How to Calculate Cut and Fill

How to Estimate Cut and Fill Volumes for Earthworks Projects Introduction On construction projects it is often necessary to modify the existing ground levels to create platforms to build on. Accurately calculating the volumes volumes of soil that must be removed (cut) or added (fill) to create the final f inal ground levels is an essential part of the planning process. In this article we are going to describe how these volumes can be calculated. We will take an example project, and use three of the most common methods to estimate cut and fill volumes. The three methods that we will go through are: 

The cross-section method

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The grid method

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Using specialist software

T he examp example le pr pr oject which will be used i n this thi s article. ar ticle. This is a (fictional) platform being added to Alcatraz I sland sland in San S an Fr F r anci anci sco B ay. ay. T he pr oject oject include includes cut ( shaded shaded r ed) ed) and fi ll (blue ( blue))

The examples described in this article have been worked through for each of these three method with an excel spreadsheet which is available here here.. You may wish to download this spreadsheet and work through the examples yourself to aid understanding of the methods described. The spreadsheet also contains a number of formulas f ormulas which automate certain aspects of these methods described below, so you may find it useful for implementing these methods on your own project.

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©Kubla Ltd 12 Sept 2014

Cross-Section Method The cross section method involves plotting cross sections of the existing and proposed levels at regular intervals across the project site. For each of the cross sections, the cut area and the fill area is determined. The volume between each pair of sections is estimated by multiplying the average cut or fill area of the two sections by the distance between them. Once these volumes have been calculated for each pair of sections the total cut and fill volumes are obtained by adding them all together. There are several different methods used to determine the areas of cut and fill once the sections have been plotted. Perhaps the simplest (but most time consuming) method is to plot the sections on gridded paper and count the grid cells of the cut and fill areas. Multiplying the cell count by the area represented by each of the grid cells gives the cut or fill area for the section. Other methods include drawing the sections in CAD and exporting areas or calculating areas mathematically using the trapezoidal rule. The spreadsheet included with this article includes formulae which have automated the process of calculating section areas using the trapezoidal rule. This can save a great deal of time if you are using the cross section method.

Sections are drawn at equal intervals through the project. For each section line the cut area and the fi ll area is determined. The volume between two sections i s determined as the average area of the two sections multiplied by the distance between them. By adding together the volumes between all of the sections the total cut and fill volumes are obtained.

The accuracy of the cross section method depends to a large degree on the distance you choose to set between the sections. Closer sections improve the accuracy of the estimate, but take longer to estimate. A balance has to be made between accuracy on the one hand, and speed of generating the estimate on the other.

An example calculation for the volumes between two sections of the example shown opposite. This calculation i s repeated for all of the sections, and the values are added together to get the total cut and fi ll volumes.


One of the great advantages of this method is that cross sections are generated in the process. These provide a useful visual summary of the estimation, which present the cut and fill depths across the project in a very clear way. One of the disadvantages off the method is that it can be extremely laborious to extract cross sections from the drawing, and to determine the areas of the sections.


Grid Method The grid method involves drawing a uniform grid onto a plan of the earthworks project, and taking off the existing and proposed ground levels at each node of the grid. With these values the average depth of cut or fill required on each cell of the grid is calculated, and the volume for each cell is obtained by multiplying the depth by the cell area. By adding the volumes for each cell together the total cut and fill volumes for the project can be estimated.

The average cut or fill depths are determined for each cell in the grid. F rom these depths the volumes of each gr id cell can be calculated, and by adding the cell volumes together the total cut and fi ll volumes are obtained

The cut or fill depth for each cell is found by subtracting the average existing level of the cell from the average proposed level. If the resultant depth is positive then this is a fill cell, while a negative value indicates a cut cell. In either case, the volume is calculated by multiplying the cut of fill depth by the area of the grid cell. Once the volume has been calculated for each grid cell, all of the cut cells are added together to obtain the total cut volume. The same is done for the fill cells t o get the total fill volume. As with the cross-section method, the accuracy of the grid method depends upon the size of grid cell which is used. A compromise has to be made between the accuracy which is required, and the time which will be taken to produce the estimate. An advantage of the grid method are that the basis of the estimate can be fully summarised on the site drawings, which presents a very clear summary of the calculations for others to check. One of the disadvantages are no graphical summary is generated for the estimation. Also, like the section method, the grid method is timeconsuming and tedious to implement. An example calculation of the volume for one of the gr id cells in the example on the ri ght



Software Modern computer software allows earthworks volumes to be calculated quicker and more accurately than either of the two manual methods described above. There are a number of software products available for this purpose. These products vary greatly in terms of complexity and price. The first stage of producing an estimate using software is to import the existing terrain. Once this is done the proposed terrain is drawn, and the software automatically calculates the cut and fill volumes required.

A screen shot from K ubla Cubed, which is software for estimating earthworks volumes. As well as calculating volumes automatically, the cut and fi ll depths are shaded. At $190, this is one o the most economical so tware

Different software products use different methods to generate the estimate. Some will essentially apply the grid method described above on a fine-resolution grid, whereas others use a triangulation of the terrain to calculate volumes directly. In any case, the processing power of modern computers means that a high level of accuracy can be achieved in a fraction of the time it would take to produce a manual estimate. There are many advantages to using software to calculate earthworks volumes, and most companies which estimate earthworks on a regular basis will use software to do so. Perhaps the principal advantage of software is that it is much quicker to produce a more accurate estimate when compared with the manual methods described above. Another major advantage is that most modern software products of this type will have useful display options which can be exported for presentations. Shading cut and fill depths across the project is a particularly useful facility. Rightly or wrongly, people tend to be more impressed by computer-generated images than they are by hand calculations, and trust them more. This is particularly important when presenting your estimates to a client as part of a tender. The primary disadvantage of using software to produce estimates is the cost of the software licence, which varies between around $200 to several $1000s. While t his cost should be offset against the time saved by using the software as well as the improved chance of winning bids with computer visualisations, it can nevertheless be a cause of concern for a company that does not need to produce many earthworks estimates.



Summary There are a number of methods available for estimating cut and fill quantities, three of which are described here. The best method for a particular organisation will depend on a number of factors, including: 

The number and complexity of the projects which you need to estimate

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The presentational requirements for the estimation

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The level of accuracy required

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The time you have available to produce the estimate

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The money you have available to buy software licences

This article is written by an employee of Kubla Ltd. who are the makers of Kubla Cubed, a software roduct which is mentioned in this article. This article, including the images, are the copyright of Kubla Ltd. They may be used by educators rovided attribution is given. In all other cases you must c ontact Kubla before using this copyrighted material. The topographic data used in the example in this article is provided courtesy of the NOAA. If you have any feedback on this article please email [email protected]



How to Calculate Cut and Fill

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