Truncated Pyramid Volume Calculator (Footings, Hoppers)
Volume and weight of a truncated pyramid with rectangular top and bottom — a tapered concrete footing, a hopper or a spoil heap — with the cross-section drawn to scale.
Results
Volume
0.3467
m³
Volume
346.7
L
Mass of material
832
kg
What this tool does
The prismoidal formula averages the top, the bottom and four times the middle section, and for any shape whose sides taper in straight lines it is exact — so it handles rectangular ends of different proportions, where the simple pyramid formula only works for similar ones. Concrete footings that step in towards the column are a common use; reinforced concrete weighs roughly 2400–2500 kg/m³. Order a little extra for waste and uneven ground.
Formula
V = h ÷ 6 × (A_bottom + A_top + 4 A_middle) (prismoidal formula)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
l1 | Bottom length | m |
w1 | Bottom width | m |
l2 | Top length | m |
w2 | Top width | m |
h | Height | m |
ro | Material density | kg/m³ |
V | Volume | m³ |
VL | Volume | L |
M | Mass of material | kg |
Worked example
- Bottom length1.2 m
- Bottom width1.2 m
- Top length0.4 m
- Top width0.4 m
- Height0.5 m
- Material density2400 kg/m³
- Volume0.3467 m³
- Volume346.7 L
- Mass of material832 kg
Limitations
- Always order a little more material than the calculated quantity. Cuts, breakage and pattern matching create waste that depends on the shape of the job.
- Density changes with temperature, moisture and composition. Use a value from the supplier's data sheet whenever precision matters.