What is the formula for the density of a cylinder?

Density equals mass divided by volume (rho = m / V). For a cylinder, the volume is V = pi x r^2 x h, where r is the radius and h is the height. So density = m / (pi x r^2 x h). Make sure your mass and volume units are consistent (for example, grams and cubic centimetres, or kilograms and cubic metres) before dividing.

How do I find the volume of a cylinder from its diameter?

If you know the diameter instead of the radius, divide the diameter by 2 to get the radius, then use V = pi x r^2 x h. For example, a cylinder with a 10 cm diameter and 20 cm height has a radius of 5 cm, giving a volume of pi x 5^2 x 20 = 1,570.8 cubic centimetres.

What units should I use for density?

Density is most commonly expressed in kilograms per cubic metre (kg/m3) for engineering and scientific use, or grams per cubic centimetre (g/cm3) for smaller lab samples. Water has a density of 1,000 kg/m3 (1 g/cm3), which is a useful benchmark: materials denser than water sink in it, and materials less dense float.

Density of a Cylinder Calculator

Work out the density of a cylindrical object from its radius (or diameter), height and mass. This calculator finds the volume using V = pi x r^2 x h, then divides mass by volume to give density in kg/m3 and g/cm3.

Useful for materials testing, engineering coursework, workshop estimates and checking whether an object will float or sink.

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Method verified Standard cylinder volume and density formulas (SI units).

1. Cylinder Dimensions

Measure by

Radius

Diameter

Height (length)

Length unit

2. Mass

Mass

Mass unit

Volume and Density

Volume

cm3

Volume

Density
-
kg/m3

Density

g/cm3

Working

Radius used-

Height used-

Volume formulaV = π × r² × h

Volume (cm3)-

Mass-

Density (kg/m3)-

Comparison to Water

Water density1,000 kg/m3 (1 g/cm3)

Your material's density-

Would it float?-

Summary: Enter your cylinder's dimensions and mass above.

How to Find the Density of a Cylinder

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.

Step by Step

Measure the radius (half the diameter) of the circular face of the cylinder.
Measure the height (or length, if the cylinder is lying on its side).
Calculate the volume: V = pi x r^2 x h.
Weigh the object to find its mass.
Divide mass by volume to get density: density = mass / volume.

Worked Example

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.

Units Matter

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.

Related Calculators

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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