How to Calculate Cut and Fill by the Grid Method
In the grid method, we are going to calculate cut and fill by dividing our site plan into equally sized grid cells and then calculating the cut or fill volume in each cell. We’ll do this by drawing sets of horizontal and vertical lines at equally spaced intervals across the plan. Then for each corner of every grid cell we will determine both the existing elevation and proposed elevation at that point. The difference between the two will be the cut or fill depth for that point. Positive differences will be fill and negative differences will be cut. Once we’ve determined the cut or fill depth for every corner, we’ll add up the cut or fill numbers for each of the four corners, average them, then multiply that number by the number of square feet in the grid cell and then finally dividing that number by 27 to calculate cut and fill in cubic yards for that grid cell. Then for every grid cell, we’ll add up all of the cuts and all of the fills separately. These are the total cuts and fills for the site. The difference between those two numbers is the import or export of dirt from the site.
Tools you’ll need
A large flat surface bigger than your plan
36 inch T-square, Fairgate T36T
A pencil (preferably mechanical)
A calculator or spreadsheet
Step 1 – Gridding off the drawing
Take your site plan and lay it on a large flat surface like a drafting table, a large desk, or your home’s dining room table. (Sorry Mrs. Reader)
With a large T-square, draw a series of equally spaced Coors auto and vertical lines across your drawing. The lines should be spaced in multiples of your drawing scale.
The spacing you choose should strike a balance between speed and accuracy. The smaller the grid cells, the more calculations will need be performed but the higher the accuracy. The larger the grid cells, the fewer calculations will need to be performed the lower the accuracy will be. A good compromise is to base the spacing on the average complexity of the job site. In more complex areas the grid cells can be further subdivided so as to increase the accuracy in those portions of the drawing.
Step 2 – Calculating the existing elevations
For the corner of each grid cell, determine the existing elevation.
To do this accurately, take a scale and find the shortest distance between two contours that form a line crossing through your corner. Use the ratio of the distance between the contours and the distance from one contour to your corner to determine the elevation at the corner. For example, if one contour is 70 feet, the next contour is 72 feet, the distance between the contours is 15 feet and the distance from the 70 foot contour to the corner is 12 feet than the math looks like this,
(First contour elevation – second contour elevation) * (distance from first contour to corner / distance from first contour to second contour) + elevation of first contour = corner elevation
Using the numbers in our example, (72 – 70) * 12 / 15 + 70 = 2 * 0.8 + 70 = 1.6 + 70 = 71.6.
If you’re stripping topsoil from the site, make sure to reduce the existing elevation by the thickness of the topsoil strip.
Step 3 – Calculating the proposed elevations
Repeat step 2 above for all your proposed elevations. If your re-spreading topsoil or adding parking lot and building pads, make sure to reduce the proposed elevation by the thickness of the topsoil re-spread or other man-made materials.
Step 4 – Calculating the cut and fill depths
For the corner of each grid cell, subtract the existing elevation from the proposed elevation. Positive quantities are fill. Negative quantities are cut.
Step 5 – Calculating the average cut/fill depth
For each grid cell, add the four corner cut or fill depths together and divide that sum by 4.0 to calculate the average cut or fill depth for that grid cell.
Step 6 – Calculating the cut or fill volume for each grid cell
For each grid cell, calculate the total cut or fill volume by multiplying the average cut or fill depth by the area of the grid cell. (To determine the area of the grid cell, multiply the length of one horizontal side by the length of one vertical side). Finally, divide this number by 27 in order to calculate cut and fill in cubic yards. Negative volumes are cut. Positive volumes are fill.
Step 7 – Calculate cut and fill volumes for the entire site
Determine the total cut for the site by adding up all of the negative volumes in every grid cell on the drawing. (You can record the cut as a positive number at this point.) Then determine the total fill for the site by adding up all the positive volumes in every grid cell on the drawing.
Step 8 – Calculating the import or export from the site
To determine the export from the site, subtract the fill from the cut. If the result is positive, this is the volume of soil that must be exported from the site. If the result is negative, this is the volume of soil that must be imported to the site.
Call me simple but I like this method more than the cross-section method. I like it because all of my numbers are right on the drawing and it’s easy for anyone to see my math. It’s very boring to do (I like to listen to books on tape while I do all the calculations) but very reliable.
PS: If you’d like to download my PDF of “How to Calculate Cut and Fill Accurately”, fill in the form below: