# How to calculate backfill for a pipe trench

Getty Creative

Filling a trench in an efficient way requires knowledge of the volume of material needed. In a simple trench, this is straightforward, but pipes and cables occupy space in the trench and reduce the volume.

To avoid buying an excess of backfill it is necessary to subtract the volume of the pipes from the overall trench volume. With the aid of a calculator, this is process requires basic math skills.

Measure the length of the trench at the top and at the base. Compare the first and second measurements. If they differ, find the average by adding them together and dividing by two. Record this value for later use.

- Filling a trench in an efficient way requires knowledge of the volume of material needed.
- In a simple trench, this is straightforward, but pipes and cables occupy space in the trench and reduce the volume.

Measure the width and depth of the trench at regular intervals along its length, recording the data as you progress along the trench. Add together the individual width measurements and divide by the number of measurements taken. This produces the mean average width of the trench. Repeat the process with the depth measurements to ascertain the average depth.

Calculate the volume of the trench using the formula; volume = length x width x depth. For example, the volume of a 10 m long trench, 80 cm wide and 1m deep is 10 x .8 x 1 = 8 cubic metres.

Measure the circumference of the pipe. Divide the circumference by pi, 3.1415, to find the diameter. Halve the diameter to establish the radius, and express it in centimetres. For example, the radius of a pipe with a circumference of 90 cm is 28.7 cm.

- Measure the width and depth of the trench at regular intervals along its length, recording the data as you progress along the trench.
- Add together the individual width measurements and divide by the number of measurements taken.

Calculate the volume of the pipe, a cylinder, using the formula: volume = pi x (radius x radius) x length of the cylinder. For example, the volume of a 10 metre long pipe with a radius of 28.7 cm is 2.46 cubic metres.

Subtract the volume of the pipe from the volume of the trench to ascertain the volume of backfill required. In the previous example, the backfill volume is 8 - 2.46, or 5.54 cubic metres.

References

- Building Green: A Complete How-To Guide to Alternative Building Methods; Clarke Snell and Tim Callahan
- Pennsylvania State University: Area and volume formulas
- Cerritos College: Circumference of a circle

Tips

- If a rectangular protective cover is placed over the pipe, calculate the volume of the cover, not the pipe.

Writer Bio

David Robinson has written professionally since 2000. He is a Fellow of the Royal Geographical Society and the Royal Meteorological Society. He has written for the "Telegraph" and "Guardian" newspapers in the U.K., government publications, websites, magazines and school textbooks. He holds an honors Bachelor of Arts in geography and education and a teaching certificate from Durham University, England.