Vertical Cylindrical Tank Volume Calculator

This calculator works out the volume of a vertical cylindrical tank from the diameter (or radius) and height you enter, and returns the result in gallons, liters, cubic feet, and cubic meters. You input the tank’s inside dimensions and the liquid depth (if not full), and it gives the filled volume as well as the total capacity. The calculation uses the standard cylinder volume formula, so it is accurate for any vertical cylindrical tank with flat ends.

Formula

The volume of a vertical cylinder is the area of the circular base multiplied by the height. In words: Volume = π × (radius)² × height. Using diameter instead of radius, it becomes:

V = π × (d/2)² × h

• V = volume (cubic feet, cubic meters, etc.)
• π (pi) ≈ 3.14159
• d = inside diameter of the tank (same unit as h)
• h = height of the liquid (or full tank height for capacity)

To convert cubic feet to US gallons, multiply by 7.48052. To convert cubic feet to liters, multiply by 28.3168. If you measure in meters, 1 m³ = 1000 L and 1 m³ = 264.172 US gallons.

Worked Example

Using the default values from the calculator: diameter = 4 ft, liquid depth = 6 ft, tank height = 8 ft.

1. Radius = d/2 = 4/2 = 2 ft
2. Base area = π × (2)² = π × 4 ≈ 12.566 ft²
3. Liquid volume = 12.566 × 6 = 75.40 ft³
4. In gallons: 75.40 × 7.48052 ≈ 564.1 US gal
5. In liters: 75.40 × 28.3168 ≈ 2135 L
6. Total capacity (full height 8 ft) = 12.566 × 8 = 100.53 ft³ × 7.48052 ≈ 752.1 US gal

The calculator shows 75.40 ft³, 564.1 gal, 2135 L, and 752.1 gal capacity – matching the steps above.

When to Use This Calculator

Use this tool for vertical cylindrical tanks that stand upright – common in water storage, fuel tanks, chemical containers, and many industrial vessels. It is also useful for:

• Estimating how much liquid is left in a partially filled tank (using liquid depth)
• Checking if a tank can hold a certain volume before purchasing
• Calculating chemical doses or mixing ratios based on tank volume
• Planning wastewater or rainwater storage

For horizontal cylindrical tanks (lying on their side), the formula is different because the cross-section is a circular segment, not a full rectangle. This calculator is only for vertical orientation.

How to Measure Correctly

Accurate measurements are critical. Follow these steps:

1. Measure the inside diameter – not the outside. If you only have the outside diameter, subtract twice the wall thickness.
2. Measure the liquid depth from the bottom to the surface. If the tank has a dished or conical bottom, the formula changes; this calculator assumes a flat bottom.
3. Use the same unit for all measurements (e.g., all feet or all meters). Mixing feet and inches is the most common error.
4. For total capacity, measure the full height of the cylindrical section, excluding any domed top or bottom.

Common Mistakes and Misconceptions

One frequent mistake is using the outside diameter. The wall thickness can reduce volume by several percent on small tanks. Another is confusing US gallons with imperial gallons – 1 US gallon = 0.8327 imperial gallons. Also, many people forget that the formula assumes a perfectly cylindrical shape; real tanks may have slight bulges or dents.

A common misconception is that a tank with a 4 ft diameter and 8 ft height holds exactly twice the volume of one with 4 ft diameter and 4 ft height – that part is true. But doubling the diameter quadruples the volume (since radius is squared). For example, a 4 ft diameter, 8 ft tall tank holds about 752 gallons; an 8 ft diameter, 8 ft tall tank holds about 3,008 gallons – four times as much.

Units and Conversions

The calculator gives results in cubic feet, US gallons, and liters. Here are useful conversions:

• 1 cubic foot = 7.48052 US gallons
• 1 cubic foot = 28.3168 liters
• 1 cubic meter = 1000 liters = 264.172 US gallons
• 1 US gallon = 3.78541 liters

If you measure in inches, convert to feet first (divide by 12) or use the formula with inches and then convert cubic inches to gallons (1 gal = 231 in³).

Limitations of the Formula

This formula is exact only for a perfect right circular cylinder with flat ends. Real tanks often have:

• Dished (curved) heads – add or subtract a small amount
• Conical or sloped bottoms – require different geometry
• Internal baffles, pipes, or heating coils that displace volume

For most practical purposes, the cylinder formula gives an excellent estimate. If you need extreme precision (e.g., for legal custody transfer), use calibration tables from the tank manufacturer or perform a strapping table (measured dip vs. volume).

Safety and Accuracy Notes

Always confirm the tank’s rated capacity from its nameplate or documentation before relying on calculations for safety-critical applications. Overfilling a tank can cause spills, structural failure, or dangerous pressure buildup. For flammable liquids, never fill to the absolute top – leave expansion space as recommended by safety guidelines. Also, be aware that liquid density affects weight, not volume; the calculator gives volume only, so multiply by density to get mass.

Frequently Asked Questions

How do I find the volume of a partially filled vertical cylinder?

Measure the liquid depth from the bottom and use that as the height in the formula. The calculator does this when you enter the liquid depth. If the tank is not on a flat bottom, the calculation may be off.

What is the difference between US gallons and imperial gallons?

US gallon is smaller: 1 US gallon = 3.785 liters, while 1 imperial gallon = 4.546 liters. The calculator uses US gallons by default. To convert to imperial, multiply the US gallon result by 0.8327.

Can I use this for a horizontal cylindrical tank?

No. Horizontal tanks have a different volume formula because the liquid surface is not parallel to the tank’s axis. Use a horizontal tank calculator instead.

Why does the calculator ask for both liquid depth and tank height?

Liquid depth gives the current volume; tank height gives the total capacity. If you only want capacity, set liquid depth equal to tank height.

What if my tank has a domed top or bottom?

The cylinder formula ignores the volume of domed ends. For a standard dished head, you can add the volume of a spherical segment, but it’s often small relative to the cylinder. For precise work, consult tank drawings.

How accurate is this calculator?

It is mathematically exact for a perfect cylinder. Real-world accuracy depends on measurement precision and tank shape. Measuring the diameter to the nearest 1/8 inch on a 4 ft tank gives an error of about 0.3% in volume.

Related

• Square Foot Calculator Multiple Sides
• Square Foot Calculator: Area in Sq Ft
• Square Foot Calculator by Inches: How to Convert

in d | Tank diameter | ft | 4 | 0
in h | Liquid depth | ft | 6 | 0
in full_h | Tank height | ft | 8 | 0
out vol_ft3 | Liquid volume | ft³ | pi * (d/2)^2 * h | 2
out vol_gal | Liquid volume | US gal | (pi * (d/2)^2 * h) * 7.48052 | 1
out vol_l | Liquid volume | L | (pi * (d/2)^2 * h) * 28.3168 | 0
out cap_gal | Total capacity | US gal | (pi * (d/2)^2 * full_h) * 7.48052 | 1