What the Tube Volume Calculator Measures

A tube volume calculator measures the amount of material in a hollow cylinder. A tube is not the same as a solid cylinder. A solid cylinder has one radius or one diameter and the whole circular cross-section is filled. A tube has an outside boundary and a hollow inside opening. The material volume is the difference between the volume of the outer cylinder and the volume of the inner cylinder. That difference is the annular cylinder, or the ring-shaped material that remains after the inner cylinder is removed.

This calculator is useful when you know the outside diameter, inside diameter and length of a pipe, sleeve, bushing, spacer, hollow shaft, washer-like part, structural tube, conduit or cylindrical shell. It is also useful when you know outside diameter and wall thickness, because the inside diameter can be found from the wall thickness. Once the calculator knows the tube geometry, it can return volume in cubic meters, cubic centimeters, cubic millimeters, liters, milliliters, cubic inches, cubic feet or US gallons.

The page focuses on tube volume, not every possible volume shape. If your object is a box, sphere, cone, tank or irregular solid, the broader volume calculator is a better starting point. If your shape is specifically a hollow tube, this page is more precise because it keeps the inner diameter, outer diameter, wall thickness, surface area and density relationships together.

The result can support practical decisions such as ordering material, estimating the amount of plastic or metal in a part, checking a CAD model, calculating approximate tube weight, planning coating volume, comparing hollow and solid sections, or explaining the formula in a math or engineering assignment. It is still important to use realistic dimensions and tolerances. Real tubes can have manufacturing variation, ovality, internal seams, bevelled ends, threaded ends, corrosion, coatings or fittings. The formula here assumes a straight tube with circular, concentric inner and outer diameters.

Tube Volume Formula

The tube volume formula starts with the volume of a cylinder. A cylinder with radius \(r\) and length \(L\) has volume:

A tube can be understood as a large cylinder minus a smaller cylinder. The outside cylinder has radius \(R_o\). The inside hollow space has radius \(R_i\). The material volume is:

Factor out \(\pi L\), and the formula becomes:

Many drawings list diameters instead of radii. Since radius is half of diameter, \(R_o=D_o/2\) and \(R_i=D_i/2\). Substituting those values gives the diameter form of the formula:

This is the main formula used by the calculator. It works for any consistent length unit. If \(D_o\), \(D_i\) and \(L\) are all in centimeters, the result is in cubic centimeters. If they are all in inches, the result is in cubic inches. The calculator lets you mix units because it converts everything to meters first, but when doing the calculation manually, convert all measurements to one length unit before substituting values.

Volume from Wall Thickness

Many tube specifications give outside diameter and wall thickness instead of inside diameter. Wall thickness is the radial distance from the outside surface to the inside surface. Because thickness exists on both sides of the tube, the inside diameter is smaller than the outside diameter by twice the wall thickness:

Once \(D_i\) is known, the same hollow-cylinder formula applies:

This mode is common in engineering, construction and fabrication. Steel tubes may be listed by outside diameter and wall thickness. Plastic tubing may be sold by outside diameter and wall. Metal sleeves and spacers may be machined from tube stock where wall thickness determines bore size. In all of these cases, thickness must be smaller than half of the outside diameter. If \(2t\ge D_o\), the inner diameter would be zero or negative, which means the inputs do not describe a hollow tube.

Wall thickness can also be a source of error because nominal pipe sizes do not always equal measured outside diameters. A pipe called "one inch" may not have a one-inch outside diameter. Standards such as schedule pipe tables define actual dimensions. When accuracy matters, use the measured outside diameter and measured inside diameter, or use the standard dimension table that applies to the material and pipe class. The calculator will do the math correctly, but it cannot correct a nominal size that does not represent the actual geometry.

Worked Example: Metric Tube Volume

Suppose a steel tube has outside diameter \(D_o=50\text{ mm}\), inside diameter \(D_i=40\text{ mm}\), and length \(L=1200\text{ mm}\). Because all dimensions are already in millimeters, the formula gives cubic millimeters:

Square the diameters:

Subtract the inner squared diameter from the outer squared diameter:

Now substitute:

Using \(\pi\approx 3.14159\), the material volume is approximately:

Since \(1\text{ cm}^3=1000\text{ mm}^3\), the same volume is about \(848.23\text{ cm}^3\). Since \(1\text{ L}=1000\text{ cm}^3\), the volume is about \(0.848\text{ L}\). The calculator performs these conversions automatically, but the manual steps show why the result is the volume of material, not the hollow internal capacity.

Worked Example: Tube Volume from Wall Thickness

Consider a tube with outside diameter \(2\text{ in}\), wall thickness \(0.125\text{ in}\), and length \(6\text{ ft}\). The first step is to convert length to inches because the diameter and wall thickness are in inches. Six feet is \(72\text{ in}\). The inside diameter is:

Now apply the tube formula:

The squared diameters are \(2^2=4\) and \(1.75^2=3.0625\), so the difference is \(0.9375\). The volume is:

This tells you the volume of tube material. If you are estimating steel weight, you can multiply by density after converting units consistently. If you are estimating the air or water capacity inside the tube, you should use the inside diameter only and calculate the volume of the hollow cylinder, not the material volume.

Material Volume vs Internal Capacity

Tube volume can mean two different things in everyday language. In manufacturing, "tube volume" often means the volume of material in the tube wall. In plumbing, fluid handling or packaging, "tube volume" may mean the internal capacity of the hollow space. This calculator is designed primarily for material volume, because it subtracts the inner cylinder from the outer cylinder. That is the correct result for estimating material required, mass, machining stock, casting volume, extrusion material, or the volume of plastic, metal or glass in the wall.

If you need internal capacity, use the inner diameter as the cylinder diameter and ignore the outer diameter. The internal capacity formula is:

For example, if the inside diameter is \(40\text{ mm}\) and the length is \(1200\text{ mm}\), internal volume is \(\pi(1200)(40^2)/4\), which is about \(1507964\text{ mm}^3\), or about \(1.508\text{ L}\). That is different from the material volume of the 50 mm outer diameter, 40 mm inner diameter tube, which was about \(0.848\text{ L}\). Both results are correct; they answer different questions.

When documenting a calculation, write the phrase clearly. "Tube material volume" means the annular wall. "Internal tube capacity" means the hollow bore. "Displaced outer volume" means the entire outer cylinder as if it were solid. The correct formula depends on which of those quantities you need.

Surface Area and Tube Volume Together

Volume and surface area are related but not interchangeable. Tube volume tells you how much material is in the wall. Surface area tells you how much area is exposed on the outside, inside and ends. Surface area matters for painting, coating, heat transfer, insulation, corrosion protection, adhesive bonding and cleaning. The calculator's surface mode reports material volume and several area values so you can see the difference.

The outside curved surface area is:

The inside curved surface area is:

The area of one annular end face is the same as the tube cross-sectional area:

If both ends are exposed, the total tube surface area is:

If you only need exposed outer coating area, use the outside surface area. If you need both inside and outside coating, include both curved areas. If the ends are welded, capped, hidden or not coated, do not include end areas. For a dedicated surface-focused calculation, the tube surface area calculator keeps the coating and exposed-area problem separate from the material-volume problem.

Tube Mass from Volume and Density

Once tube material volume is known, mass can be estimated from density. The relationship is:

Here, \(m\) is mass, \(\rho\) is material density, and \(V\) is material volume. The units must be consistent. If density is in kilograms per cubic meter, volume must be in cubic meters to produce kilograms. If density is in grams per cubic centimeter, volume must be in cubic centimeters to produce grams. The calculator converts density entries to kg/m^3 internally and reports mass in kilograms and pounds.

Density-based mass is an estimate unless you use the exact material density and exact dimensions. Manufacturing tolerances, surface coatings, seams, fittings, threaded ends and cut quality can change the real weight. For aluminum-specific planning, the aluminum weight calculator can be useful when the material is known and the goal is weight rather than geometry explanation. For the formula behind density itself, see the density formula resource.

Unit Conversion Rules for Tube Volume

Most tube-volume mistakes are unit mistakes. The formula contains squared diameters and one length, so a small unit error can become large. If diameter is in millimeters and length is in meters, the calculation will be wrong unless one is converted. The safest manual method is to convert all lengths to the same unit before applying the formula. The calculator accepts mixed units because it converts each input to meters first.

Common volume conversions include:

If you need to convert a finished result to another volume unit, the volume converter is useful. If you need a broader measurement reference for length, mass, volume and other unit types, the unit conversion calculator chart can help keep related conversions organized. For length-only conversions before calculating geometry, use the length conversion calculator.

In engineering drawings, units are sometimes implied rather than repeated. A drawing may state "all dimensions in mm" once in the title block. A US fabrication note may list tube size in inches and length in feet. A supplier listing may give wall thickness in gauge or schedule rather than direct units. Read the unit context before calculating. If a dimension seems unrealistic, check whether it is nominal, actual, metric, imperial, or a shorthand convention.

Tube, Pipe, Cylinder and Annulus: Terminology Matters

A tube is usually described by its outside diameter and wall thickness, especially when the outside dimension matters for fitting, structure or appearance. A pipe is often described by nominal pipe size and schedule, especially in fluid systems. A hollow cylinder is the mathematical shape behind both. An annulus is the ring-shaped cross-section between two concentric circles. Understanding these words helps you choose the correct dimensions and formula.

The cross-sectional area of the tube wall is the area of the outer circle minus the area of the inner circle:

Tube material volume is that annular area multiplied by length:

If there is no inner opening, the object is a solid cylinder, and the correct formula is \(V=\pi r^2L\). In that case, use the cylinder volume calculator or the cylinder volume formula explanation. If you are reviewing the circle measurements used in the tube formula, the circle diameter calculator, circle area calculator and circle circumference calculator can help with the underlying geometry.

Accuracy, Tolerances and Practical Measurement

The formula assumes perfect circular diameters, straight length and concentric walls. Real parts are never perfect. Tube walls can vary in thickness, the inside and outside circles may not be perfectly concentric, cut ends may not be square, and the tube may be slightly oval. These differences are usually small, but they matter in precision engineering, pressure work, aerospace, medical devices and quality control.

For practical measurements, use calipers or micrometers for diameter and wall thickness. Measure outside diameter in more than one direction if ovality is possible. Measure wall thickness at several positions around the tube if the material is extruded, rolled or welded. Use actual cut length, not nominal stock length, if you are estimating the mass of one finished part. If the tube includes holes, slots, chamfers, threads, grooves, weld beads or attached fittings, subtract or add those volumes separately.

Rounding should also match the use case. For classroom work, two or three significant figures may be enough. For purchasing, round up slightly if waste, cutting loss or tolerance could increase required material. For engineering drawings, follow the drawing tolerance and significant-figure requirements. For financial estimates, keep enough precision to avoid systematic underestimation across many pieces. A tiny error in one tube may not matter, but the same error repeated across thousands of tubes can affect material cost and shipping weight.

If you are checking a result from CAD software, make sure both calculations describe the same object. CAD may include end caps, fillets, holes or features that the simple hollow-cylinder formula does not include. The calculator is best for straight, uniform tubes. Complex parts require a model-based volume calculation or a breakdown into multiple simpler shapes.

Tube Volume in Construction, Fabrication and Manufacturing

Tube volume appears in many practical fields. In construction, hollow steel sections are used for frames, railings, supports, trusses, columns and temporary structures. Material volume helps estimate weight, cost and transport requirements. In fabrication, tube volume supports cutting plans, welding preparations, stock comparisons and material takeoffs. In manufacturing, it helps estimate resin, metal, glass or composite material in a tube-shaped part.

For a steel tube, mass estimate often matters more than volume itself. Suppliers may price by weight, shipping may be limited by load, and installation crews may need lifting plans. The mass mode in the calculator uses volume and density to estimate weight. For liquids or gases inside a tube, internal capacity is the relevant quantity instead. That is a different calculation, even though it uses the same diameter and length ideas.

In coating and finishing, volume is usually not the main number. Surface area matters more because paint, galvanizing, powder coating, insulation and corrosion protection are applied to surfaces. The tube volume calculator includes a surface mode for quick combined checking, but a coating job should usually be planned from surface area, coating thickness, coverage rate, loss factor and application method. The cylinder surface area calculator can help when the object is a solid or closed cylinder rather than a hollow tube with an inside wall.

Step-by-Step Manual Method

1. Identify whether you need material volume or internal capacity. Material volume uses both outer and inner diameters. Internal capacity uses only the inner diameter.
2. Write down the known measurements. Typical inputs are outer diameter, inner diameter and length. If you have wall thickness instead of inner diameter, calculate \(D_i=D_o-2t\).
3. Convert all lengths to one unit. Do not mix millimeters, meters, inches and feet inside the formula unless you convert first.
4. Square the outer and inner diameters. Because the diameters are squared, unit and measurement errors are amplified.
5. Subtract the inner squared diameter from the outer squared diameter. This gives the diameter-squared difference for the annular cross-section.
6. Multiply by length and pi, then divide by four. The result is material volume in the cubic version of your length unit.
7. Convert the final volume if needed. Convert cubic millimeters to cubic centimeters, liters, cubic inches or another unit after calculating.
8. Check the result against physical intuition. A thin-walled tube should have much less material volume than a solid cylinder with the same outside diameter.

For formula review across common shapes, the volume formulas page is helpful. For tube-specific work, keep the annular cross-section in mind: the tube is not simply a cylinder unless the inside diameter is zero.

Common Mistakes to Avoid

Choosing the Best Output Unit

The best output unit depends on context. Small machined parts are often easier to understand in cubic millimeters or cubic centimeters. Laboratory and fluid-adjacent calculations often use milliliters or liters. Construction and shipping estimates may use cubic feet or cubic meters. US fabrication drawings often use inches for dimensions and cubic inches for intermediate volume, then convert to pounds using density.

When reporting results, include both the number and the unit. "Volume = 0.848" is incomplete. "Volume = 0.848 L" or "Volume = 848 cm^3" is meaningful. If you convert to mass, include density and its source. A statement such as "Mass estimated using 7850 kg/m^3 for carbon steel" is clearer than simply listing a weight.

For comparison across shapes, use a consistent unit. If one option is in liters and another in cubic inches, convert them before deciding. The advanced volume converter is useful when you need several volume units at once, while this page should remain focused on calculating the tube's material volume from its geometry.

Why the Difference of Squares Matters

The tube formula depends on the difference of squared diameters, not the difference of diameters. This is one of the most important ideas to understand. If the outer diameter is 50 mm and the inner diameter is 40 mm, the wall thickness is only 5 mm, but the material area is not found by \(50-40=10\). A circle's area grows with the square of its diameter, so the correct cross-sectional material area is based on \(50^2-40^2\).

The expression \(D_o^2-D_i^2\) can also be factored:

This factorization gives useful intuition. The first factor, \(D_o-D_i\), is twice the wall thickness. The second factor, \(D_o+D_i\), represents the overall size of the tube. A thin wall on a large tube can still contain a large amount of material because the circumference is large. A similar wall thickness on a small tube contains less material because the ring is shorter around the outside. That is why tube weight does not depend on wall thickness alone.

For example, compare two tubes with the same 2 mm wall thickness and 1 meter length. Tube A has outer diameter 20 mm and inner diameter 16 mm. Tube B has outer diameter 100 mm and inner diameter 96 mm. The wall thickness is the same, but Tube B has much more material because its annular area wraps around a much larger circle. This is why designers look at both diameter and wall thickness when choosing tube stock.

The difference-of-squares view is also helpful for checking whether a result makes sense. If the wall is very thin compared with the diameter, the material volume should be close to circumference times wall thickness times length. If the wall is thick, the exact annular formula is safer because curvature and the inner opening size matter more. The calculator always uses the exact formula, so it handles both thin and thick walls without changing method.

Thin-Wall Approximation and When Not to Use It

Engineers sometimes approximate tube material volume using mean diameter, wall thickness and length. The idea is that a thin tube wall is like a rectangular sheet rolled into a circle. The approximate cross-sectional area is circumference at the mean diameter multiplied by wall thickness:

Here, \(D_m\) is the mean diameter:

The approximate tube volume is therefore:

For a perfectly concentric circular tube, this approximation is actually equivalent to the exact annular formula when \(D_m\) is defined as the average of outer and inner diameter and \(t=(D_o-D_i)/2\). Substituting those values gives the same area. However, problems arise when people use nominal diameter as the mean diameter, use outside diameter instead of mean diameter, or estimate wall thickness from a schedule without checking the real dimensions. Then the approximation becomes a shortcut that can introduce error.

The thin-wall view is still useful for mental checks. If a tube has outside diameter 100 mm, wall thickness 2 mm and length 1 m, the mean diameter is about 98 mm. The wall is thin compared with the diameter, so material volume should be close to circumference times thickness times length. The exact calculator result should not be wildly different from that quick estimate. If it is, there is probably a unit mistake or the wrong diameter was entered.

Do not use a thin-wall shortcut for thick-walled sleeves, bushings, pressure components, bearings or parts where the inside opening is much smaller than the outside diameter. In those cases, the full annular formula is simple enough and more reliable. The calculator is designed to remove the need for shortcuts, but understanding the approximation helps you recognize unreasonable answers.

Measurement Checklist Before Calculating

Good tube volume calculations begin with good measurements. Before entering values, identify exactly what was measured. Outside diameter should be measured across the full outer circle. Inside diameter should be measured across the hollow opening. Wall thickness should be measured radially from outside surface to inside surface, not across the tube wall twice. Length should be the actual straight length of the part, not the stock length before cutting unless you are estimating raw stock.

Use the same measurement system whenever possible. If a drawing gives outside diameter in millimeters and length in meters, convert one before doing manual math. If a supplier gives dimensions in inches but your report needs liters, calculate in a consistent unit first and convert the final volume. The calculator handles mixed input units, but the person entering data still needs to choose the correct unit from each dropdown.

For a real manufactured tube, measure more than once. Take outside diameter readings in two directions at the same cross-section to check roundness. Measure at both ends if the tube may be tapered or damaged. If the tube has a weld seam, wall thickness near the seam may differ slightly from wall thickness elsewhere. For high-precision work, use several measurements and decide whether to use a nominal, average, minimum or maximum value based on the task.

The correct value also depends on purpose. For minimum material strength, a designer may care about minimum wall thickness. For maximum weight, a shipping estimate may use maximum wall thickness or a safety allowance. For cost estimating, an average dimension may be reasonable. For classroom geometry, the exact numbers in the problem statement are usually treated as perfect. The formula is the same, but the input choice reflects the practical question.

Finally, check whether the tube has features that invalidate the simple hollow-cylinder model. Holes, slots, threads, notches, bevels, flanges, welded attachments, end caps and fittings all add or remove volume. A plain tube formula cannot include those features unless you calculate them separately. If the tube is one part of a more complex assembly, calculate the simple tube first, then account for additional geometry as needed.

Estimating Multiple Tubes, Stock Lengths and Waste

Many practical jobs involve more than one tube. Once the volume of one tube is known, total material volume for identical pieces is:

Here, \(n\) is the number of pieces. If each tube has the same diameter and wall thickness but different lengths, calculate the volume per unit length and multiply by the total length. The cross-sectional material area \(A\) stays constant, so:

This is useful for fabrication takeoffs. Instead of calculating every piece separately, group tubes by size and wall thickness. Add all lengths within the same size group, then multiply by the annular area. If there are offcuts, saw kerf, trimming allowance or damaged stock, include an allowance. For example, if the required finished tube length is 120 meters and expected waste is 5%, order material for about 126 meters. The geometry volume and the purchasing quantity are related, but they are not always the same.

Waste allowance depends on process. Saw cutting removes material as kerf. Miter cuts can create more waste than square cuts. Bending may require extra straight length. Weld preparation may remove material at the ends. If the tube will be machined after cutting, leave stock for facing and finishing. If the material is expensive, calculate pieces from available stock lengths to reduce offcuts. If delivery lead time is long, consider spare material for mistakes or rework.

For mass estimates across many pieces, calculate total material volume first and then multiply by density. This avoids rounding each piece too early. If one tube weighs 1.236 kg and you need 500 pieces, rounding to 1.24 kg before multiplication gives 620 kg. Using the unrounded value gives 618 kg. The difference may matter for shipping, lifting and procurement. Keep internal calculations precise and round only the final reported values.

When preparing a quote or bill of materials, record the assumptions: dimensions, units, density, waste allowance, number of pieces and whether the result includes coatings or fittings. Clear assumptions make the calculation easier to audit and reduce disputes when real weights differ slightly from estimates.

Comparing Hollow Tubes with Solid Rods

A hollow tube can have much less material volume than a solid rod with the same outside diameter, while still providing useful stiffness and shape. The solid outer-cylinder volume is:

The tube material volume is:

The fraction of solid material retained in the tube is:

For example, if \(D_o=50\text{ mm}\) and \(D_i=40\text{ mm}\), the material fraction is \((2500-1600)/2500=0.36\). The tube contains only 36% of the material volume of a solid 50 mm rod of the same length. That is a major weight reduction. This is one reason tubes are widely used in frames, handles, supports, shafts and structures where shape and stiffness matter.

However, hollow is not automatically better. A tube may buckle, dent, crush, corrode internally or fail at holes and welds. A solid rod may be better for threads, pins, heavy bearing contact, impact or machining. Tube volume tells you material amount, not complete mechanical performance. Strength, stiffness, load direction, wall thickness, alloy, heat treatment, manufacturing method and connections all matter. The calculator can support early estimates, but design decisions should use the appropriate engineering standards and safety factors.

For students, the hollow-versus-solid comparison is a good way to understand why subtracting the inner cylinder matters. The hollow space may look small in a diagram, but because area depends on squared diameter, changing the inner diameter can remove a large fraction of volume. Increasing the inner diameter from 40 mm to 45 mm in a 50 mm outside tube removes much more material than it may visually appear to remove.

Interpreting Calculator Results in Real Projects

A calculator result is a model. It is useful because it isolates the geometry of a straight round tube, but real projects usually need interpretation. If the result is material volume, ask what the next decision is. If you are buying raw material, add waste. If you are estimating shipping, multiply by density and include packaging. If you are designing a tank, calculate internal capacity instead. If you are coating the tube, calculate surface area and coverage. If you are checking a classroom problem, show the formula steps clearly.

It is also helpful to compare the result with a simpler reference. A hollow tube's material volume must be less than the solid cylinder volume with the same outside diameter and length. It must be greater than zero. If the wall is thin, material volume should be a small fraction of the solid cylinder. If the inner diameter is close to zero, the tube volume should approach the solid cylinder volume. These checks catch many mistakes before they become costly.

When using density, remember that density is not the same as unit weight in every measurement system. In SI calculations, density in kg/m^3 multiplied by volume in m^3 gives mass in kilograms. In some engineering contexts, weight density or specific weight may be used instead, giving force units. This calculator reports mass estimates, not structural load ratings. If you need load capacity, pressure rating or structural design, use the relevant mechanical formulas and standards in addition to volume.

For reporting, include a short calculation trail: dimensions, unit conversions, formula, volume and any density used. A line such as "OD 50 mm, ID 40 mm, length 1200 mm, material volume 0.000848 m^3, density 7850 kg/m^3, estimated mass 6.66 kg" is much clearer than a standalone number. That clarity is useful in worksheets, inspection notes, manufacturing travelers and procurement requests.

How to Verify a Tube Volume Answer

A quick verification routine can prevent most mistakes. First, check the geometry. The outer diameter must be larger than the inner diameter, and wall thickness must be positive. Second, check the unit scale. A tube measured in millimeters should not produce a result that looks like a building-sized volume unless the length is extremely large. Third, compare the material volume with the solid outer-cylinder volume. The tube material volume should always be smaller than the solid outer volume and larger than zero.

Next, estimate the order of magnitude. A tube that is 1 meter long with a 50 mm outside diameter and a thin wall should have a material volume measured in fractions of a liter, not hundreds of liters. A large drainage pipe or industrial shell may have much larger volume, but the diameter and length should explain it. If the answer seems unreasonable, look for mixed meters and millimeters, inches and feet, or diameter and radius confusion.

Finally, verify the purpose of the calculation. If the answer is being used for material cost, the wall volume is correct. If the answer is being used for how much liquid the tube holds, the inside capacity is correct. If the answer is being used for paint, outside or total surface area is correct. A mathematically correct number can still be the wrong number if it describes the wrong physical quantity. Good verification is not only arithmetic; it is matching the result to the real decision.

Frequently Asked Questions

Final Notes for Reliable Tube Volume Results

Use the tube volume calculator when the shape is a straight round hollow cylinder and you need material volume. Measure or confirm the outer diameter, inner diameter or wall thickness, and length. Convert units carefully, especially when mixing metric and imperial dimensions. If you need surface coating, use area. If you need internal fluid capacity, use the inside cylinder. If you need weight, multiply material volume by density.

The most reliable calculation is the one that matches the real question. For material purchasing, use material volume and density. For water or air inside a pipe, use internal capacity. For paint or insulation, use surface area. For classroom geometry, show the outer-cylinder-minus-inner-cylinder reasoning so the formula is easy to verify. A tube is a simple shape, but the correct interpretation of its volume depends on what you are trying to measure.