Vertical Tank Volume Calculator: How to Find Capacity

This calculator works out the volume of a vertical cylindrical tank from its diameter and height, giving you the result in litres, cubic metres, and US gallons. You enter the inside diameter and the liquid height (or total height for full capacity), and it returns the volume instantly. It uses the standard cylinder formula, so it suits storage tanks, pressure vessels, and process vessels with flat or dished ends when you need a quick capacity check.

Formula

The volume of a vertical cylinder is the cross-sectional area of the circle times the height of the liquid:

V = π × (d/2)² × h

Where:

• V = volume (m³, L, or US gal)
• π ≈ 3.14159
• d = inside diameter of the tank (m)
• h = height of the liquid (m)

If you measure in feet and inches, convert to metres first: 1 ft = 0.3048 m, 1 inch = 0.0254 m. For litres, multiply the cubic metre result by 1000. For US gallons, multiply by 264.172 (or 7.4805 if you are working in cubic feet).

Worked Example

Using the default values from the calculator: diameter = 2 m, liquid height = 3 m.

1. Radius = d/2 = 1 m
2. Area of circle = π × (1)² = 3.14159 m²
3. Volume = 3.14159 × 3 = 9.42477 m³
4. In litres: 9.42477 × 1000 = 9424.77 L (calculator shows 9425 L)
5. In US gallons: 9.42477 × 264.172 = 2489.3 US gal (calculator shows 2489.3)

The calculator’s first output shows 9.425 m³, which matches the step-by-step calculation.

When to Use This Calculator

Use a vertical tank volume calculator when you need to know:

• How much liquid a vertical storage tank holds at full capacity
• How much liquid is currently in a partially filled tank (using the liquid height)
• Whether a tank can hold a required volume for a process or delivery
• Approximate contents for inventory or transfer purposes

It is common in water treatment, chemical storage, fuel storage, and agriculture (e.g., vertical silos or liquid fertilizer tanks). The formula assumes the tank is a perfect cylinder with vertical sides and a flat bottom. For tanks with conical or dished bottoms, the calculation is more complex because the bottom adds extra volume that depends on the shape.

How to Read the Result

The first output is the volume in cubic metres, which is the standard SI unit. The second is litres (1 m³ = 1000 L), and the third is US gallons. If your tank is measured in feet and inches, you can still use this calculator by converting the dimensions to metres first, or you can use a dedicated imperial calculator that handles feet and inches directly.

Remember that the calculator gives the geometric volume. The actual usable volume may be less because of internal fittings (baffles, heating coils, agitators), the thickness of the tank wall (you should use the inside diameter, not the outside), and the fact that you cannot fill a tank completely to the rim for safety reasons. Always leave a headspace (typically 5–10% of the height) for expansion, especially for volatile liquids.

Common Mistakes and Misconceptions

• Using outside diameter instead of inside diameter – the wall thickness reduces the internal volume; for a large tank the difference may be small, but for small tanks it can be significant.
• Mixing units – if you enter diameter in metres and height in feet, the result is meaningless. Convert everything to one unit system first.
• Forgetting the radius – the formula uses radius (half the diameter), not the full diameter. Squaring the diameter directly gives a volume four times too large.
• Assuming a flat bottom – many vertical tanks have a dished or conical bottom. The cylinder formula only covers the straight cylindrical section. For a dished bottom, you need additional formulas or a tank chart from the manufacturer.
• Confusing US gallons with imperial gallons – 1 US gallon = 3.78541 L, while 1 imperial gallon = 4.54609 L. This calculator uses US gallons.

Limits of the Formula

The cylinder volume formula is exact for a perfect right circular cylinder. Real tanks deviate because of:

• Wall thickness (use inside dimensions)
• Dished, conical, or elliptical heads (adds or subtracts volume)
• Internal fittings that displace liquid
• Thermal expansion of the tank and liquid
• Measurement errors in diameter and height

For precise inventory or custody transfer, you need a calibration chart (often called a strapping table) that gives volume as a function of liquid level, based on actual internal measurements. For rough estimates, the cylinder formula is usually within a few percent.

Practical Tips for Measuring a Tank

1. Measure the inside diameter at several heights and average them – tanks are not perfectly round.
2. Measure the liquid height with a dipstick or level sensor, not the total tank height, unless the tank is full.
3. If the tank has a dished bottom, measure the straight side height separately and add the bottom volume using the appropriate head formula (e.g., 2:1 elliptical head volume ≈ 0.131 × d³).
4. For a horizontal tank, the volume calculation is different because the cross-section is a circular segment – do not use this vertical calculator for horizontal tanks.

Frequently Asked Questions

How do I convert the volume to litres or gallons?

The calculator already gives litres and US gallons. If you need imperial gallons, multiply the cubic metre result by 219.969. For cubic feet, multiply cubic metres by 35.3147.

What if my tank has a conical bottom?

For a conical bottom, add the volume of the cone: V_cone = (1/3) × π × (d/2)² × h_cone, where h_cone is the height of the cone. Add that to the cylindrical section volume. For a dished bottom, use the specific head volume formula or a tank chart.

Can I use this for a horizontal tank?

No. Horizontal tank volume depends on the liquid level and the tank’s length and diameter, and the formula involves a circular segment area. Use a dedicated horizontal tank calculator instead.

Why does the calculator show 9425 L but my tank is rated 9000 L?

The rated capacity is often the nominal or usable capacity, which excludes the top headspace and accounts for internal fittings. Also, the rated capacity may be based on outside dimensions. The geometric volume from the calculator is the theoretical maximum.

What is the difference between capacity and volume?

Capacity usually refers to the maximum amount a tank can hold, while volume is the amount of liquid actually in it. The calculator gives the geometric volume for a given height; if you enter the total height, you get the full capacity (minus any headspace).

How accurate is this calculator?

It is exact for a perfect cylinder with flat ends. Real tanks have tolerances in manufacturing and may have irregular shapes. For most practical purposes, the result is accurate to within a few percent if you measure the inside dimensions carefully.

Related

• Square Tank Volume Calculator: Gallons
• Square to Square Foot Calculator: How to Convert
• Tank Dish Volume Calculator: How It Works

in d | Tank diameter | m | 2 | 0
in h | Liquid height | m | 3 | 0
out vol_m3 | Volume | m³ | pi * (d/2)^2 * h | 3
out vol_l | Volume | L | pi * (d/2)^2 * h * 1000 | 0
out vol_usgal | Volume | US gal | pi * (d/2)^2 * h * 264.172 | 1