Hollow Cylinder Volume - Wall and Inner Volume

A hollow cylinder volume is the volume of the material that makes up a right circular hollow cylinder, the solid that remains after you remove a smaller coaxial cylinder from inside a larger one. Use this hollow cylinder volume calculator when you know the outer radius R, the inner radius r, and the perpendicular height h, and you need the wall volume, the inner empty-space volume, the outer full-cylinder volume, the annulus cross-section area, and the total surface area without rederiving the formula.

• • Pipe, tube, and roller material volume: Compute the volume of metal, plastic, or composite material in a pipe, tube, shaft, sleeve, or roller so you can convert to mass, cost, or scrap yield.
• • Hollow container capacity vs wall material: Compare the inside capacity of a hollow tank, cup, or sleeve to the material volume of its wall to size insulation, coating, or reinforcement.

A right circular hollow cylinder is the solid that you get by drilling a coaxial cylindrical bore through a solid cylinder. Two numbers, the outer radius R and the inner radius r, describe the cross section, and the height h completes the description. The wall volume is the difference between pi * h * R^2 and pi * h * r^2.

If you also need the volume of a solid cylinder of the same outer radius and height, the cylinder volume calculator returns the outer full-cylinder volume V = pi * h * R^2 in the same length unit.

The calculator uses the closed-form formula V = pi * h * (R^2 - r^2), where R is the outer radius, r is the inner radius, and h is the perpendicular height. It reports the wall volume, the inner bore volume, the outer full-cylinder volume, the annulus cross-section area, and the total surface area in the same unit you entered, and switches the area and volume labels to the matching square and cubic units.

• R: Outer radius. The radius from the centerline to the outside surface. Must be greater than 0.
• r: Inner radius (bore radius). The radius from the centerline to the inside surface. Use 0 for a solid cylinder; must not exceed R.
• h: Perpendicular height (axial length) of the hollow cylinder.

The total surface area sums the two lateral walls (inside and outside) with the two ring-shaped ends. The lateral walls combine to 2 * pi * h * (R + r), and the two end rings combine to 2 * pi * (R^2 - r^2). The page uses full-precision pi and rounds only for display.

According to Wolfram MathWorld, the volume of a right circular cylinder is V = pi * r^2 * h, and the total surface area is 2 * pi * r * h + 2 * pi * r^2.

According to Wikipedia Cylinder, the volume of a right circular cylinder is V = pi * r^2 * h.

For an engineering take that returns the inner bore volume in gallons or liters for flow, capacity, or weight of liquid, the pipe volume calculator in the construction-diy category uses the same R, r, and h inputs.

Four ideas show up every time you work with a hollow cylinder, and understanding each one makes the formula and the result panel easier to read.

When you only need the annulus cross-section area without the height, the area calculator returns the ring area from R and r and switches to the matching square unit.

Run the calculator in five short steps, then read the result panel for the value you actually need.

1. 1 Measure the outer radius R: Measure from the centerline to the outside surface. If you only have the outer diameter, divide it by 2. Use the same unit for r and h.
2. 2 Measure the inner radius r: Measure from the centerline to the inside bore. If you only have the inner diameter, divide it by 2. If the cylinder is solid, enter 0.
3. 3 Measure the height h: Measure the perpendicular height (axial length) of the hollow cylinder, not a slanted length, so the result panel matches the closed-form formula.
4. 4 Pick the unit you measured in: Choose centimeters, meters, inches, or feet. The result panel will switch the area label to the matching square unit and the volume label to the matching cubic unit.
5. 5 Read the wall volume and supporting values: Use the wall volume for material mass, cost, or scrap estimates. Use the inner volume for bore capacity, the outer volume for the reference solid, the cross-section area for cross-section checks, and the total surface area for paint, coating, or sheet stock.

A workshop is cutting a steel pipe with outer radius R = 5 cm, inner radius r = 3 cm, and length h = 50 cm. The operator reads wall volume 2513.27 cm^3, inner 1413.72 cm^3, outer 3926.99 cm^3, annulus 50.27 cm^2, and total surface 1450.13 cm^2 to size the order and the paint.

To compare the wall volume in cm^3 to a quote or a fluid flow spec in liters, gallons, or cubic feet, the volume converter converts the cubic units without you cubing the conversion factor by hand.

The page is built for the way people actually use a hollow cylinder measurement in real work, with each benefit tied to a concrete decision or workflow.

• • Three inputs cover every hollow cylinder: Enter R, r, and h, and the page returns the wall volume, inner volume, outer volume, cross-section area, and total surface area in the same unit, so there is no second measurement to take.
• • Works in four common length units: Centimeters, meters, inches, and feet cover most craft, school, fabrication, and engineering tasks without manual unit conversion, and the area and volume outputs are labeled with the matching square and cubic units.
• • Handles the two limit cases automatically: Entering r = 0 returns the solid cylinder volume, and entering r = R returns zero wall volume with the inner and outer volumes equal. The same page replaces a solid cylinder tool for the limit shapes.
• • Cites the formula source: The page links to a Wolfram MathWorld reference, a Wikipedia Cylinder article, and the Omni Calculator worked example, so the result is traceable for classwork or technical documentation.

Because the closed-form wall volume formula depends only on R, r, and h, the same one-form workflow handles a 1 cm model pipe, a 5 m industrial tube, and a 20 ft structural sleeve, and the result panel lets you copy values straight into a quote, a bill of materials, or a report.

When the project needs only the inside, only the outside, or both wall areas without the end rings, the surface area calculator returns the surface area of each part of a hollow cylinder in the same unit.

The closed-form formula does not have hidden variables, but the inputs and the unit choice still affect what the number means in practice.

• • The calculator is for right circular hollow cylinders. A frustum-shaped hollow cone, a tapered tube, or an elliptical hollow cylinder has a different formula and is not the same shape as the page handles.
• • The page does not draw the hollow cylinder, accept a wall thickness in place of one of the radii, or compute the centroid or moment of inertia. The page uses the full-precision pi constant internally and rounds only for display.

If the result is used for code, fabrication quotes, or classwork, keep the unrounded value until the final step.

According to Omni Calculator, a hollow cylinder with R=5, r=3, h=10 has a wall volume of pi * 10 * (5^2 - 3^2) = 160 * pi ≈ 502.65.

If the next decision is heat transfer, reaction rate, or coating thickness, the surface area volume ratio calculator takes the total surface area and the wall volume from this page and returns the surface-area-to-volume ratio in the same unit.