Cross-section method

How to Calculate Cut and Fill by the Cross-Section Method

Now the cross-section method is not my most favorite method for calculate cut and fill volumes but some of my colleagues like it and it is one of the widely accepted ways to calculate cut and fill so I’m going to go ahead and teach it here anyway.

Overview

How the cross-section method works is that you draw a series of equally spaced horizontal lines across our site. And then for each cross-section you are going to plot out, on graph paper, a graph that shows the distance from the left edge of the drawing on the horizontal axis versus both the proposed and existing elevations on the vertical axis. We will then use the graph to figure out the calculate the cut area and fill area for each cross-section. Once we’ve completed every cross-section, we will use the cut areas and fill areas and the distance between each cross-section to calculate cut and fill volumes for each pair of cross sections and then add them up for the whole job.

Tools you’ll need

A large flat surface bigger than your plan
36 inch T-square, Fairgate T36T
11 x 17 graph paper, Staples #814566
24 inch engineer scale, Fairgate TE24
A pencil (preferably mechanical)
A calculator or spreadsheet

Step 1 – Cross-sectioning the drawing

First find a nice stable surface to place your drawing such as a large desk, drafting table or your dining room table (sorry Mrs. Reader) and lay the drawing out nice and flat.

Then take your T-square and draw a series of horizontal lines across your drawing. They should be equally spaced and in multiples of your drawing scale. (That will make the math easier.) The number of cross-sections required depends on how busy the drawing is. Simple drawings require fewer cross-sections, more complex drawings require more cross-sections. It all depends on how accurate you want your estimate to be and how much time you are willing to spend doing the estimate.

Step 2 – Prepare your graph paper

Using your engineer’s scale, determine the total width of your drawing in feet. Now find your drawing scale in the table below. Look to the right to find the number of feet per grid square to use on your 11 x 17” paper.

Drawing Scale  vs.   Feet per grid square on a 36” wide drawing and on 17” wide paper

1:10            5’
1:20            10’
1:30            15’
1:40            20’
1:50            25’
1:60            30’
1:80            40’
1:100            50’
1:200            100’

Along the bottom of your page, draw the horizontal axis and mark the distance every four grid squares. For example, if I had a 30 scale drawing, the width of each grid square would be 15 feet.

For the vertical axis, you will need to determine the number of feet per grid square. To do that, examine the drawing and find both the lowest and highest elevations. Find the difference between those two elevations and divide it by 40 (the usable number of grid squares on the 11 inch side of the drawing). Round that number down to get a usable distance for each vertical grid square. For example, if the high elevation was 77 and low elevation was 51, the difference between the elevations would be 26. Dividing 40 into 26’ gives us 0.65’/grid square. Using 0.65 would be an awkward number so let’s rounded it down to 0.5. That means our vertical scale is 0.5 feet per grid square.

Now draw the vertical scale and mark the elevations every four grid squares.

And finally, reproduce this graph on enough new sheets of graph paper that you have one for every cross-section that you’ve drawn across the drawing.

Step 3 – Determine the area of each grid square

To calculate cut and fill volumes later, we will need to know the area, in square feet, represented by each grid square. To determine that, multiply the grid cell’s width in feet by its height in feet. In the example in Step 2 above, the grid square was 15 feet across horizontally and 0.5 feet vertically. Multiplying that out …. 15×0.5 gives us 7.5 square feet for each grid square.

Step 4 – Graph the existing surface

Lay your engineer’s scale on the first cross-section with the zero mark on the left edge of the drawing and determine the distance to your first existing elevation. Mark that elevation and distance on your graph paper. Repeat for each existing elevation that crosses that horizontal cross-section line. Once you reach the end of the line, go to each of the points you plotted and draw a line between them to show the existing surface.

Step 5 – Graph the proposed surface

Go back to the beginning of the horizontal line and determine the distance to your first proposed elevation. Mark that elevation and distance on your graph paper. Repeat for each proposed elevation that crosses the horizontal cross-section line. When you reach the end of the line go back to the points you plotted and draw a line between them to show the proposed surface.

Step 6 – Determine the cut area

Now on each graph, find the section or sections where the existing surface is above the proposed surface. Count the total number of full and partial squares in each of those sections. Then multiply the total number of grid squares you counted by the area of the grid square you determined in step 3 and record that on the graph paper. For example, if you found 27.2 grid squares of cut, the total cut area would be 27.2 X 7.5 = 204.0 square feet of cut area.

Step 7 – Determine the fill area

Now find the section or sections were the proposed surface is above the existing. Count the total number of full or partial grid squares. Then multiply the total number of grid squares of fill by the area of a grid square and record that on the graph paper. For example, if you found 129.1 grid squares of fill, the total fill area would be 129.1 X 7.5 = 968.25 square feet of fill area.

Step 8 – Repeat steps 4 through 7 for each of the remaining horizontal cross-sections

Using a new graph paper sheet for each horizontal cross-section repeat steps 4 through 7.

Step 9 – Determine the cut volume

For each adjacent pair of cross-sections, add the two cut areas together. Now divide that number by two to determine the average cut area. Finally, multiply that average cut area by the distance between the two cross-sections. That’s your cut volume for that pair of cross-sections.

Repeat this for each cross-section.

Step 10 – Determine the fill volume

For each adjacent pair of cross-sections, add the two fill areas together. Now divide that number by 2 to determine the average fill area. Finally, multiply that average fill area by the distance between the two cross-sections. That’s your fill volume for that pair of cross-sections.

Repeat this for each cross-section.

Step 11 – Determine the total cut volume

Add up all the cut volumes you just calculated to determine your total cut volume.

Step 12 – Determine the total fill volume

Add up all the fill volumes you just calculated to determine your total fill volume.

Step 13 – 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.

Some final thoughts

Now do you see why I prefer to use the grid method? If you have your cross-sections fairly close together, this method can be a very accurate way to calculate cut and fill. But it’s also very tedious and requires a lot of attention to detail. And because the cross-sections are not shown directly on the plan is very hard to double check your work.

But some people swear by it… Go figure!

- Ed

PS: If you’d like to download my PDF of  “How to Calculate Cut and Fill Accurately”, fill in the form below:

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