Calculating Earthworks Cut & Fill With A Spreadsheet | Grid Method

The grid method allows you to estimate the cut and fill volumes of an earthworks project by rationalising the site into a grid of cells. Cut and fill for each cell can be calculated separately and then each fill cell can be added together and each cut cell, to get the total cut and fill. 

Each grid cell volume is estimated using the formula:

V_i = A_{i *} (P – E)

The volume (V) of a grid cell (i) equals the area (A) of the cell multiplied by the difference between the average existing ground (E) and the average proposed ground (P) levels.

E = The average of the existing elevation at the four corners of the cell.

P = The average of the proposed elevation at the four corners of the cell.

(P – E) = The difference between the existing and the proposed

Multiply by the area (A) of the grid cell (i)

Then all the cells that have negative difference (cut) are added together to find the total cut volume and all the sells with a positive difference (fill) are added together to find the total fill volume. 

To find the Net Volume, the total Cut is subtracted from the total Fill to find the difference for the whole site.

What the Spreadsheet Does

As the above formula will need to be repeated 10’s if not 100’s of times to get an estimate it is a good idea to use a spreadsheet for the calculations. 

The spreadsheet : 

• Calculates the difference between E and P for each vertex.  This is written in grey in each defined cell.
• Shades the cell. When the difference is a positive number it turns Blue for Fill and when it is negative it turns Red for Cut.
• Calculates average Cut/Fill of every 4 vertices. This is shown in the second grid, that you can view when you scroll across to the right of the sheet. WARNING: Do not edit this second grid, it may remove the formulae needed to generate the calculations. 
• Calculates the overall total Cut, Fill and Net Volume. These are shown in the Results table. 

1. Print the Site Plan :  Print a copy of the site plan ensure it has existing and proposed levels defined.  These are known as ‘grading plans’

2. Decide on the units and scale of your Grid Squares :  My plan is in metric units so I have used centimetres (cm) for the grid. It should be written on the plan what scale it is.  You need to decide how large you want each grid cell to be and then calculate using the scale the dimensions of the grid squares in paper space.  For instance if the plan is 1:200 and you want grid squares of 0.5m in the real world then your grid squares will need to be 2.5cm in paper space as 2.5cm x 200 = 500cm (0.5m). 

When you are deciding the size of your grid squares, it is important to consider the trade off between dense grids that are more accurate but are potentially very time consuming to complete and larger grids that are less accurate and faster.  This topic is discussed in more detail in the article : How Accurate is the Grid Method For Calculating Earthworks Cut & Fill Volumes?

3. Draw the grid :  Once you have established the size of each cell you need to draw a grid over your whole site. A roller ruler can be a handy tool for this but a standard ruler works just fine also.

Rather than drawing a grid directly over the site plan it is a good idea to do it over an semi transparent sheet like acetate.  This way you can make mistakes and don’t have to print another site plan.  Another options is to print the grid by downloading a template offline.     

4. Label the Grid Lines : You also need to label the X axis lines (not the cells) from A – Z and the Y axis lines from 1 ..2…3 so the cells correlate to cells in the spreadsheet we are using to do the calculations.

5. Record the elevations .  Once you have established a grid and have it overlaid on your site plan you need to take off the existing (E) and proposed (P) levels and write them next to each vertex for every grid square.  An example, showing one way to do this, is in the photo. It is key to use your fine pen or pencil here to ensure you can fit in the two levels and so they remain legible.

In this example, the elevations are indicated on the plan using contour lines.  You will find that plans usually have contours or points but sometimes other elevation features like building pads or slopes.  As a result it will often be the case that there is not an exact elevation at the intersection lines of the grid cells.  Therefore you have to extrapolate as best you can.  For instance if a point lies between two contour lines you can just take the mid point between them.  It is not always easy but it is an estimate after all, sometimes you have to use your knowledge of site visits and photos to guess elevations that aren’t always clearly marked at the grid intersection points.