Horizontal Cylindrical Tank Volume Calculator
Litres in a horizontal round tank from the depth of liquid, plus the percentage full.
Results
What this tool does
A dipstick in a horizontal tank lies to you, because the cross-section of a circle is nothing like a rectangle: the same centimetre of depth means very little near the bottom and near the top, and a lot in the middle. The exact answer is the area of a circular segment times the length of the tank, which is what this works out. Dished or hemispherical ends add a little more and are not counted here.
Formula
A = R² acos((R-h)/R) - (R-h) √(2Rh - h²) ; V = A L
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dd | Diameter | mm |
ll | Length | mm |
hh | Depth of liquid | mm |
VL | Volume in the tank | L |
VM | Volume | m³ |
VF | Volume when full | L |
PC | Percentage full | % |
Worked example
- Diameter2000 mm
- Length5000 mm
- Depth of liquid600 mm
- Volume in the tank3963.4 L
- Volume3.9634 m³
- Volume when full15,708.0 L
- Percentage full25.23 %
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
Frequently asked questions
Why is a horizontal tank half empty at more than half the height?
It is, exactly — half the height of a horizontal cylinder is exactly half its volume, by symmetry. What surprises people is everywhere else: the first quarter of the height holds only about 20% of the tank, because the cross-section is narrow at the bottom. That is why a dipstick on a cylindrical tank is never evenly spaced.