Spherical Tank Volume Calculator (Partly Filled)
How much liquid a spherical tank holds at a given level, its total capacity and the free space left, with the level-to-volume curve drawn.
Results
Liquid volume
654.5
L
Tank volume
4188.8
L
Share of the full volume
15.6
%
Space still free
3534.3
L
Width of the liquid surface
1.732
m
The dashed line marks the value you entered.
What this tool does
In a sphere the level is a poor guide to the contents: the first and last tenths of the height hold very little, while the middle holds a lot. A sphere filled to a quarter of its height is only about 16 % full — the chart shows the whole S-shaped curve, which is what a dipstick scale for a spherical tank has to follow. The formula is the volume of a spherical cap.
Formula
V(y) = π y² (3R − y) ÷ 3 · V_total = π D³ ÷ 6
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d | Tank diameter | m |
y | Liquid level (from the bottom) | m |
VF | Liquid volume | L |
VT | Tank volume | L |
FP | Share of the full volume | % |
ES | Space still free | L |
SD | Width of the liquid surface | m |
Worked example
- Tank diameter2 m
- Liquid level (from the bottom)0.5 m
- Liquid volume654.5 L
- Tank volume4188.8 L
- Share of the full volume15.6 %
- Space still free3534.3 L
- Width of the liquid surface1.732 m
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.