Cut and Fill Calculations: Grid and Section Methods

Cut and fill calculations tell you how much earth has to come off the high spots, how much has to go onto the low spots and whether you will have dirt to haul away or need to bring some in. They drive the price of nearly every site job, from a house pad or driveway to a parking lot or road. This guide covers the two hand methods most people use, the grid method and the average end area method, then the swell and shrink factors that turn ground volume into truckloads and tons.

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Start with the right elevations

Every method compares two surfaces:

Existing grade: the ground as it is now, from a survey, drone model or careful level shots.
Proposed subgrade: where the dirt needs to end up. This is finished grade minus whatever goes on top: asphalt, base stone, a slab and its stone, or topsoil.

Where existing is higher than proposed, you cut. Where it is lower, you fill. If topsoil gets stripped first, handle it as its own volume, since it should be stockpiled for reuse, not buried under fill.

The grid method

The grid method suits pads, lots and other broad areas.

Lay a grid of equal squares over the site, such as 25 × 25 feet. Smaller squares give better accuracy on uneven ground.
At each grid corner, subtract proposed subgrade from existing grade. Positive numbers are cut depth, negative are fill depth.
For each square, average the four corner depths and multiply by the square's area.
Add up the cut cells and the fill cells separately. Divide cubic feet by 27 to get cubic yards.

Worked example: a 25 × 25 foot square (625 square feet) has corner cuts of 1.2, 0.8, 1.0 and 0.6 feet. The average is 0.9 feet, so the cut is 0.9 × 625 = 562.5 cubic feet, about 20.8 cubic yards.

Now picture a pad made of four such squares with average depths of 0.9, 0.6 and 0.3 feet of cut and 0.2 feet of fill. Cut is (0.9 + 0.6 + 0.3) × 625 = 1,125 cubic feet, about 41.7 cubic yards. Fill is 0.2 × 625 = 125 cubic feet, about 4.6 cubic yards. That site has plenty of extra dirt to move off.

Squares where some corners are cut and some are fill need extra care, because simple averaging blurs the two. Split them into smaller squares or triangles for a better answer.

The average end area method

For roads, driveways, ditches and other long jobs, cross sections work better than a grid.

Pick stations along the centerline, often every 25 to 100 feet, plus extra wherever the ground changes sharply.
At each station, draw the existing ground and the proposed section and measure the cut area and fill area in square feet.
Between two stations, volume = (area 1 + area 2) ÷ 2 × distance.
Add all the segments and divide by 27.

Worked example: cut areas of 40 and 60 square feet at stations 50 feet apart give (40 + 60) ÷ 2 × 50 = 2,500 cubic feet, about 92.6 cubic yards.

The method tends to run slightly high where a section shrinks to a point, and the more exact prismoidal formula corrects for that on big jobs. Design software such as civil grading programs builds surface models and compares them directly, but checking its totals with a quick hand method catches input mistakes.

Swell and shrink factors

Soil does not keep the same volume from the ground to the truck to the finished pad.

Bank yards are measured in the ground. Your cut and fill math gives bank or compacted yards, not truck yards.
Loose yards are what fills a truck. Dug soil fluffs up, so loose yards = bank yards × (1 + swell).
Compacted yards are what you end up with after rolling. Many soils end up tighter than they were in the ground, so compacted yards = bank yards × (1 − shrink).

Factors vary a lot by soil and moisture. Often-quoted planning ranges put swell at roughly 10 to 15 percent for sand and gravel, 20 to 30 percent for common earth, and more for clay and much more for blasted rock. Use your geotechnical report or contractor experience when you have it.

Example: the 92.6 bank yards above, at an assumed 25 percent swell, is about 116 loose yards to haul. If your trucks carry 12 loose yards each (check your actual trucks), that is about 10 loads. On the fill side, if you need 100 compacted yards and the soil shrinks an assumed 10 percent, you need about 100 ÷ 0.9 = 111 bank yards of cut or borrow.

From yards to tons and truckloads

Imported fill and haul-off are often priced by the ton. Our how much a yard of dirt weighs guide puts dry, loose dirt near 1 ton per yard and damp or clay-heavy dirt at 1.2 to 1.5 tons. Truck limits are covered in how many tons of gravel in a dump truck, and smaller jobs moved by machine can use how much a skid steer bucket holds.

Once the dirt work is figured, the layers that go on top have their own volumes. The topsoil calculator, gravel calculator and asphalt base calculator handle those.

Common mistakes

Grading to finished grade instead of subgrade.
Forgetting topsoil stripping and respreading.
Mixing bank yards with loose truck yards.
Using a grid too coarse for rolling ground.
Assuming unsuitable cut soil, such as wet clay or organic soil, can be reused as fill.

Questions people ask

How do you calculate cut and fill?

Compare existing ground elevations with proposed elevations at many points, find the depth of cut or fill at each, and turn those depths into volumes with the grid method or the average end area method. Divide cubic feet by 27 for cubic yards.

What is the grid method for cut and fill?

Lay a grid of equal squares over the site, find the cut or fill depth at each corner, average the four corners of each square and multiply by the square's area. Add up all cells for total cut and total fill.

What is the average end area method?

Measure the cut and fill area on cross sections spaced along a road or trench, average each pair of neighboring areas and multiply by the distance between them. It is the standard quick method for long, narrow jobs.

What are swell and shrink in earthwork?

Soil dug from the ground fluffs up and takes more room in a truck, which is swell. Once spread and compacted it usually ends up tighter than it was in the ground, which is shrink. Both change how many truckloads and how much borrow a job needs.

What is a balanced site?

A site where the cut, after shrink is accounted for, roughly equals the fill needed, so little soil has to be hauled in or out.

Do I subtract the pavement or slab thickness?

Yes. Grading targets subgrade elevation, which is finished grade minus the thickness of pavement, base, slab or topsoil. Forgetting this is one of the most common reasons cut and fill numbers come out wrong.

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