Calculator
Example Data Table
| Tank diameter | Straight height | Bottom head | Top head | Fill height | Approximate filled volume |
|---|---|---|---|---|---|
| 2 m | 5 m | Flat | Flat | 2.5 m | 7,854 L |
| 2 m | 5 m | Conical, 0.8 m | Flat | 2.5 m | 6,074 L |
| 2 m | 5 m | Ellipsoidal, 0.5 m | Ellipsoidal, 0.5 m | 3 m | 8,901 L |
Formula Used
Cylindrical shell: V = πr²h.
Conical bottom segment: V = πr²h³ ÷ 3H².
Conical top segment: V = πr²(h − h² ÷ H + h³ ÷ 3H²).
Hemispherical bottom segment: V = πh²(r − h ÷ 3).
Hemispherical top segment: V = πr²h − πh³ ÷ 3.
Ellipsoidal bottom segment: V = πr²(h² ÷ H − h³ ÷ 3H²).
Ellipsoidal top segment: V = πr²(h − h³ ÷ 3H²).
Here, r is tank radius. H is head depth. h is the filled height within the current tank section.
How to Use This Calculator
- Enter the internal tank diameter.
- Enter the straight vertical shell height.
- Enter the liquid fill height from the lowest inside point.
- Select the bottom and top head shapes.
- Add head depths for conical and ellipsoidal heads.
- Select length and output volume units.
- Enter density if liquid mass is needed.
- Press Calculate, then download CSV or PDF if required.
About Vertical Tank Volume Calculations
Why Tank Shape Matters
A vertical tank looks simple, but its useful volume can change by head shape. A straight cylinder gives a direct relationship between level and volume. A shaped bottom or top does not. A small change in level can add little volume near a cone tip. The same change can add more volume near the center of a rounded head. This calculator handles those changes with separate geometry for each section.
How the Level Is Read
Many storage tanks have a cylindrical shell with flat, conical, hemispherical, or ellipsoidal ends. Each part is measured along the vertical axis. The fill height starts from the lowest inside point. When the entered level rises through the bottom head, only that head is partly filled. After it reaches the straight shell, the shell volume grows linearly. If the level enters the top head, the remaining curved section is counted with its own equation.
Common Uses
This method is useful for water tanks, chemical vessels, fuel storage, process tanks, brewery vessels, and farm tanks. It helps estimate current inventory, delivery room, overflow risk, and liquid mass. The density field is optional. When density is entered, the tool also estimates liquid weight. That makes the result more useful for transport, supports, and loading checks.
Accuracy Tips
Use inside dimensions whenever possible. Outside diameter can overstate capacity because wall thickness is included. For lined tanks, use the usable internal diameter. For dished heads, an ellipsoidal approximation is often helpful when the exact manufacturer chart is not available. For critical work, compare the result with the tank calibration table.
Reports and Limits
The output shows total capacity, filled volume, empty volume, fill percentage, and mass. It also shows a small level table so users can compare several fills quickly. CSV export is useful for spreadsheets. PDF export is helpful for a saved job note. The calculator is still an estimating tool. Real tanks can have nozzles, slopes, weld offsets, sediment, floating roofs, dead space, or internal parts. Field measurement and certified calibration remain the best source for custody transfer, safety limits, and regulated reporting. For everyday planning, keep one consistent unit system. Record the chosen head depths, liquid density, and measured level. These details make repeated checks easier and reduce mistakes when several operators share the same tank each day.
FAQs
1. What is a vertical tank volume calculator?
It estimates liquid volume inside an upright tank using diameter, height, fill level, and head shape. It can also estimate empty space, capacity percentage, and liquid mass when density is provided.
2. Should I enter inside or outside diameter?
Use inside diameter whenever possible. Outside diameter includes wall thickness, coatings, or insulation. That can make the calculated capacity higher than the usable internal capacity.
3. What is straight shell height?
Straight shell height is the cylindrical section between the bottom and top heads. Do not include conical, hemispherical, or ellipsoidal head depths in this value.
4. How is fill height measured?
Measure fill height from the lowest internal point of the tank. For a conical bottom, this starts at the cone tip, not at the cylinder base.
5. Why is head depth ignored for hemispherical heads?
A true hemispherical head has a depth equal to the tank radius. The calculator applies that geometry automatically to keep the formula consistent.
6. Can this calculator handle partial tanks?
Yes. Enter the current liquid level as fill height. The result shows partial volume, remaining capacity, fill percentage, and a level reference table.
7. What density should I use?
Use the liquid density in kilograms per cubic meter. Water is often near 1000 kg/m³. Oils, fuels, chemicals, and syrups can differ greatly.
8. Is this suitable for legal custody transfer?
No. It is an estimating tool. For custody transfer, regulated storage, or safety limits, use certified tank calibration data and approved measurement procedures.