Cut and fill volume calculator from a grid of elevations (earthworks)
Paste the grid of ground elevations (one grid row per line, as in Excel), enter the grid spacing and the pad elevation: you get the cut, the fill, the net balance, the balance elevation (where cut and fill offset each other) and a map of where you cut and where you fill.
One number per node, separated by spaces, tabs or semicolons; every line with the same count. The 1st line is the top (north) row. Leave the pad elevation blank to use the balance elevation. Pad grade: the elevation applies at the 1st node (top-left corner); X increases to the right and Y downwards (positive rises, negative falls). Elevations and spacing in meters.
Result
Paste the elevation grid above (at least 2 × 2 nodes).
How the volume is computed
Grid method (borrow pit method): at each node the height is h = ground elevation − design elevation (positive = cut, negative = fill). In each grid cell of area A = Δx·Δy the volume is A × the mean of its 4 corner heights. When a cell has corners in cut and in fill, the zero-line (transition) formula is used: Vcut = A·(Σh+)² ÷ (4·Σ|h|) and Vfill = A·(Σh−)² ÷ (4·Σ|h|).
The balance elevation is the weighted mean of the elevations: weight 1 at the grid corners, 2 on the edges and 4 at the interior nodes. Swell (bulking) is the increase in volume of excavated soil (the “loose volume” the trucks haul): roughly 20% to 40% for common soils.
FAQ
How do I calculate the cut and fill volume of a site?
Survey the site on a grid (e.g. every 10 m), record the elevation of each node and paste the grid here. With the pad elevation, the calculator adds up the volume of every grid cell and separates cut from fill. A denser grid gives a more accurate volume.
What is the balance elevation?
It is the pad elevation at which the cut volume equals the fill volume (no surplus or shortfall of earth, ignoring swell and compaction). Leave the pad elevation blank and the calculator uses it.
What is swell and how do I use it?
It is how much the soil “grows” when it is dug out: 100 m³ of cut (bank volume) becomes about 125 m³ loose (25% swell). Use it to estimate truck loads. In a compacted fill the soil shrinks again (shrinkage factor).
What if the survey is not on a regular grid?
With scattered points (an irregular survey), the proper way is to build a surface model (TIN) in surveying software and compare it with the design surface. For a quick estimate, you can interpolate the elevations onto a grid and use this calculator.