This calculator works out the density of a cylindrical object by combining its volume with its mass, so you can identify what a material might be, check whether it will float or sink, or verify a calculation for a materials science or engineering assignment. You enter the cylinder's radius (or diameter, if that is easier to measure), its height or length, and its mass, then choose your length unit (millimetres, centimetres or metres) and mass unit (grams or kilograms). The calculator first finds the volume using V = pi x r^2 x h, then divides your mass by that volume to return density in both kilograms per cubic metre and grams per cubic centimetre, alongside the volume itself in cubic centimetres and cubic metres. A working panel shows the radius and height used, the volume formula and result, and your mass, so you can follow every step of the calculation rather than just seeing an answer. It also compares your result against the density of water, 1,000 kg/m3, telling you straight away whether the object would float or sink, which is a handy sanity check if you already know the material. Because density calculations are only as accurate as your measurements, take radius and height readings at a few points if the cylinder tapers, and make sure your length and mass units are entered correctly before relying on the result. This tool assumes a solid, uniform cylinder with no hollow sections, so for pipes, tubes or composite objects you will need to calculate the volume of each section separately and combine the results.
Density describes how much mass is packed into a given volume. It is calculated as density = mass / volume (rho = m / V). For a cylinder, the volume depends on the radius (or diameter) and the height, using the formula V = pi x r^2 x h. Once you know the volume, divide the mass of the object by that volume to get its density.
A cylinder has a radius of 5 cm and a height of 20 cm. Its volume is V = pi x 5^2 x 20 = 1,570.8 cm3. If the cylinder has a mass of 1,570.8 g, its density is 1,570.8 / 1,570.8 = 1.00 g/cm3, which is the same as 1,000 kg/m3, equal to the density of water.
| Quantity | SI Unit | Common Alternative |
|---|---|---|
| Length (radius, height) | Metres (m) | Centimetres (cm), millimetres (mm) |
| Mass | Kilograms (kg) | Grams (g) |
| Volume | Cubic metres (m3) | Cubic centimetres (cm3), litres |
| Density | kg/m3 | g/cm3 (1 g/cm3 = 1,000 kg/m3) |
Always convert your measurements to consistent units before dividing mass by volume. Mixing units (such as mass in kilograms with volume in cubic centimetres) is the most common source of error in density calculations.
Sources: Standard geometric formula for cylinder volume (V = pi r^2 h) and the physics definition of density (rho = m/V), as used in NCEA and university level maths and physics.
This calculator assumes a uniform, solid cylinder with no hollow sections or voids. For hollow cylinders or composite objects, calculate volume separately for each section.
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