Enter the area of the lower and upper portions of the footing and the height of the trapezoid into the calculator to determine the volume. This tool also solves for any missing variable when three of the four values are known.
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Trapezoidal Footing Volume Formula
The following equation is used to calculate the Trapezoidal Footing Volume.
V = \frac{H}{3}\left(A_1 + A_2 + \sqrt{A_1 A_2}\right)- Where V is the Trapezoidal Footing Volume
- H is the height of the footing (vertical distance between the lower and upper faces)
- A1 is the area of the lower (larger) base
- A2 is the area of the upper (smaller) base, where the column sits
This formula is the prismoidal formula applied to a frustum. It works for both square and rectangular base shapes. For a square lower base of side length a and a square upper base of side length b, the areas are simply A1 = a² and A2 = b².
What is a Trapezoidal Footing?
A trapezoidal footing is a spread footing with sloped sides that taper from a wider base at the bottom to a narrower top where a column or wall bears on it. Geometrically, it forms a frustum, which is a truncated pyramid. The wider base distributes the structural load across a larger soil contact area, while the tapered profile uses less concrete than a rectangular footing of the same base dimensions and depth.
This footing type appears in both residential and commercial construction. It is common under isolated columns, along property lines where the footing cannot extend symmetrically, and in combined footings carrying two columns with unequal loads. Building codes typically require that the bottom of the footing sit below the frost line, which ranges from 12 inches in the southern United States to over 60 inches in northern states and Canada.
Worked Example
A column footing has a 5 ft x 5 ft lower base, a 2 ft x 2 ft upper base, and a height of 1.5 ft. Find the concrete volume.
A1 = 5 x 5 = 25 ft², A2 = 2 x 2 = 4 ft²
V = (1.5 / 3) x (25 + 4 + sqrt(25 x 4)) = 0.5 x (25 + 4 + 10) = 0.5 x 39 = 19.5 ft³
Converting to cubic yards: 19.5 / 27 = 0.722 yd³. At a standard 10% waste factor, you would order roughly 0.80 yd³ of ready-mix concrete for this single footing.
Volume and Concrete Reference Table
The table below shows calculated volumes and approximate concrete quantities for common trapezoidal footing sizes. All footings use a height of 1.5 ft. Concrete weight assumes 150 lb/ft³ (normal-weight concrete). The 80 lb bag column uses standard pre-mixed bags at 0.6 ft³ per bag.
| Lower Base (ft) | Upper Base (ft) | Volume (ft³) | Volume (yd³) | Weight (lb) | 80 lb Bags |
|---|---|---|---|---|---|
| 3 x 3 | 1.5 x 1.5 | 7.88 | 0.29 | 1,181 | 14 |
| 4 x 4 | 2 x 2 | 14.00 | 0.52 | 2,100 | 24 |
| 5 x 5 | 2 x 2 | 19.50 | 0.72 | 2,925 | 33 |
| 5 x 5 | 3 x 3 | 24.50 | 0.91 | 3,675 | 41 |
| 6 x 6 | 2.5 x 2.5 | 28.62 | 1.06 | 4,294 | 48 |
| 6 x 6 | 3 x 3 | 31.50 | 1.17 | 4,725 | 53 |
| 8 x 8 | 3 x 3 | 48.50 | 1.80 | 7,275 | 81 |
| 4 x 6 | 2 x 3 | 21.00 | 0.78 | 3,150 | 35 |
| 5 x 8 | 2 x 3 | 30.75 | 1.14 | 4,613 | 52 |
Concrete Savings vs. Rectangular Footings
A rectangular (flat-sided) footing with the same base and depth uses a volume of simply Base Area x Height. For the 5 ft x 5 ft example above, that gives 25 x 1.5 = 37.5 ft³. The trapezoidal version at 19.5 ft³ uses 48% less concrete. The actual savings depend on the ratio of upper to lower area and the footing height. As a general guide, trapezoidal footings save between 30% and 55% of concrete compared to a rectangular footing of the same footprint and depth, with greater savings when the upper base is much smaller than the lower base.
When to Use Trapezoidal Footings
Trapezoidal footings are preferred in several situations. They are used under isolated columns when the footing depth exceeds about 12 inches, as the sloped sides eliminate unnecessary concrete in the outer portions where shear and bending stresses are low. They are also used in combined footings that support two columns with different loads, where the trapezoidal plan shape shifts the centroid of the footing to align with the resultant of the column forces. Property-line conditions are another common case. When a column sits at or near a property boundary, the footing cannot extend beyond the lot line, and a trapezoidal shape allows the wider portion to extend inward while keeping the outer edge flush.
Soil bearing capacity also drives the choice. On weaker soils (bearing capacity below about 1,500 lb/ft²), footings need larger base areas. The trapezoidal profile delivers that contact area without the full material cost of a rectangular section. On competent rock or dense gravel with bearing capacities above 4,000 lb/ft², the footing can be smaller overall and the taper becomes less critical.
Structural Geometry of the Footing
A trapezoidal footing can be thought of as two stacked shapes: a rectangular slab (cuboid) at the top equal to the column pedestal area times its height, and a truncated pyramid below it. The prismoidal formula V = (H/3)(A1 + A2 + sqrt(A1 x A2)) accounts for both regions in a single calculation. This is mathematically equivalent to splitting the footing into the cuboid and frustum and summing the two volumes separately, but the single formula avoids the need to measure intermediate dimensions.
For rectangular (non-square) bases, A1 = length1 x width1 and A2 = length2 x width2. The geometric mean term sqrt(A1 x A2) corrects for the changing cross-section along the height. If the upper and lower bases are identical (A1 = A2), the formula reduces to V = H x A, the simple volume of a prism, confirming it as a generalization of the rectangular case.
