2–11 columns. Whitespace/comma-separated elevations, magnitudes ≤1,000,000 and at most 6 decimal places. Row/column order defines a local grid, not a map orientation.
Plain decimal, up to 6 decimal places.
Plain decimal, up to 6 decimal places.
Plain decimal, up to 6 decimal places.

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Your result

Ready when you are

Enter your numbers and select Calculate.

Try it, understand it

Explore the result

Try one measured cell with mixed height differences. Keep the nodes fixed and change the diagonal to see how the interpolation assumption affects the volumes.

Worked example comparison
ExampleOutputWhat to notice
Connect the two high nodesGeometric cut volume10.416667 m³Cut is 125/12 ≈ 10.416667 m³ and fill is 25/12 ≈ 2.083333 m³. A zero four-corner mean has not erased both regions.
Connect the two low nodesGeometric cut volume2.083333 m³The same measured nodes now give cut 25/12 m³ and fill 125/12 m³. Choosing the diagonal changes the modeled surface between nodes.
Uniformly 1 m above designGeometric cut volume25 m³A 5 × 5 m cell, everywhere 1 m above target, gives 25 m³ cut and zero fill.

Check your understanding

Does an average corner difference of zero prove there is no earthwork?

No. A cell may have positive cut and negative fill regions at the same time. This method integrates their quantities separately.

Does the diagonal toggle discover the real terrain?

No. It chooses between two explicitly different interpolation models from the same nodes. More measurements or an appropriate surveyed model can be needed to resolve terrain between them.

Behind the numbers

How this calculation works

Interpolate existing and design elevations on the same two triangles per cell. Clip their linear height difference at zero before integrating cut and fill, so mixed regions do not cancel into an incorrect zero. The chosen diagonal is part of the surface model.

THE FORMULAHeight difference = existing − design; integrate positive and negative regions on each chosen planar triangle

A worked example

A 5 × 5 m cell with all existing elevations 101 m and target 100 m has 25 m³ cut and no fill. A mixed-sign cell needs separate positive/negative integration; averaging its four corners can hide both quantities.

Good to know

At most 10 × 10 cells, uniform horizontal spacing, a common unit/reference and explicitly chosen planar interpolation. This describes supplied nodes, not unmeasured terrain. Diagonal choice can change the volume. No shrink/swell, suitability of cut material for fill, haul, topsoil stripping, survey accuracy or earthworks specification is inferred.

Reference: FHWA: geometric earthwork representation and material-state context (opens in a new tab) ↗

Check the land-unit definitions and sources

The standard factors use the international foot and an acre of 43,560 sq ft. Cent means 1/100 acre; gunta means 1/40 acre; the selected Chennai ground means 2,400 sq ft.

The Assam report defines bigha as 14,400 sq ft, katha as 2,880 sq ft and lecha as 144 sq ft. The cited West Bengal court order mentions a 720-sq-ft katha convention. These are explicit presets, not an automatic definition for every record or every place using the same name. Match your record to the stated convention, or use its verified custom factor.

The acre relationships are converted using exact base factors. Rounded or unrelated regional values in a reference table are not substituted for these definitions.

Mixed cut and fill require separate regions

Existing minus design elevation is positive where the model requires cut and negative where it requires fill. A zero average of mixed corner values does not mean every part of the cell is already at design level.

For a 5 × 5 m cell with height differences +1, −1 on the first row and −1, +1 on the second, the selected top-left to bottom-right diagonal gives cut 125/12 m³ and fill 25/12 m³. Both quantities are positive, even though the unweighted average of the four corners is zero.

The tool splits a cell into two stated planar triangles. On each triangle it clips the linear height difference at zero, then integrates each region using its area and vertex heights. No positive and negative volumes are cancelled before their individual totals are retained.

The diagonal is part of the surface assumption

Switching the diagonal in that mixed example reverses which high or low nodes are connected. The cut and fill totals then swap. The four measured nodes alone do not determine all the terrain between them, so choosing an interpolation method is a real modeling decision.

A matching design grid allows a varying target; flat-target mode supplies one target elevation at every node. Both surfaces use the same cell triangles and common unit/reference. Column and row spacing are horizontal, not distances along slopes.

The land elevation profile is useful for inspecting a one-dimensional measured section. This grid adds a two-dimensional surface model, but neither one certifies unmeasured terrain. Soil delivery loads also require separate material-state factors; geometric cut minus fill is not automatically a haul surplus or suitable fill supply.

A few questions, answered

Why not average four corner differences and multiply by cell area?

That shortcut can hide simultaneous cut and fill. This tool keeps both regions and explicitly chooses triangular interpolation.

Are the row names compass directions?

No. Top-left and bottom-right describe the input table’s order. No map orientation, coordinate datum or location is assigned.

Can cut volume directly replace the fill volume?

No material suitability or bank/loose/compacted conversion is determined. These are geometric surface-difference quantities only.

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