Calculate the mass of solid cylinders and hollow tubes from dimensions or known volume and material density in metric or imperial units.
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Cylinder Mass Formula
Mass equals volume times density. The volume formula changes with the shape.
Solid cylinder:
m = pi * r^2 * L * rho
Hollow tube:
m = pi * (R^2 - r^2) * L * rho
Known volume:
m = V * rho
- m = mass (kg)
- r = inner radius for a tube, or radius for a solid cylinder (m)
- R = outer radius of a tube (m)
- L = length or height (m)
- V = total volume (m³)
- rho = density of the material (kg/m³)
Assumptions: the cross section is a perfect circle, the wall thickness of a tube is uniform, and the material density is constant. If you enter a diameter, the calculator divides by two before squaring. All inputs are converted to SI units before the math runs, then the result is reported in kg, lb, metric tons, and short tons.
The three modes match the three formulas above. Solid uses one diameter or radius. Hollow tube subtracts the inner cross section from the outer one. Known volume skips the geometry and applies density directly to a volume you already have.
Reference Tables
Density values for the built-in materials and a few common additions:
| Material | kg/m³ | lb/ft³ | lb/in³ |
|---|---|---|---|
| Steel / iron | 7850 | 490 | 0.284 |
| Stainless 304 | 8000 | 499 | 0.289 |
| Aluminum | 2700 | 169 | 0.098 |
| Copper | 8960 | 559 | 0.324 |
| Brass | 8500 | 531 | 0.307 |
| Concrete | 2400 | 150 | 0.087 |
| Plastic (PE) | 950 | 59 | 0.034 |
| Wood (avg) | 600 | 37 | 0.022 |
| Water | 1000 | 62.4 | 0.036 |
Quick mass per meter for a steel solid round bar (rho = 7850 kg/m³):
| Diameter | kg per meter | lb per foot |
|---|---|---|
| 10 mm | 0.62 | 0.41 |
| 20 mm | 2.47 | 1.66 |
| 25 mm | 3.85 | 2.59 |
| 40 mm | 9.86 | 6.62 |
| 50 mm | 15.41 | 10.35 |
| 75 mm | 34.67 | 23.29 |
| 100 mm | 61.65 | 41.41 |
Worked Examples and FAQ
Example 1: Solid steel shaft. Diameter 50 mm, length 2 m, steel at 7850 kg/m³.
Radius = 0.025 m. Volume = pi × 0.025² × 2 = 0.003927 m³. Mass = 0.003927 × 7850 = 30.83 kg.
Example 2: Aluminum tube. Outer diameter 4 in, inner diameter 3.5 in, length 24 in, aluminum at 2700 kg/m³.
Outer radius = 0.0508 m, inner radius = 0.04445 m, length = 0.6096 m. Volume = pi × (0.0508² - 0.04445²) × 0.6096 = 0.001154 m³. Mass = 0.001154 × 2700 = 3.12 kg, or 6.87 lb.
Example 3: Concrete column from a known volume. Volume = 1.2 m³, density = 2400 kg/m³.
Mass = 1.2 × 2400 = 2880 kg.
Does the orientation of the cylinder matter? No. Mass depends only on volume and density.
What if my material is not in the list? Pick "Custom density" and enter the value. Any nonzero density entered in the override field overrides the dropdown choice.
Can I use this for liquids in a tank? Yes. Use the solid cylinder mode with the inside diameter and the fill height, then choose the liquid density. Water is 1000 kg/m³, diesel about 832, gasoline about 740.
Why does my tube weight not match a supplier chart? Suppliers often use nominal pipe sizes where the listed diameter is not the actual outer diameter. Enter the measured outer and inner dimensions to get a true result.
How do I convert g/cm³ to kg/m³? Multiply by 1000. So 7.85 g/cm³ equals 7850 kg/m³.
