User Rating 0.0 ★★★★★

Total Usage 1 times

Category Foundation Concrete

Shaft Dimensions

Shaft Diameter (inches)

Shaft Height (feet) Height of the straight cylinder part only

Bell Dimensions (Optional)

Bell Diameter (inches) Diameter at the widest bottom point

Bell Height (inches)

Number of Piers

Single Pier Volume 0.00 cubic yards

        Total Volume (All Piers)
        0.00
        cubic yards
      

Shaft Vol: 0.00 yd³ | Bell Vol: 0.00 yd³

Is this tool helpful?

Your feedback helps us improve.

★ ★ ★ ★ ★

About

Deep foundations utilize piers (or piles) to transfer structural loads past unstable surface soil to stronger strata below. These are typically cylindrical shafts drilled into the ground and filled with concrete. In many regions, especially those with expansive clay soils, these piers are "belled" at the bottom—widened into a cone shape—to increase the surface area for bearing and to anchor the foundation against uplift forces.

Calculating the volume of a simple cylinder is straightforward, but the geometry of a belled pier (a cylinder atop a truncated cone) introduces complexity. Errors here can lead to significant concrete shortages, as the bell volume can be surprisingly large. This tool accurately computes the total volume for straight-shaft and belled piers, accommodating the specific geometry of the auger bell.

Formulas

The total volume is the sum of the cylindrical shaft and the belled base (if applicable). The bell is modeled as a frustum of a cone.

V_shaft = π × r_shaft² × h_shaft

For the belled section:

V_bell = π × h_bell3 (R_base² + R_baser_shaft + r_shaft²)

Reference Data

Auger Diameter	Shaft Area (sq ft)	Vol per Foot (cu yd)	Standard Bell Ratio	Typical Use
10 inches	0.55	0.020	2:1 or 3:1	Deck Posts, Light Porches
12 inches	0.79	0.029	2:1 or 3:1	Residential Foundation
16 inches	1.40	0.052	3:1	Heavy Residential
18 inches	1.77	0.065	3:1	Commercial Columns
24 inches	3.14	0.116	3:1	Industrial/Bridge
30 inches	4.91	0.182	3:1	High Load Bearing
36 inches	7.07	0.262	3:1	Major Infrastructure

Frequently Asked Questions

A belled pier has a widened base, shaped like a bell or cone. This shape increases the contact area with the soil, allowing the pier to support heavier loads and resisting 'heave' or uplift forces in expansive soils.

Calculations are theoretically exact, but actual usage is often 10-20% higher. Drilled holes are rarely perfect cylinders; the walls may collapse slightly or be over-excavated (overbreak), requiring more concrete to fill the voids.

Most drilling rigs create a bell with sides at a 45-degree or 60-degree angle relative to the horizontal. The ratio of Bell Diameter to Shaft Diameter is typically 2:1 or 3:1 depending on the tooling.

Yes. Sonotubes create a perfect cylinder. For these, simply set the Bell Height and Bell Diameter to 0 (or equal to the shaft) to calculate the straight shaft volume.

The bell height is not the total depth of the pier. It is only the height of the conical section at the bottom. The total depth of the hole = Shaft Height + Bell Height.