Frustum Volume Calculator (Bucket, Pot, Hopper)
Volume of a truncated cone such as a bucket, a flower pot or a hopper, the volume up to any fill line, and its surface area, drawn to scale.
Results
Volume
16.098
L
Volume up to that height
10.760
L
Share of the full volume
66.8
%
Slant height
28.16
cm
Area of the sides
2388.6
cm²
Total surface area
3547.9
cm²
The dashed line marks the value you entered.
What this tool does
A bucket that is wider at the top holds much more in its upper half than in its lower half, so a line drawn halfway up is nowhere near half the volume — the chart shows how far off it is. The formula is the cone's, with the missing tip subtracted. Measure the inside diameters if you want what it holds, the outside ones if you want the material.
Formula
V = (π h ÷ 3) × (R² + R r + r²)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dt | Top diameter | cm |
db | Bottom diameter | cm |
h | Height | cm |
y | Depth of liquid | cm |
V | Volume | L |
VF | Volume up to that height | L |
FP | Share of the full volume | % |
SL | Slant height | cm |
LA | Area of the sides | cm² |
TA | Total surface area | cm² |
Worked example
- Top diameter30 cm
- Bottom diameter24 cm
- Height28 cm
- Depth of liquid20 cm
- Volume16.098 L
- Volume up to that height10.760 L
- Share of the full volume66.8 %
- Slant height28.16 cm
- Area of the sides2388.6 cm²
- Total surface area3547.9 cm²
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.