Density of a Cylinder Calculator
Enter the cylinder's mass and dimensions to find its density instantly. The calculator works for solid and hollow cylinders, supports metric and imperial units, and shows every step of the calculation so you can follow the math. Common reference material densities are listed below to help you verify your result.
Formula
Worked example
A solid aluminum cylinder has mass 500 g, radius 5 cm, and height 10 cm. Volume = π × 5² × 10 = 785.4 cm³. Density = 500 / 785.4 = 0.6366 g/cm³. This is well below the aluminum reference value of 2.70 g/cm³, suggesting the cylinder is hollow or made of a lighter material.
What is the density of a cylinder?
Density is a material property defined as mass per unit volume. For a cylinder, the volume is determined by its geometry: a solid cylinder's volume is V = πr²h, where r is the radius and h is the height. A hollow cylinder (a tube or pipe) has a cylindrical bore removed from its center, so its volume is V = πh(r_out² - r_in²). In both cases, density equals mass divided by volume, giving the result in grams per cubic centimetre (g/cm³) or kilograms per cubic metre (kg/m³). Density is a key property in material identification, engineering design, and quality control. If you measure a cylinder's mass on a scale and its dimensions with a calliper, you can calculate its density and compare it against known values to identify or verify the material.
How to use this calculator
Select metric (g and cm) or imperial (lb and in). Choose whether the cylinder is solid or hollow. For a solid cylinder, enter the mass, outer radius, and height. For a hollow cylinder, also enter the inner radius (the bore radius). The calculator converts all values to metric internally, computes the volume, and divides mass by volume to get the density. Results are shown in g/cm³ and kg/m³ (the SI base unit). Volume, lateral surface area, and total surface area are reported as secondary outputs. The step panel below the result card walks through every arithmetic step with your actual numbers substituted, so you can check the calculation by hand.
Solid vs hollow cylinder density
Two cylinders can have the same outer dimensions but very different densities if one is hollow. A 5 cm-radius, 10 cm-tall aluminum rod weighs about 2.12 kg; a same-size aluminum tube with a 4 cm bore weighs only about 0.77 kg, giving an apparent density of only 0.98 g/cm³ if you forget the bore exists. This is why specifying the cylinder type matters. In practice, apparent density (mass divided by the total envelope volume including the cavity) is different from material density (mass divided by the volume of solid material). This calculator computes material density: it subtracts the hollow bore from the volume before dividing, so the result reflects the actual density of the material the cylinder is made from.
Interpreting your result and identifying materials
Comparing your calculated density against the reference table below is a fast way to narrow down possible materials:
- Under 1.0 g/cm³: lighter than water - foams, corks, some softwoods, or most polymers at low packing density.
- 1.0 to 2.5 g/cm³: water range - many common plastics, glass-filled composites, concrete.
- 2.5 to 4.5 g/cm³: light metals - aluminum, magnesium, titanium alloys.
- 7.0 to 9.0 g/cm³: ferrous and copper-group metals - steel, cast iron, copper, nickel.
- Above 10 g/cm³: heavy metals - lead, bismuth, gold, platinum.
Typical densities of common materials
| Material | Density (g/cm³) | Density (kg/m³) |
|---|---|---|
| Cork | 0.12-0.24 | 120-240 |
| Ice (water) | 0.92 | 917 |
| Water (liquid) | 1.00 | 1000 |
| Polyethylene (HDPE) | 0.93-0.97 | 930-970 |
| PVC (rigid) | 1.30-1.45 | 1300-1450 |
| Nylon (PA 6) | 1.12-1.15 | 1120-1150 |
| Concrete (typical) | 2.30-2.40 | 2300-2400 |
| Aluminum alloy (6061) | 2.70 | 2700 |
| Glass (borosilicate) | 2.23 | 2230 |
| Titanium (Grade 5) | 4.43 | 4430 |
| Stainless steel (304) | 7.93 | 7930 |
| Carbon steel | 7.85 | 7850 |
| Iron (cast) | 7.20 | 7200 |
| Copper | 8.96 | 8960 |
| Nickel | 8.91 | 8910 |
| Lead | 11.34 | 11340 |
| Gold | 19.32 | 19320 |
Reference values at room temperature (~20 °C). Actual density varies with alloy, grade, temperature, and porosity.
Frequently asked questions
What is the formula for the density of a cylinder?
For a solid cylinder: density = mass / (π × radius² × height). For a hollow cylinder: density = mass / (π × height × (outer radius² - inner radius²)). In both cases the volume formula changes; the density equation (mass divided by volume) stays the same.
Does the density of a cylinder depend on its shape?
No - density is a material property, not a shape property. A steel cylinder and a steel sphere made from the same alloy have the same density (~7.85 g/cm³). The cylinder's shape determines its volume, and volume affects how much mass fits in a given space, but the density of the solid material is independent of geometry.
Why is my calculated density different from the published value for that material?
Several factors can cause a discrepancy: the cylinder may be a different alloy or grade than you assumed; coatings, plating, or surface treatments add mass without much volume; internal porosity or voids reduce effective volume; measurement errors in dimensions or mass accumulate; and published values are typically measured at 20 °C, so a hot or cold sample will differ slightly due to thermal expansion.
How do I calculate the density of a hollow cylinder (tube or pipe)?
Measure the outer radius, inner radius (bore radius), height, and mass. Volume of material = π × height × (outer radius² - inner radius²). Density = mass / volume. In the calculator, switch the cylinder type to Hollow, enter the inner radius, and all the arithmetic is done for you.
Can I use this calculator to identify what material a cylinder is made of?
Yes, with some caution. Measure the mass (on a scale), outer radius and height (with calipers), and compare the result against the reference table below. The density narrows the material class reliably, for example distinguishing aluminum (~2.7 g/cm³) from steel (~7.85 g/cm³). However, many alloys and composites share similar densities, so a precise match requires additional testing such as XRF or chemical analysis.
What units does this calculator use?
Results are always reported in g/cm³ and kg/m³, the two most common units for material density, regardless of whether you enter metric or imperial inputs. Internally, all imperial values (lb, inches) are converted to metric (g, cm) before the calculation. Volume is shown in cm³ and surface areas in cm².
What is the density of a steel cylinder?
Carbon steel has a density of about 7.85 g/cm³ (7850 kg/m³). Stainless steel (grade 304) is slightly higher at about 7.93 g/cm³. If you have a steel cylinder of known dimensions, enter the expected mass from that density to cross-check, or enter the actual measured mass to verify the material.