The Tube Calculator finds material volume in a hollow circular cylinder (a pipe) from outer radius, inner radius and length. The cross section is an annulus. The page redraws a labelled figure with both radii and the length marked.
Enter outer radius R, inner radius r with R greater than r, and length L. Related pages cover the solid Cylinder Calculator when there is no bore, the planar Annulus Calculator for ring area alone, and the Capsule Calculator when ends are rounded rather than open.
Calculate the volume of a tube
Cross-section area is the annulus pi * (R^2 - r^2). Multiplying by length L gives the volume of material in the wall. The Tube Calculator requires R > r > 0 and L > 0. Diameter inputs convert to radii before the square difference runs.
V = pi * (R^2 - r^2) * LVolume scales with length and with the difference of squared radii. Doubling length doubles material volume. Widening the wall by increasing R or decreasing r increases the annular area.
For R = 5, r = 3, L = 20:
V = pi * (25 - 9) * 20 = pi * 16 * 20 = 320 * pi approx 1005.31Exact form 320 * pi matches the outline fixture. A solid cylinder of radius 5 and length 20 has volume 500 * pi; removing the inner cylinder of radius 3 leaves 500 * pi - 180 * pi = 320 * pi, the same result.
Calculate the material volume
Material volume is the wall volume above when the bore is empty. If the question asks for fluid capacity inside the bore, use the inner cylinder pi * r^2 * L instead. The Tube Calculator labels material volume explicitly so those two intents do not collide.
For the reference radii and length:
Material V = 320 * pi approx 1005.31
Inner fluid V = pi * 9 * 20 = 180 * pi approx 565.49
Outer envelope V = pi * 25 * 20 = 500 * pi approx 1570.80Material plus fluid equals the outer envelope: 320 * pi + 180 * pi = 500 * pi. That check catches swapped R and r. Manufacturing scrap and metal order quantities track material volume; tank fill problems track fluid volume.
Calculate the wall thickness
Thickness measured radially is outer minus inner radius when both share the same center line. Specs sometimes give outer diameter OD and wall thickness t; then inner radius is OD/2 - t. The Tube Calculator reports t = R - r alongside volume.
t = R - rFor R = 5 and r = 3:
t = 2Thickness is not the difference of diameters unless that difference is halved. Confusing diameter difference with radius difference doubles the reported wall. Annulus width on the planar page is the same R - r quantity without a length.
Solve a tube with radii 5 and 3, length 20
Substitute the reference values into the annulus-times-length formula. Wall thickness is 2. Material volume is 320 * pi. 1. Wall thickness
t = 5 - 3 = 22. Annular cross-section area
A = pi * (25 - 9) = 16 * pi approx 50.273. Material volume
V = 16 * pi * 20 = 320 * pi approx 1005.314. Inner fluid volume (for comparison)
V_fluid = 9 * pi * 20 = 180 * pi approx 565.49The annular area 16 * pi matches the Annulus Calculator fixture at R = 5 and r = 3. This page multiplies by length; the annulus page stops at area and circumferences.
Pipe schedules often list nominal size, outer diameter and wall thickness rather than both radii. Convert OD to R = OD/2 and set r = R - t when thickness is given. Confirm whether length L is the cut length of the pipe or a centerline length on a bend; this page models a straight circular tube of constant cross section.
Mass estimates multiply material volume by density. Steel near 7850 kg/m^3 and aluminum near 2700 kg/m^3 are common references, but alloy and temperature shift density, so treat mass as an estimate until a supplier sheet confirms the figure. The Tube Calculator itself returns geometric volume only.
Choose material volume or fluid capacity
Order metal or plastic by material volume V = pi * (R^2 - r^2) * L. Size a pump or tank fill by fluid capacity V_fluid = pi * r^2 * L. For R = 5, r = 3, L = 20 those values are 320 * pi and 180 * pi.
Adding them recovers the outer envelope 500 * pi, which is a quick swap check if R and r might have been reversed on entry.
Wall thickness t = R - r should match the cut sheet. Specs that give OD and t convert with R = OD/2 and r = R - t before volume runs. Specs that give OD and ID convert both diameters to radii, then confirm t = R - r equals half the diameter difference.
Unit note: outer radius, inner radius and length share one length unit. Annular area is in square units; material and fluid volumes are in cube units. Do not mix millimetres of wall with metres of cut length without converting first.
Frequently asked questions
What is tube volume?
Tube material volume is V = pi * (R^2 - r^2) * L. For R = 5, r = 3, L = 20, V = 320 * pi approx 1005.31.
What is wall thickness?
Wall thickness is t = R - r. For R = 5 and r = 3, t = 2.
How is fluid capacity different from material volume?
Fluid capacity inside the bore is pi * r^2 * L. Material volume uses the annular cross section instead.
Can the Tube Calculator use diameters?
Yes. Convert OD and ID to radii, or enter diameters if the fields accept them and halve internally before squaring.
How does a tube relate to an annulus?
An annulus is the 2D ring cross section. Tube volume is annulus area times length. Use the Annulus Calculator for planar ring area.
What if the tube is solid?
If there is no inner hole, use the Cylinder Calculator with a single radius.
What units does the Tube Calculator use?
Radii and length share one length unit. Volume uses cube units of that length.
Must outer radius exceed inner radius?
Yes. If r >= R the annular area is zero or negative and the inputs are rejected.
How do I convert OD and wall thickness?
Set R = OD/2 and r = R - t. Then V = pi * (R^2 - r^2) * L with those radii.
Does the Tube Calculator include end faces in surface area?
This page focuses on material volume of the wall. Closed-end surface treatments belong on dedicated surface-area workflows or the solid cylinder page when ends are capped disks.
What if the bore is not empty for shipping weight?
Shipping weight tracks material volume times density. Fluid fill is a separate capacity calculation using pi * r^2 * L.
What is the reference tube volume?
For R = 5, r = 3, L = 20, material volume is 320 * pi approx 1005.31.
How does tube volume relate to two cylinders?
Subtract the inner cylinder volume from the outer: 500 * pi - 180 * pi = 320 * pi for the reference inputs.
Summary
Tube Calculator returns wall thickness and material volume for a hollow circular cylinder from outer radius, inner radius and length, with substituted arithmetic and a labelled figure. Worked numbers match R = 5, r = 3, L = 20: t = 2 and V = 320 * pi.
Use the Annulus Calculator for the ring area alone and the Cylinder Calculator for a solid pipe blank.