Get the volume of a pier that tapers.
⚙️Calculation Parameters
📊Calculated Output
How Tapered Pier Volume Calculator Works?
To calculate a tapered pier, the Tapered Pier Volume Calculator treats the shape as a frustum, a cone with the tip cut off. The process takes 4 steps.
Measure the top diameter
Enter the diameter at the top of the pier, where the post base sits.
Measure the bottom diameter
Enter the diameter at the base of the hole. Augered holes widen at the bottom when the auger wobbles.
Enter the height
Type the vertical distance between the 2 measurements.
Read the frustum volume
The calculator applies the frustum formula and reports cubic feet (ft³), cubic yards (yd³) and liters (L).
Tapered Pier Volume Calculator Formula
The Tapered Pier Volume Calculator uses the frustum formula, which averages the 2 end areas with a geometric middle term.
Frustum volume
V = π × h ÷ 3 × (R² + R × r + r²)R is the bottom radius, r is the top radius and h is the height.
Inches to ft³
R = D_bottom ÷ 24, r = D_top ÷ 24, h = H ÷ 12All 3 values become feet.
Error check
V_frustum < π × R² × hA frustum always holds less than a cylinder of the bottom diameter.
Worked example: 10 in top, 16 in bottom, 48 in tall
- r = 10 ÷ 24 = 0.4167 ft, R = 16 ÷ 24 = 0.6667 ft, h = 4 ft
- R² + Rr + r² = 0.4444 + 0.2778 + 0.1736 = 0.8958
- V = 3.1416 × 4 ÷ 3 × 0.8958 = 3.752 ft³ (106 L)
Tapered Pier Volume Calculator Conversion Table
The tapered pier conversion table compares 6 frustum shapes with a straight cylinder at the bottom diameter.
| Top dia. | Bottom dia. | Height | Frustum ft³ | Cylinder ft³ at bottom dia. | Frustum yd³ |
|---|---|---|---|---|---|
| 8 in | 12 in | 48 in | 2.21 | 3.14 | 0.082 |
| 10 in | 16 in | 48 in | 3.75 | 5.59 | 0.139 |
| 12 in | 18 in | 48 in | 4.97 | 7.07 | 0.184 |
| 12 in | 24 in | 36 in | 5.50 | 9.42 | 0.204 |
| 16 in | 24 in | 60 in | 11.05 | 15.71 | 0.409 |
| 18 in | 30 in | 60 in | 16.04 | 24.54 | 0.594 |
Ordering for a straight cylinder at the bottom diameter over-orders on every shape in the table.
What is Tapered Pier Volume Calculator?
A Tapered Pier Volume Calculator is a concrete calculator for piers that change diameter from top to bottom, using the truncated-cone (frustum) formula instead of the cylinder formula.
Tapered piers appear in 3 situations: hand-dug holes that widen at the base, precast tapered forms, and flared plastic footing forms. A cylinder formula at either end diameter gives the wrong volume. The frustum formula gives the exact volume.
A 12 in top and 18 in bottom pier, 48 in tall, holds 4.97 ft³. A cylinder at 18 in holds 7.07 ft³, which is 42% more than needed.
What are the uses of Tapered Pier Volume Calculator?
There are 4 main uses of the Tapered Pier Volume Calculator.
Belled auger holes
Crews measure top and bottom widths of holes that flared during digging.
Precast tapered forms
Installers fill tapered plastic or fiber forms with a known top and bottom size.
Earth-formed piers
Builders pour without a tube into hand-dug holes with sloped walls.
Architectural columns
Designers size tapered round columns for porches and entries.
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