Concrete footings spread column loads over enough ground area to keep bearing pressure within safe limits. When a column carries a heavy load and the base must be large, a flat slab of uniform thickness becomes wasteful, because the outer parts of the slab need little depth. A trapezoidal footing, also called a sloped or truncated pyramid footing, tapers from a wide base up to a smaller top that matches the column. The sloped shape saves concrete while still transferring the load, and its volume can be worked out with a standard formula. Where columns sit close together, the combined footing design with example and types of combined footing explains the alternative used when individual pads would overlap.
What Is a Trapezoidal Footing?
A trapezoidal footing has two rectangular faces: a bottom base of length A and breadth B, and a smaller top of length a and breadth b, joined by sloping faces. In section it looks like a trapezoid, which is where the name comes from. The column bears on the top face, and the slope spreads the load out to the wider base, so the soil pressure stays as uniform as the stiffness of the footing allows.
The shape is a standard solution for isolated columns under moderate to heavy loads. Compared with a prismatic pad of the same base size, it removes concrete that carries little stress. The sloped trapezoidal footing volume formula treats the shape in two parts: the rectangular base slab and the truncated pyramid above it. The two parts are computed separately and added, and the same geometry guides the reinforcement layout.
Why Use a Sloped Shape?
The slope keeps the bending moment capacity roughly proportional to the demand. Near the column the section is deep, so the footing resists the maximum moment; near the edges the section is shallow because little moment remains. The result is a footing that uses less concrete and less steel than a uniform pad of the same base, at the cost of slightly more complex formwork and a slope that is harder to finish.
The saving is easy to overstate, so the numbers matter. A flat 1.5 m by 1.5 m pad with a uniform thickness of 0.9 m needs about 2.03 m3 of concrete. The sloped version with a 0.3 m base slab and a 0.6 m sloped portion needs about 1.31 m3, a reduction of roughly 35 percent for the same base size. The steel saving is smaller, but the concrete saving alone usually justifies the extra formwork cost.
The Trapezoidal Formula
The volume of the sloped portion is calculated with the prismoidal formula: V = h/3 x (A1 + A2 + sqrt(A1 x A2)), where A1 is the area of the bottom face, A2 is the area of the top face, and h is the vertical height between them. The formula is exact for a truncated pyramid with parallel rectangular faces, so it applies to any size of footing. For a second worked example, the article that shows how to calculate concrete volume for a trapezoidal or sloped footing walks through the same expression with different dimensions.
Units must be consistent. If the dimensions are in meters, the volume comes out in cubic meters; if they are in feet, the volume comes out in cubic feet. Mixing units is the most common error in footing takeoffs, so the drawing should state the unit once and the calculation should keep it throughout.
Understanding Each Term
- A1 = bottom area = length A x breadth B
- A2 = top area = length a x breadth b
- h = vertical height of the sloped portion
- sqrt(A1 x A2) = geometric mean of the two end areas
Where the Formula Comes From
The expression h/3 x (A1 + A2 + sqrt(A1 x A2)) is the standard volume of a frustum of a pyramid. When the top area equals the bottom area, it reduces to A x h, the volume of a prism. When the top area is zero, it reduces to one-third of the base area times the height, the volume of a full pyramid. Those two limits make it easy to sanity-check any calculation, because the answer must always fall between the prism and pyramid values for the same base.
Step-by-Step Volume Calculation
Field measurements follow a fixed order so that nothing is missed. The steps below match the way the dimensions are usually shown on a footing drawing, and they work for both hand calculation and spreadsheet use.
- Measure the bottom length A and breadth B of the base slab
- Measure the top length a and breadth b at the column face
- Measure the total height of the footing and the height of the sloped portion
- Compute A1 = A x B and A2 = a x b
- Apply the trapezoidal formula and add the rectangular base slab volume
- Order concrete with 5 to 10 percent extra for wastage and uneven excavation
Worked Example
Take a footing with a base of 1.5 m by 1.5 m, a top of 0.45 m by 0.45 m, and a sloped height of 0.6 m. The bottom area A1 is 2.25 m2 and the top area A2 is 0.2025 m2. The product A1 x A2 is 0.4556, and its square root is 0.675. The volume is 0.6 / 3 x (2.25 + 0.2025 + 0.675) = 0.63 m3 of concrete for the sloped portion alone.
Measuring on site, the top dimensions are taken at the column face, not at the top of the slope, because the column is what the footing supports. When the column is larger than the top face, the drawing usually shows a short pedestal above the slope, and its volume is added as a rectangular block.
Adding the Base Slab
When the drawing shows a separate rectangular base slab of height H1 below the slope, its volume is A x B x H1, and the total is the sum of the two parts. For the example above, a 0.3 m thick base slab adds 1.5 x 1.5 x 0.3 = 0.675 m3, giving 1.305 m3 in total, or about 1.4 m3 after the ordering allowance. The trapezoidal footing design volume calculation, together with the advantages and typical applications of the shape, uses the same two-part method, and the numbers above show where the concrete savings come from.
Footing Types and Alternatives
The trapezoidal pad is one option in a wider family of shallow foundations. Isolated footings support single columns, combined footings support two or more columns on one pad, and strip footings carry walls. The choice depends on column spacing, soil bearing capacity, and the available budget, and the same site can use several types at once.
A combined footing takes over when two columns sit so close that their individual pads would overlap or when an exterior column must share a pad to keep the resultant pressure inside the middle third of the base. The trapezoidal plan shape of many combined footings uses the same volume mathematics, with the top face stretched to the full width of the pad.
Comparing Footing Options
| Footing type | Shape | Typical use |
|---|---|---|
| Isolated pad | Square or rectangular slab | Single column on firm soil |
| Combined footing | Rectangular or trapezoidal plan | Two or more close columns |
| Sloped trapezoidal footing | Truncated pyramid | Heavy column where concrete saving matters |
| Stepped stone masonry | Stepped stone courses | Light structures where stone is local |
Where local materials dominate, stone masonry footing construction spreads the load in stepped courses and remains common for boundary walls and small buildings. It follows the same principle as the concrete trapezoidal pad: a wider base under a narrower top, so the pressure on the soil stays within the allowable bearing value.
Reinforcement and Site Practice
A trapezoidal footing is reinforced with a mesh of bars near the bottom face, sized for the bending moments at the column face. Bars run in both directions, and the concrete cover follows the exposure class. The detailing rules for bar spacing, hooks, and laps are covered in the reinforcement detailing of footing notes, which apply to sloped pads as well as flat ones.
Placing and Curing
The slope makes the top surface hard to finish, so most crews place the concrete in one continuous pour from the base up, using the formwork as a guide. Vibration must reach the full depth of the base slab without causing the mix to run down the slope. After placing, the footing is kept damp and covered for at least seven days.
- Check the excavated base for soft spots before placing
- Set the reinforcement on chairs to hold the cover
- Pour in one lift and vibrate the full depth
- Strike the top to the finished level shown on the drawing
Concrete is ordered by volume, so the takeoff must include the pedestal, the base slab, and the sloped portion. Most suppliers charge per cubic meter delivered, and small loads carry a short-load fee, so batching several footings into one pour reduces the unit cost. The 5 to 10 percent allowance in the steps above covers excavation overbreak, spillage, and the concrete left in the chute.
Design Checks Before Pouring
The structural design verifies bearing pressure, sliding, overturning, and the punching shear around the column. For isolated pads, the isolated footing design guidelines based on ACI 318-14 set out the load combinations, strength checks, and minimum reinforcement that the trapezoidal shape must also satisfy. Running those checks before the concrete order avoids costly changes after excavation is complete, and it gives the site team a clear record of the sizes and bar schedules they are expected to build.