Cut and Fill Calculator
Compute earthwork cut and fill from a grid of existing and proposed levels, road cross-sections or a uniform depth, with swell, shrinkage and haul balance.
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About this toolWhat is the Cut and Fill Calculator?
Grading a building pad, a car park or a road changes the ground surface. Where the finished level is below the existing ground you cut; where it is above you fill. This calculator turns survey levels into separate cut and fill volumes, the net difference, and how much material has to be trucked in or out once swell and shrinkage are allowed for.
Three methods are available. The grid method takes existing levels at the corners of a regular grid and either a flat pad level or a second grid of proposed levels, then applies the four-point (borrow-pit) method cell by cell, splitting cells that change from cut to fill. The cross-section method takes stations with cut and fill areas and applies the average end area rule, plus the prismoidal rule when the sections are equally spaced and odd in number. The uniform method multiplies area by an average depth for quick checks.
A colour map of the grid shows where the site is in cut and where it is in fill, which helps when you are adjusting a pad level to balance the earthwork.
- Grid four-point method with split cut and fill cells
- Average end area and prismoidal rules for cross-sections
- Flat pad level or a full proposed grid
- Swell, shrinkage and export or import balance in loose volume
- Colour cell map, metric or imperial, copy and share
How to use the Cut and Fill Calculator
- Choose metres or feet and pick the method: grid levels, cross-sections or uniform depth.
- For a grid, paste existing levels as rows and columns, then enter a flat pad level or a proposed grid of the same shape and the grid spacing.
- For cross-sections, enter one line per station with the cut area and fill area.
- Set swell and shrinkage percentages from the soil report or typical values.
- Read cut, fill, net and the export or import volume in loose truck measure, and use the cell map to adjust the design level.
Worked examples
Building pad on a gentle slope
Input
4 x 4 grid at 10 m, levels 99.2 to 101.2 m, pad at 100.2 m, swell 25%, shrinkage 10%
Output
Cut 181.1 m³, fill 133.6 m³, net 47.5 m³; export 40.8 m³ loose
Fill needs 148.5 m³ of bank material once shrinkage is allowed for, so only 32.7 m³ of bank cut is surplus, which swells to 40.8 m³ in the trucks.
Lowering the same pad to 100.0 m
Input
Same grid, pad at 100.0 m
Output
Cut 296.7 m³, fill 69.2 m³
Dropping the pad 200 mm adds about 115 m³ of cut and removes 65 m³ of fill across the 900 m² site.
Road cross-sections at 20 m
Input
Five sections from station 0 to 80, cut 12.5 to 0 m², fill 0 to 11.8 m²
Output
Prismoidal: cut 343.3 m³, fill 488.0 m³; average end area: cut 351, fill 466 m³
The two methods differ by a few percent. With 10% shrinkage the road needs about 199 m³ of borrow in bank measure.
Background and insight
For a cell of plan area A whose four corners are all in cut or all in fill, the volume is A times the mean corner depth. Summed over a grid, every interior corner counts in up to four cells, which gives the textbook borrow-pit formula V = A/4 (Σh1 + 2Σh2 + 3Σh3 + 4Σh4). A cell that has both cut and fill corners is split with Vcut = A (Σc)² / (4 (Σc + Σf)) and Vfill = A (Σf)² / (4 (Σc + Σf)), where Σc and Σf are the corner depths in cut and fill as positive numbers. The two parts always net to A times the mean signed depth, so the net volume is exact for a planar cell.
Road earthwork is computed from cross-sections. The average end area method V = L (A1 + A2) / 2 is standard in highway practice and tends to overestimate when sections change shape quickly; the prismoidal formula V = L/6 (A1 + 4Am + A2) is exact for a prismoid, and with sections at equal spacing it becomes Simpson's rule. Bank (in-situ) soil swells when excavated, commonly 20 to 30% for common earth and more for rock, and shrinks below its bank volume when compacted in fill, often 10 to 20%. Balancing a site means comparing cut bank volume with fill divided by (1 - shrinkage), not raw cut with raw fill.
Common use cases
Building pads and slabs
Find a pad level that balances cut and fill and avoids paying for import or disposal.
Road and track earthworks
Total cut and fill between cross-sections along a centreline.
Pond and basin excavation
Estimate the volume dug out and the trucks needed to remove it.
Checking contractor quantities
Recompute volumes from the survey grid before agreeing a bill of quantities.
Tips and limitations
- Use a grid fine enough to catch breaks in slope. Volumes assume the ground is a plane between survey points.
- Strip topsoil first and handle it as a separate quantity; it is not suitable fill.
- Add the pavement or slab build-up to the proposed level so the cut is measured to formation, not to finished surface.
- Swell and shrinkage vary widely with soil type and moisture. Use values from a geotechnical report for anything large.
- Average end area is the contractual method on many highway contracts even though the prismoidal rule is more accurate. Check which one your contract uses.
Frequently asked questions
How do you calculate cut and fill volume?
Find the depth of cut or fill at each survey point as existing level minus proposed level. For each grid cell, multiply the plan area by the average corner depth, splitting cells that change sign. Sum the cut cells and the fill cells separately to get the two volumes.
What is the four-point method in earthwork?
It treats each grid cell as a prism with four corner heights and computes its volume as area times the mean height. For cells with both cut and fill corners, it splits the volume in proportion to the squares of the summed cut and fill depths, so both parts are counted.
What is the difference between average end area and prismoidal methods?
Average end area multiplies the distance between two sections by the mean of their areas. The prismoidal formula adds a weighted middle area, L/6 (A1 + 4Am + A2), and is exact for prismoidal solids. Average end area usually overestimates slightly when sections change shape.
What are swell and shrinkage factors?
Swell is the increase in volume when bank soil is dug and loosened, so trucks carry more cubic yards than the hole. Shrinkage is the loss of volume when soil is compacted in fill. Common earth swells about 25% and shrinks about 10 to 15%.
Why does the site need import when cut is bigger than fill?
Because compacted fill needs more than its own volume in bank material. With 15% shrinkage, 1,000 m³ of fill needs 1,176 m³ of bank cut, so a site with 1,100 m³ of cut is still short.
How fine should the survey grid be?
Fine enough that the ground is close to planar inside each cell. 5 to 10 m (15 to 30 ft) grids are common for building pads; uneven ground, ditches and banks need extra spot levels or a surface model.
Is there an in-depth guide to the Cut and Fill Calculator?
Yes. “Cut and Fill Earthwork Volumes: Grid, End Area and Prismoidal” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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