Circular Tank Volume Calculator: How It Works

This calculator works out the volume of a vertical or horizontal circular (cylindrical) tank in litres, cubic metres, US gallons, and imperial gallons. You enter the tank diameter, length (or height), and the liquid depth if the tank is partially filled, and you get the total capacity and the current content volume. The same geometry applies to a cylindrical water tank, a fuel storage drum, or a round process vessel.

Formula

The volume of a circular cylinder is the area of the circular base times the height (or length) of the cylinder:

V = π × r² × h

where:

• V = volume (cubic metres, litres, gallons)
• π ≈ 3.14159
• r = radius of the circular base = diameter ÷ 2 (metres, feet, etc.)
• h = height (for a vertical tank) or length (for a horizontal tank) (same unit as r)

To convert cubic metres to litres, multiply by 1000 (1 m³ = 1000 L). To convert cubic metres to US gallons, multiply by 264.172 (1 m³ ≈ 264.172 US gal). If you measure in feet, the volume comes out in cubic feet; then multiply by 7.48052 for US gallons or by 28.3168 for litres.

Worked Example

Using the default values from the calculator: diameter = 2 m, length = 3 m, liquid depth = 1.5 m.

1. Radius = diameter ÷ 2 = 2 ÷ 2 = 1 m
2. Area of base = π × r² = 3.14159 × 1² = 3.14159 m²
3. Total volume = area × length = 3.14159 × 3 = 9.42477 m³
4. Total volume in litres = 9.42477 × 1000 = 9424.77 L (calculator shows 9425 L)
5. Liquid volume (at 1.5 m depth) = 3.14159 × 1.5 = 4.71239 m³ = 4712.39 L (calculator shows 4712 L)
6. Total volume in US gallons = 9.42477 × 264.172 = 2489.6 US gal (calculator shows 2490 US gal)

The calculator rounds to the nearest whole number for litres and gallons, which is fine for most practical purposes.

When to Use This Calculator

Use it when you need to know:

• How much water a cylindrical tank can hold (e.g., a rainwater tank, aquarium, or storage drum).
• How much liquid is currently in a partially filled tank (e.g., a fuel tank or chemical vessel).
• What size tank you need for a given volume – you can work backwards: set the diameter and length to find the capacity.
• How much space a cylindrical container occupies, if you need to plan transport or installation.

The calculator assumes a perfect cylinder with flat ends. Real tanks often have domed or dished ends (like pressure vessels) or are slightly tapered, so the actual volume may differ by a few percent. For those, you need a more complex formula that accounts for the head shape.

Horizontal vs. Vertical Tanks

For a vertical tank (stand-up cylinder), the height is the vertical dimension and the liquid depth is measured from the bottom. The formula works directly: volume = π × r² × depth.

For a horizontal tank (laying on its side), the liquid depth is measured from the bottom of the side. The formula above only gives the total volume. To find the partial volume in a horizontal cylinder, you need a more complex formula that involves the segment area of a circle:

V_partial = L × [r² × cos⁻¹((r – d)/r) – (r – d) × √(2rd – d²)]

where d is the liquid depth. This calculator uses the simple vertical formula for the partial volume, so it is accurate for vertical tanks. For horizontal tanks, the partial volume will be overestimated (especially at low fill levels). If you need precise horizontal tank partial volumes, look for a dedicated horizontal tank calculator.

Common Mistakes and How to Avoid Them

• Mixing units: If you enter diameter in metres and length in feet, the volume is wrong. Always use the same unit for all dimensions.
• Using diameter instead of radius: The formula uses radius (half the diameter). Forgetting to divide by 2 makes the volume four times too large.
• Confusing litres and cubic metres: 1 m³ = 1000 L, not 1 L. A 1 m³ tank holds 1000 litres.
• Assuming the tank is perfectly cylindrical: Many tanks have rounded ends or are slightly bulged. The error is usually small (1–5%) but can be significant for precise measurements.
• Measuring the outside diameter instead of the inside: The wall thickness reduces the internal volume. For thick-walled tanks, use the internal diameter.

Limits of the Formula

The formula is exact for a perfect right circular cylinder. It does not account for:

• Domed, dished, or elliptical heads (common on pressure vessels).
• Internal baffles, pipes, or other obstructions that reduce usable volume.
• Thermal expansion of the liquid (volume changes with temperature).
• Sloped or irregular tank bottoms.

For most practical purposes (water storage, fuel tanks, aquariums), the error is negligible. For safety-critical applications like pressure vessels, always use the manufacturer’s certified capacity.

Frequently Asked Questions

How do I calculate the volume of a circular tank in litres?

Measure the diameter and height (or length) in metres. Divide the diameter by 2 to get the radius. Square the radius, multiply by π (3.14159), then multiply by the height. The result is in cubic metres. Multiply by 1000 to get litres.

How many gallons are in a 2m diameter x 3m tank?

Using the formula: radius = 1m, area = π × 1² = 3.14159 m², volume = 3.14159 × 3 = 9.42477 m³. Multiply by 264.172 to get 2489.6 US gallons. In imperial gallons, multiply by 219.969 to get 2073.2 imperial gallons.

What is the formula for a horizontal cylindrical tank?

Total volume is the same: π × r² × L. For partial volume, use the segment area formula: V = L × [r² × cos⁻¹((r – d)/r) – (r – d) × √(2rd – d²)], where d is the liquid depth.

How do I convert cubic feet to gallons?

Multiply the volume in cubic feet by 7.48052 to get US gallons, or by 6.22884 to get imperial gallons. For litres, multiply by 28.3168.

Does the calculator work for a tank with rounded ends?

No, it assumes flat ends. For rounded ends, you need to add the volume of the heads. A common approximation is to treat the head as a sphere or an ellipsoid. For precise values, use a tank chart from the manufacturer.

Why is my measured volume different from the calculated volume?

Possible reasons: the tank is not a perfect cylinder (dents, bulges), you measured the outside instead of the inside, the liquid is at a temperature different from the calibration temperature, or there are internal components taking up space. Also, if the tank is horizontal and you used the simple vertical formula for partial volume, that would cause a significant error.

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in d | Tank diameter | m | 2 | 0
in h | Tank length/height | m | 3 | 0
in depth | Liquid depth (for partial fill) | m | 1.5 | 0
out vol_total | Total volume | litres | pi * (d/2)^2 * h * 1000 | 0
out vol_partial | Liquid volume | litres | pi * (d/2)^2 * depth * 1000 | 0
out usgal | Total volume (US gal) | gal | pi * (d/2)^2 * h * 264.172 | 0