When to use this calculator
Find partial fill volume from liquid depth in a horizontal cylindrical tank. Assumes a level horizontal cylinder with flat circular ends.
Explore the volume & surface area calculators for other questions in this topic. For a related calculation, use the Pyramid Lateral Area Calculator: Find side-face area of a regular pyramid.
PUTTING IT INTO PRACTICE
Horizontal Cylinder Liquid Volume: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Internal radius | 1 |
| Cylinder length | 5 |
| Liquid depth | 1 |
| Result | 7.853982 cubic units |
- Check the input labels and enter the example values above.
- Apply the relationship: Filled volume = length × (r² acos((r−h)/r) − (r−h)√(2rh−h²)).
- The result is 7.853982 cubic units, rounded for display.
How to interpret your result
Assumes a level horizontal cylinder with flat circular ends.
Volume and surface area have different units and answer different questions. Use internal dimensions for capacity. A closed-solid surface area includes bases and lids unless the calculator explicitly describes an open shape.
Frequently asked questions
Should I use internal or outside measurements?
Use internal measurements for capacity and outside measurements for covering the exterior. Match the formula to the part being measured.
When is the horizontal cylinder liquid volume calculator useful?
Find partial fill volume from liquid depth in a horizontal cylindrical tank. Assumes a level horizontal cylinder with flat circular ends.
How do I use the horizontal cylinder liquid volume calculator?
Enter internal radius, cylinder length, liquid depth. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Filled volume = length × (r² acos((r−h)/r) − (r−h)√(2rh−h²)).
What should I check before using the result?
Assumes a level horizontal cylinder with flat circular ends.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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