Tank Volume Calculator: Cylinder, Sphere & Rectangle Tanks

What is a tank volume calculator?

A tank volume calculator works out how much liquid a tank can hold, based on its shape and dimensions. This tool covers the three shapes used in most storage tanks: cylinders, spheres, and rectangular boxes.

Knowing tank volume matters for choosing the right tank size, dosing chemicals correctly, and estimating how long a stored supply will last.

Tank volume formulas

Cylindrical tank formula

A cylindrical tank is a tube shape, either standing upright or lying on its side. Its volume is:

V = π × r² × h

Here, r is the radius (half the diameter) and h is the height. On a tank lying on its side, h is the length of the tube instead.

Spherical tank formula

A spherical tank is shaped like a ball, sometimes raised on legs. Its volume is:

V = (4/3) × π × r³

Here, r is the radius, measured from the center of the sphere to the inner wall.

Rectangular tank formula

A rectangular tank is a box shape. Its volume is:

V = l × w × h

Here, l is length, w is width, and h is height.

For all three shapes, measure the inside of the tank, not the outside. The tank wall takes up space and reduces how much liquid actually fits inside.

How to calculate tank volume

1. Choose the tank shape: cylindrical, spherical, or rectangular.
2. Choose a unit for the dimensions: meters, centimeters, feet, or inches.
3. Enter the radius (for cylindrical or spherical tanks) or the length and width (for rectangular tanks).
4. Enter the height (for cylindrical or rectangular tanks).
5. Choose a unit for the result: cubic meters, cubic feet, liters, or gallons.

The calculator converts the units automatically and shows the volume right away.

Worked example

A cylindrical tank has an inside radius of 1.5 meters and a height of 3 meters.

V = π × 1.5² × 3 = π × 2.25 × 3 ≈ 21.21 cubic meters

That is about 21,206 liters, or about 5,602 US gallons.

Converting between volume units

• 1 cubic meter = 1,000 liters
• 1 cubic meter ≈ 264.17 US gallons
• 1 cubic foot ≈ 7.48 US gallons
• 1 cubic foot ≈ 28.32 liters
• 1 US gallon ≈ 3.785 liters

Measuring tanks accurately

Small measurement errors add up. On a cylindrical tank with a 3-foot radius and a 6-foot height, an error of just 1/8 inch in the radius changes the calculated volume by roughly 9 gallons. Errors in height cause similar shifts, so measure carefully and use inside dimensions wherever possible.

Wall thickness matters too. A steel wall 1/4 inch thick takes up 1/4 inch on each side of the tank, so it reduces the inside diameter by about half an inch compared with the outside diameter. On thicker-walled tanks, such as pressure vessels, the difference is larger and should not be ignored.

Internal fittings reduce usable space further. Baffles, pipes, mixers, and support structures can take up 5 to 10 percent of a tank's geometric volume. The formulas above give the empty geometric volume; the real, usable storage capacity is often somewhat less.

Common uses for tank volume calculations

Rainwater storage. A household uses roughly 80 to 100 gallons of water per person per day. Three days of emergency water for a family of four calls for around 1,000 to 1,200 gallons of storage. A cylindrical tank 5 feet in diameter and 7 feet tall holds about 1,030 gallons, within that range.

Municipal water towers. Water utilities size elevated tanks to cover peak demand and firefighting needs, typically one to two days of average use. A spherical tank holding 500,000 gallons has an inside diameter of roughly 50 feet.

Fuel storage. Underground tanks at filling stations commonly hold 10,000 to 20,000 gallons per fuel type. Regulators such as the U.S. Environmental Protection Agency require secondary containment sized to at least 110 percent of the largest tank's volume.

Chemical and food processing. Batch reactors and fermentation tanks need accurate, known volumes, because reaction and recipe ratios depend on them. Process engineers usually verify a tank's true volume instead of relying only on the manufacturer's stated size.

Septic systems. Local building codes commonly require a three-bedroom house to have a septic tank of at least 1,000 to 1,500 gallons.

Limitations

The formulas above apply to plain cylinders, spheres, and rectangular boxes. Many real tanks are more complex.

• Combined shapes. A tank with a cylindrical body and rounded (hemispherical) ends must be split into sections, calculated separately, then added together.
• Partial fill levels. This calculator gives total capacity, not the volume at a given depth. In a horizontal cylindrical tank, volume does not rise in a straight line with depth, because the cross-section is a circle rather than a rectangle. Finding that volume needs trigonometry.
• Tanks that cannot be measured directly. Buried or sealed tanks sometimes need other methods, such as metering the water used to fill them or hiring professional calibration.
• Legal or regulatory measurement. Industries that transfer custody of liquids, such as petroleum storage, generally require certified tank calibration, known as strapping, rather than a general-purpose calculator. Strapping tables map liquid level to volume at fine intervals, following standards such as American Petroleum Institute Chapter 2 and ISO 7507.

History

Calculating the volume of a cylinder is an old problem. The Moscow Mathematical Papyrus, an Egyptian document from around 1800 BCE, includes a calculation of the volume of a cylindrical grain store. The Greek mathematician Archimedes worked out the volume formula for a sphere around 250 BCE, in his treatise On the Sphere and Cylinder. Both formulas are unchanged today. What has changed is the speed of the calculation, from tables and slide rules to an instant result in a browser.

Frequently asked questions

What is a tank volume calculator?

A tool that works out how much a tank holds, based on its shape and measurements. It covers cylindrical, spherical, and rectangular tanks, with results in liters, gallons, cubic meters, or cubic feet.

How do I find the radius of a tank?

Measure the diameter, the distance straight across the tank through its center, then divide by two. A tank with a 6-foot diameter has a 3-foot radius.

Should I measure inside or outside dimensions?

Inside dimensions. The tank wall takes up space that liquid cannot fill, so using outside dimensions overstates the true capacity.

Can this calculator handle a tank that is only partly full?

No. It gives the tank's total capacity. Finding the volume at a partial fill level, especially in a horizontal cylindrical tank, needs a separate formula, because volume does not rise in a straight line with depth.

How do horizontal and vertical cylindrical tanks differ?

They use the same formula. On a vertical tank, height is the upright dimension. On a horizontal tank, the "height" in the formula is really the length of the tube lying on its side.

Is the result accurate enough for legal or regulatory use?

For planning and design, yes. For custody transfer, insurance, or regulatory filings involving large or hazardous tanks, use certified professional tank calibration instead.