Levels and earthworks
Cut and fill from a 3 × 3 grid of levels
- where
- weighted average existing level (m)
- corner levels (m)
- mid-side levels (m)
- centre level (m)
- net volume, cut + or fill − (m³)
- plot length (m)
- plot width (m)
- formation level (m)
Explain this equation
This works out the net cut or fill to bring a rectangular plot to a level formation, from nine spot levels on a 3 × 3 grid, and the level that would balance them.
h1 to h9 are the existing ground levels: corners h1, h3, h7, h9; mid-sides h2, h4, h6, h8; and the centre h5. Hm is their weighted average, Lf the formation level, and L and W the plot size. V is positive for cut and negative for fill.
Each level stands for the grid squares it touches: corners touch one, mid-sides two and the centre all four, hence weights 1, 2 and 4 out of 16. Area times the average depth between ground and formation gives the net volume.
Sense check: a 20 × 16 m plot averaging 150 mm above formation gives 320 × 0.15 = 48 m³ of cut. Setting the formation at Hm would give zero net.
Watch out: this is a net figure; where ground is partly above and partly below formation, cut and fill partly cancel, and bulking and compaction are not included.
Net cut or fill for a rectangular plot from nine spot levels on a 3 × 3 grid, and the level that would balance cut against fill.
Enter your values to see the result.
Good to know
Points: 1, 2, 3 along the first side, 4, 5, 6 across the middle, 7, 8, 9 along the far side. Each grid level is weighted by the number of grid squares it touches (corners 1, mid-sides 2, centre 4), which is the standard grid method for volumes. Setting the formation at the average level balances cut and fill in the ground, before bulking and compaction. Excavated soil bulks and compacted fill shrinks, so a true balance usually needs the formation set slightly different from the average.
Common mistake
Taking a simple average of the nine levels. That gives the corners too much say; weight them as above.
Limits
Assumes the ground is a plane surface within each grid square. For uneven ground, survey on a closer grid. Formation is level; for falls, work it in parts.
Sources
- Uren & Price, Surveying for Engineers: volumes from spot heights on a grid (each level weighted by the number of squares it touches)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow BS 8500, BS EN 206, BS EN 752, Building Regulations Part H, manufacturers’ data and your engineer’s design. Structural concrete and foundations need a competent designer.