Footings are the foundations of a building so they must be strong under compression. Concrete has excellent compressive strength and is easily poured on site, so it is the material of choice for filling footing trenches. The expense associated with footings increases as more concrete is required. Accurate estimation of the volume of concrete required reduces costs and, at the same time, assists project management by ensuring that sufficient concrete is available when it is needed.
Things You'll Need
 Tape measure

Measure the length of the footing trench. If the footings consist of more than one trench, measure each separately. Record the measurements for later use.

Measure the depth of the footing trench. If the trench slopes or has an uneven depth, measure it at several points along its length. Add the depths together and then divide by the number of measurements to calculate the average depth. For example, a sloping trench with four depth measurements of 4 feet, 6 feet , 5 feet and 9 feet has an average depth of 6 feet: (4 + 6 + 5 + 9) / 4 = 6.

Measure the width of the trench at regular intervals along the length. Sum the individual widths and divide by the total number of measurements. The result is the average width.
For example, a trench with width measurements of 3 feet, 3.5 feet, 3.25 feet and 2.75 feet has an average width of 3.125 feet. 
Calculate the volume of the footing by multiplying the length by the average depth by the average width. The result is the volume expressed in cubic feet. For example, a footing 40 feet long, with an average depth and width of 6 feet and 3.125 feet has a volume of 750 cubic feet: 40 6 3.125 = 750

Divide the volume in cubic feet by 27, the number of cubic feet in one cubic yard, and round the result up to the next nearest whole cubic yard. The result is the number of cubic yards of concrete required to fill the footing. To conclude the example, a footing trench with a volume of 750 cubic feet requires 28 cubic yards of concrete because 750 / 27 = 27.78.
Tips & Warnings
 Try to cut footing trenches as precisely as possible to avoid large differences in width or depth.
 If a trench varies widely in width or depth, break the trench into smaller sections and calculate the width, depth and length for each different size section. Combine the results to obtain the overall volume.
 Work safety in trenches. Deep trenches with inadequate side support may collapse and trap you.
Related Searches
References
 University of Missouri Extension; Concrete Basement Construction; oseph M. Zulovich
 "Building Green: A Complete HowTo Guide to Alternative Building Methods"; Clarke Snell and Tim Callahan; 2005
 College of Saint Benedict and Saint John's University: Descriptive Statistics
 Pennsylvania State University: Area and Volume Formulas
 Washington State University; Math for Gardeners; Joan Helbacka; September 2002
 Photo Credit Kim Steele/Photodisc/Getty Images