Tank Volume Calculator: Horizontal Cylinder, Vertical Cylinder, Rectangular and Spherical Tanks at Any Fill Level
Tank capacity in litres and the volume at any liquid level.
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How this calculator works
Choose the tank shape and enter its inside dimensions.
Enter the depth of the liquid. Optionally enter a volume to find the depth for.
The calculator gives the total volume in litres, the volume of liquid, how full it is and the space left.
Formulas used
- V = \pi r^2L
- A_{seg} = r^2\arccos\frac{r - h}{r} - (r - h)\sqrt{2rh - h^2}
- V_{cap} = \frac{\pi h^2(3r - h)}{3}
Worked example
With the default numbers in the calculator above:
- Total volume of the horizontal cylinder (flat ends): 3392.92 litres
- Volume of liquid at the depth you gave: the circular segment area times the length: 990.025 litres
- How full the tank is, and the space left: 29.179 % full, with 2402.9 litres of space
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Shape of the tank Sphere; Inside diameter (cylinder or sphere), or the width of a rectangular tank 2000 mm; Depth of the liquid 500 mm.
- Total volume of the sphere: 4188.79 litres
- Volume of liquid at the depth you gave (a spherical cap): 654.498 litres
- How full the tank is, and the space left: 15.625 % full, with 3534.29 litres of space
Common questions
How do I find the volume in a horizontal tank?
Find the area of the circular segment that is covered by liquid and multiply it by the length of the tank.
Why is a horizontal tank not linear?
The tank is narrow near the top and bottom, so a given depth at either end holds less volume than the same depth near the middle.
Do dished ends change the volume?
Yes. This calculator uses flat ends. Dished or conical ends add volume, so use the maker's chart for those.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Standard geometry of the circular segment and spherical cap.
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