Density of a Cylinder Calculator

Created by Krishna Nelaturu
Reviewed by Rijk de Wet
Last updated: Apr 27, 2022

This density of a cylinder calculator is helpful to determine the density of any cylindrical structure, given its mass and volume. If you're uncertain about the cylinder's volume, you can use its dimensions instead.

In this article, let's discuss some basic concepts:

  • What is density?
  • What is the formula for cylinder density?
  • How to find the density of a cylinder?
  • FAQ

What is density?

Density is the amount of mass of a substance per unit volume. It is given by:

ρ=mV\rho = \frac{m}{V}

where:

  • ρ\rho is the density of the substance;
  • mm is the mass of the substance; and
  • VV is the volume of the substance.

The SI unit of density is kilogram per cubic meter (kg/m3\text{kg}/\text{m}^3), while its imperial unit is pound per cubic feet (lb/ft3\text{lb}/\text{ft}^3).

Cylinder density formula

To derive a cylinder density formula, let's start by calculating its volume:

V=πr2hV = \pi r^2 h

where:

  • VV is the cylinder's volume;
  • rr is the cylinder's radius; and
  • hh is the cylinder's height.
Image of a cylinder with radius and height marked. Cylinder volume formula displayed.
A cylinder with radius r and height h.

Combining this with the general formula for density we've seen in the previous section, we get the formula for cylinder density:

ρ=mV=mπr2h\rho = \frac{m}{\textcolor{red}{V}} = \frac{m}{\textcolor{red}{\pi r^2 h}}

How do I find the density of a cylinder?

To calculate the density of a cylinder, follow these steps:

  1. Measure the mass m of the cylinder if it is not already known.
  2. Determine the cylinder's volume V from its radius r and height h using the formula V = πr²h.
  3. Divide the cylinder's mass by its volume to get its density ρ = m/v.
  4. Verify your results using our density of a cylinder calculator.

How to use this cylinder density calculator?

This density of a cylinder calculator is easy to use. It has two modes of calculation to suit your needs:

  • In the default Simple mode, you can enter the cylinder's Mass and Volume to calculate its density. Use this mode if both the mass and volume are known quantities.
  • Using the Advanced mode, you can also feed the cylinder's Height and Radius instead of its volume to calculate the cylinder's density. Use this mode if you don't know the cylinder's volume.

FAQ

What is the density of a 500g cylinder with a 5cm radius and 10cm height?

636.6 kg/m³ is the density of this cylinder. To calculate this answer yourself, follow these steps:

  1. Calculate the cylinder's volume using V = πr²h to get V = π×(5 cm)²×(10 cm) = 785.40 cm³.
  2. Divide the cylinder's mass by its volume to get its density as ρ = (500 g)/(785.40 cm³) = 0.6366 g/cm³.
  3. Convert this density into SI unit to get ρ = 0.6366 × 1000 = 636.6 kg/m³.
  4. Verify this result using our density of a cylinder calculator.

How do I calculate the density of an oblique cylinder?

The density of an oblique cylinder is given by: ρ = m/πr²h. As long as you measure the cylinder's height h perpendicular to its base, the formula for the volumes of oblique and right cylinders are the same: V = πr²h. Hence, their densities will also be the same.

Krishna Nelaturu
Density of a cylinder
Image of a cylinder with radius and height marked. Cylinder volume formula displayed.
Weight/mass
lb
Volume
cu ft
Density
lb/cu ft
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