Fusion Tank Volume Calculator: How to Size a Reactor

This fusion tank volume calculator works out the internal volume of a cylindrical or rectangular tank used in a fusion research setup, based on the dimensions you enter (diameter or side lengths, and height). You get the volume in liters and gallons, plus the approximate water weight, which is the first step in sizing a cooling or vacuum system. The calculator uses the standard geometric formulas for cylinder and box volume, so you can use it for any tank shape that matches those two forms.

Formula

The calculator uses two basic geometry formulas, depending on the tank shape you select:

• Cylinder: V = π × (d/2)² × h, where d is the internal diameter (m), h is the internal height (m), and V is the volume in cubic meters.
• Rectangular box: V = d × l × h, where d is the width (m), l is the length (m), and h is the height (m).

To convert cubic meters to liters, multiply by 1000 (1 m³ = 1000 L). To convert liters to US gallons, divide by 3.78541. The water weight is simply the volume in liters, because 1 liter of water weighs 1 kilogram at room temperature (slightly less at higher temperatures, but close enough for sizing).

Worked Example

Using the default values: a cylinder with diameter 0.5 m and height 1 m.

1. Radius = d/2 = 0.5/2 = 0.25 m
2. Area of the circular base = π × (0.25)² = 3.14159 × 0.0625 = 0.19635 m²
3. Volume = area × height = 0.19635 × 1 = 0.19635 m³
4. Convert to liters: 0.19635 × 1000 = 196.35 L
5. Convert to gallons: 196.35 / 3.78541 = 51.87 US gal
6. Water weight ≈ 196.35 kg

The calculator shows 196.35 L, 51.87 gal, and 196.3 kg for the defaults.

What Is a Fusion Tank and Why Volume Matters

In fusion research, a “fusion tank” usually refers to the vacuum vessel or the cooling water tank that surrounds a test reactor or a neutron source. It is not a commercial product; it is a custom-built component. The volume determines how much water you need to circulate for cooling, how large a vacuum pump you need to evacuate the chamber, and how much shielding material you need to surround it. For example, a spherical tokamak might have a vacuum vessel with a volume of 30 m³, which requires a pump that can handle that volume at the target pressure. Similarly, the cooling tank volume affects the thermal mass and the flow rate needed to remove heat from the plasma-facing components.

The calculator is also useful for hobbyists building a fusor (a simple electrostatic fusion device). A typical fusor chamber is a small stainless steel sphere, often 6 to 12 inches in diameter. The volume of that chamber tells you how much deuterium gas you need to fill it to a certain pressure, and how long the vacuum pump must run to reach the required base pressure. For instance, a 10-inch sphere has a volume of about 8.5 liters, which is a common size for amateur fusors.

How to Use the Calculator Correctly

To get an accurate volume, you must measure the internal dimensions, not the external ones. The wall thickness of the tank reduces the internal volume, and for a vacuum vessel this difference can be significant if the walls are thick. For a cylinder, measure the internal diameter and the internal height (from the bottom to the top flange). For a rectangular box, measure the internal width, length, and depth.

If your tank is not exactly a cylinder or a box, you can approximate it by breaking it into simpler shapes and adding the volumes. For example, a cylindrical tank with hemispherical heads (like a pressure vessel) is a cylinder plus a sphere. You would calculate the cylindrical section and the two half-spheres separately. The calculator does not handle that directly, but you can compute the sphere volume separately and add it to the cylinder result.

Common Mistakes and Misconceptions

• Using outer dimensions: This overestimates the volume, sometimes by 10-20% if the walls are thick. Always use inside measurements.
• Mixing units: If you enter the diameter in inches and the height in meters, the result is nonsense. Convert everything to the same unit before entering.
• Forgetting the shape: A rectangular box with the same width and height as a cylinder will have a larger volume (because the cylinder loses the corners). The calculator handles this via the shape selector, but you must choose correctly.
• Assuming water weight equals volume for other fluids: The weight output is for water at 4°C. If you are using a different fluid (like oil or a molten salt), multiply the volume by the fluid’s density in kg/L.

A common misconception is that a larger tank always means better cooling. In fusion systems, a larger volume gives more thermal mass, but it also requires more pumping power and more space. The volume is just one parameter; you also need the surface area for heat exchange and the flow rate. Use the volume to size the pump and the heat exchanger, not to judge performance.

Choosing the Right Tank Size for Your Project

The right volume depends on your application:

• Amateur fusor: A 6-8 inch sphere (about 2-4 liters) is typical. Smaller volumes are easier to evacuate and need less deuterium, but they also have less room for diagnostics and viewports.
• Test blanket module (TBM) mockup: These are often rectangular boxes with volumes of 0.1 to 1 m³, depending on the fusion reactor design. The volume must match the neutronics and thermal-hydraulic requirements.
• Cooling water tank: This can be large, from a few cubic meters to hundreds, depending on the heat load. A rough rule is 1 liter of water per kilowatt of heat for a temperature rise of about 1°C per minute, but that is a very rough estimate.

For a vacuum chamber, the volume affects pump-down time. The time to reach a given pressure is roughly proportional to the volume divided by the pumping speed. So a 10-liter chamber with a 10 L/s pump will take about 1 second to pump down one order of magnitude (in the molecular flow regime, it is more complex). Use the volume to estimate the required pumping speed.

Limitations of the Formula

The formulas assume perfect geometric shapes with uniform cross-sections. Real tanks have flanges, ports, viewports, and internal components that reduce the free volume. For precise work, you should subtract the volume of any internal structures (e.g., a grid in a fusor) and add the volume of attached pipes and gauges. The calculator gives the ideal volume; the actual free volume may be 5-10% less.

Also, the water weight is based on fresh water at 4°C. If you are using seawater or a different coolant, the density changes. For example, seawater is about 1.025 kg/L, so the weight would be 2.5% higher. The calculator is not a substitute for engineering design; it is a quick sizing tool.

Frequently Asked Questions

What is a fusion tank exactly?

A fusion tank is a generic term for the vessel that holds the fusion reaction (the vacuum chamber) or the water tank that cools it. In research, it is often a custom stainless steel chamber. The volume is a key parameter for vacuum and cooling system design.

Can I use this calculator for a spherical tank?

No, the calculator only handles cylinders and rectangular boxes. For a sphere, use the formula V = (4/3)πr³, where r is the internal radius. For example, a 10-inch sphere (radius 5 in = 0.127 m) has a volume of about 8.5 liters.

How do I convert liters to cubic feet?

1 liter = 0.0353147 cubic feet. So multiply the liters by 0.0353. For example, 100 liters = 3.53 cubic feet. The calculator gives liters and gallons, but you can do this conversion easily.

What pressure does a fusion tank operate at?

Vacuum vessels typically operate at very low pressures, from 10⁻⁶ to 10⁻³ Torr (roughly 10⁻⁴ to 10⁻¹ Pa). The volume does not affect the pressure, but it affects how long the pump takes to reach it. Cooling tanks operate at near atmospheric pressure, but may be pressurized to raise the boiling point.

Why does the calculator show water weight in kilograms?

Because 1 liter of water weighs 1 kg, the weight in kg is numerically equal to the volume in liters. This is convenient for estimating the load on supports and the thermal mass. For other fluids, multiply by the density in kg/L.

Can I use this for a tank that is not perfectly cylindrical?

Yes, if the deviation is small, you can approximate. For a tank with elliptical or torispherical heads, add the volume of the heads separately. The calculator is a starting point; for final design, use CAD or detailed calculations.

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in sel | Tank shape | Cylinder=1, Rectangular box=2 | 1 | 0
in d | Diameter (cyl) or Width (box) | m | 0.5 | 0
in l | Length (box only, 0 for cylinder) | m | 0 | 0
in h | Height (or depth) | m | 1 | 0
out vol | Volume | liters | (sel == 1 ? pi * (d/2)^2 * h : d * l * h) * 1000 | 2
out gal | Volume | US gallons | vol / 3.78541 | 2
out weight | Water weight | kg | vol | 1