How to use the average end area earthwork volume calculator
- Choose feet or meters for the distance along the line.
- List each cross section in order: its distance along the line, its cut area and its fill area.
- Add rows for more stations. Each one must be farther along than the one before.
- Read the cut, fill and net volumes, the table between stations and the running net.
Formula
Volume between two stations = (A1 + A2) / 2 x L
A1 and A2 are the end areas and L the distance between them
Cubic yards = cubic feet / 27 when the lengths are in feet
Running net = sum of (cut - fill) from the first station
Cut and fill are added separately. The method treats the ground between two sections as a prism whose volume is the average of the two ends times the length.
Three stations, 50 feet apart
Stations at 0, 50 and 100 ft have cut areas of 0, 120 and 80 square feet and fill areas of 40, 10 and 0. From 0 to 50 ft the cut is 3,000 cubic feet (111.11 cubic yards) and the fill 1,250 (46.30 cubic yards). From 50 to 100 ft the cut is 5,000 and the fill 250. In total there are 296.30 cubic yards of cut and 55.56 of fill, a net of 240.74 cubic yards of extra soil.
In meters, four stations 20 m apart with cut areas 12.5, 18, 6 and 0 and fill areas 0, 3.5, 9 and 14 give 605 cubic meters of cut and 390 of fill, a net of 215 cubic meters. The running net after each segment is 270, 385 and 215.
Cut, fill and balance
A cut is where ground is dug out to reach the planned level and a fill is where soil is added. When the cut is larger than the fill the extra soil has to be taken away. When the fill is larger, soil must be brought in. The running net in the table is the ordinate you would plot on a mass diagram, where a rising line shows excess soil and a falling line shows a shortage.
For simple shapes use the excavation volume calculator and the tank volume calculator. The sections themselves come from levels, which you can reduce with the differential leveling calculator, and roads from the horizontal curve calculator.
How accurate is the method
The average of two end areas slightly overstates the volume when the areas are very different, because the ground between them is not a true prism. Closer stations reduce the error. Soil also swells when it is dug and shrinks when compacted, so a haul plan multiplies the volumes by factors for the soil involved. Those factors are not applied here.
Assumptions and limits
- Cross-section areas are in square feet or square meters and are measured square to the centerline.
- The ground between two stations changes in a straight way from one section to the next.
- Swell, shrinkage and the prismoidal correction are not applied.
- Stations must increase, and areas cannot be negative.
Frequently asked questions
How do I calculate earthwork volume?
Average the cut areas at two stations and multiply by the distance between them. Do the same for fill. Add up all the segments.
What is the average end area method?
It estimates the volume between two cross sections as the mean of their areas times the distance. It is a standard hand method for roads and grading.
How do I convert cubic feet to cubic yards?
Divide by 27, because a cubic yard is 3 feet by 3 feet by 3 feet. The page does this for you when you pick feet.
What does a positive net mean?
It means more cut than fill, so there is extra soil to move away. A negative net means soil must be brought in.