Vertical Tank Volume Calculator for Excel
- Volume (liters)
- L
- Result
- Volume (cubic feet)
- ft³
- Result
- Tank diameter
- 10 ft
- You entered
This page explains how to calculate the volume of a vertical cylindrical tank using a spreadsheet formula you can build in Excel, Google Sheets, or any similar program. You enter the tank’s diameter and liquid height, and the formula returns the volume in gallons, liters, or cubic units, depending on how you set it up. The calculator below does the same math automatically, so you can verify your Excel formula against it.
Formula
The volume of a vertical cylindrical tank is the area of the circular base times the liquid height. The base area is π × (radius)², where radius is half the diameter. So the full formula is:
V = π × (D/2)² × H
Where:
- V = volume (cubic units, same as the units of D and H)
- π ≈ 3.14159
- D = diameter of the tank (same unit as H)
- H = height of the liquid (same unit as D)
If your tank has flat ends and is completely full, the same formula gives the total capacity. For a partially filled vertical cylinder, the liquid height is simply the distance from the bottom to the liquid surface.
Worked Example
Using the default values from the calculator above: a tank with a diameter of 10 feet and a liquid height of 5 feet.
- Radius = 10 / 2 = 5 ft
- Base area = π × (5)² = π × 25 ≈ 78.5398 ft²
- Volume in cubic feet = 78.5398 × 5 = 392.699 ft³
- Convert to US gallons: 392.699 × 7.48052 ≈ 2,937.6 gallons
- Convert to liters: 392.699 × 28.3168 ≈ 11,119.0 liters
The calculator rounds the gallon output to one decimal, so it shows 2,937.6 gallons. The cubic feet output shows 392.70 ft³.
How to Build the Formula in Excel
In Excel, you can place the diameter in cell A1 and the height in cell B1, then use the following formulas in other cells:
- Cubic feet:
=PI()*(A1/2)^2*B1 - US gallons:
=PI()*(A1/2)^2*B1*7.48052 - Liters:
=PI()*(A1/2)^2*B1*28.3168
If you want to input the diameter in inches and get gallons, convert the diameter to feet inside the formula: =PI()*(A1/24)^2*B1*7.48052 (assuming B1 is also in inches). For metric, if both are in meters, the result is cubic meters; multiply by 1,000 to get liters.
Choosing the Right Units
The most common mistake is mixing units. The formula requires that D and H be in the same linear unit. If you measure diameter in feet and height in inches, you must convert one to the other first. Here are the common conversion factors:
- 1 US gallon = 231 cubic inches
- 1 US gallon = 0.133681 cubic feet
- 1 cubic foot = 7.48052 US gallons
- 1 liter = 1,000 cubic centimeters
- 1 cubic meter = 1,000 liters
When working with large tanks, it is often easier to convert everything to feet or meters before applying the formula. For small tanks (e.g., a home aquarium), inches and gallons are typical.
Common Pitfalls and Misconceptions
One common misconception is that a tank with a cone bottom or a dished head can be approximated by a vertical cylinder. That is only valid if the liquid is above the cone or head. For a cone-bottom tank, the lower section uses a different formula (volume of a cone), and the cylindrical section uses the cylinder formula. Another pitfall is using the outside diameter instead of the inside diameter. The volume calculation should use the inside dimensions, because the wall thickness takes up space. If you only have the outside diameter, subtract twice the wall thickness to get the inside diameter.
Rounding errors can also accumulate. In Excel, it is best to keep the full precision of PI() and only round the final result. If you round intermediate steps, the final number may be off by more than you expect, especially for large tanks.
When to Use a Full Tank vs. Partial Height
The same formula works for any liquid height, from empty to full. For a completely full tank, H equals the tank’s total height. For a partially filled tank, H is the measured liquid depth. If the tank is filled to only 60% of its height, the volume is 60% of the full capacity, because the cross-sectional area is constant along the height. That linear relationship is true only for vertical cylinders with straight sides. For horizontal cylinders, the volume is not linear with liquid height, and a different formula is needed.
Frequently Asked Questions
How do I calculate the volume of a vertical tank in Excel if I only know the circumference?
If you know the circumference (C), you can find the diameter using D = C / π. Then use the same formula. For example, if C = 31.4 ft, D ≈ 10 ft, and then you proceed with the cylinder formula.
What if my tank has a cone bottom?
Calculate the cone volume separately: V_cone = (1/3) × π × (r²) × h_cone, where h_cone is the height of the cone. Add that to the cylindrical volume above it. The total volume is the sum of both sections.
Can I use this formula for a tank with elliptical heads?
No. The formula assumes flat ends. Elliptical or dished heads add extra volume. For those, you need the head volume formula, which depends on the head shape (2:1 elliptical, torispherical, etc.). The cylindrical section is still the same, but the total includes the heads.
How do I convert the result to barrels or other units?
After calculating cubic feet or liters, use conversion factors. For example, 1 US oil barrel = 42 US gallons. So if you have gallons, divide by 42 to get barrels. For imperial gallons, the factor is different (1 imperial gallon = 4.54609 liters).
Is there a difference between US gallons and imperial gallons?
Yes. The US gallon is 231 cubic inches, while the imperial gallon is about 277.42 cubic inches. The conversion factor from cubic feet to US gallons is 7.48052, but to imperial gallons it is 6.22884. Always check which gallon your application uses.
Why does my Excel formula give a different result than an online calculator?
Usually it is a unit mismatch or a rounding difference. Check that you are using the same units for diameter and height, and that you are using the correct conversion factor. Also, some online calculators use the outside diameter, while others use the inside diameter.