How to Calculate Cut and Fill Accurately

How to Calculate Cut and Fill Accurately The Grid method Overview 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. Final thoughts 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. - Ed

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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

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 …. 15x0.5 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 ======================== Calculating Cut and Fill with software

Now both of those by hand methods will get you by if you are just starting out or if you only have to bid a job once in a while. But neither is particularly fast or accurate. If you calculate cut and fill by hand, you’ll be able to do maybe one or two jobs today with accuracy somewhere around 10 to 20%. If you are serious about your work or you need to calculate cut and fill for a lot of bids, you will need to use cut and fill software and a computer. The great thing about using cut and fill software is that it will increase your bidding speed three or four fold. Then instead of doing one bid a day, you’ll be able to crank out four bids in the same amount of time and with tighter numbers. That’s particularly important now when people are having to bid 10 or 20 jobs in order to win a single one. I just can’t tell you how much productivity are going to be using cut and fill software. It’s like night and day difference. I used to spend an entire day or two taking a single sheet. And even then, I was only withing 15% to 10% of the actual numbers. Once I got my first cut and fill program, that time got cut in half. And not only was I faster but I was a lot more accurate. More like 3% to 5%. That allowed us to be a lot tighter with our bids and not always leaving so much money on the table. I’ll tell you, it’s a lot more comfortable putting in a bid knowing how much cut and fill your are going to have versus knowing within 20% what your real numbers are. So, here’s my take on buying software to calculate cut and fill projects: The Pros It’s faster - 3 to 5 times faster. It’s more accurate - 3% to 5% vs. 15% to 20% It makes you far more productive. I can’t stress this enough. It’s easy for other people to check your work. If you are the boss it makes it easier for you to check your estimators work. It’s much easier to update your cut and fill takeoff when change orders come in. It frees up a lot of your time to do more productive and profitable work. And if you have the proper equipment and software, it allows you make a 3-D model to allow automatic grading of your site. The Cons Cut and fill software costs money. You have to learn something new. It is a few days to a few hours of downtime learning a new piece of software. If you are a computer-phobe, you have to learn how to use one.

(As for the cost, it’s really not that big a deal compared to what we get for your money. I’m just amazed the number of people who plead poverty in their business, and yet have the money for a new bass boat, ATV or new giant flatscreen TV.) What to look for when you buy cut and fill software First, decide what you want the software to do for you. Do you want to calculate just cut and fill volumes? Do you needed to figure out material quantities like asphalt, base course and concrete? Do you need to measure areas, length and counts? Then plan to spend between $3000 and $5000 on an on-screen cut and fill program. (an on – screen program will allow you to do your takeoff directly from a PDF right on your computer screen) If you’re working from paper plans, then plan to spend an extra $2300-$2800 on a digitizer board. These are large electronic drafting boards that allow you to trace information from the paper plan into the software. These used to be all the rage, but now with onscreen takeoff PDFs, they are not used that much anymore. If you’re definitely going to be using GPS hardware on your equipment, then plan between spending $8000 and $20,000 on your cut and fill software. Make sure to work closely with your GPS equipment supplier so that you get exactly the right software to use their equipment. It’s especially smart to buy all of your software and hardware from one company and that way when something goes wrong (because it will) only one company will be responsible to fix it. You don’t want to companies pointing at each other’s hardware or software and saying “Hey, it’s the other guy’s problem!” Recommendations Paydirt - If you need to generate 3-D models for your machine control grading systems, then you should get both equipment and software from Trimble. that would be both the Paydirt software and GCS 900 grade control systems. The Paydirt software runs between $8000 and $10,000. If you’re using AutoCAD drawings make sure to get the TerraModel software as well. That software is required to import and correct the AutoCAD files. EarthWorks - If you need an affordable and straightforward program to figure your cut and fill material quantities from on-screen drawings or paper plans, then get EarthWorks from www.Trakware1.com. It is a very straightforward and easy to use program with lots of built-in help. I got up and running just a couple hours, and was cranking outbid by the end day. As I recall, they start around $3500. Copyright, 2010 Edward Kenney at http://www.calculatecutandfill.com/. All rights reserved