All common slicers for 3D printing require the specification of the relative density of the filament. This information has no influence on the printing behavior, but is required to calculate the costs, print volume and length of the required filament.
In principle, it is possible to calculate this value using the mass and a little geometry. If you have a (possibly straight cut) piece of filament, its exact length and the exact weight of it, you can easily determine the density using the formula for calculating the volume of a cylinder.

V_c = \pi r^2 h

The volume (V) results from the radius (r) of the filaments squared, corresponding to (1.75 mm/2)². Multiplied by π and the height (h) which in our case would be the exact length of the filament. This value must be converted into cm³. Using the rule of three and the measured weight, the relative density can be determined (relatively inaccurately).

Density measurement with a pycnometer

The way described above was somehow too imprecise and unscientific for me. Like Archimedes in the bathtub, I would like to make use of the principle of displacement and determine the relative density of several filament samples with a pycnometer.
The relative density (ρF)is calculated from the mass of the empty pycnometer (m0), the mass of the pycnometer filled with water (m1), the mass of the pycnometer with the filament sample inside (m2), the mass of the pycnometer with filament and filled with water (m4), and finally the density of the water at a defined temperature (ρw).

\rho_F = \frac{(m_2 - m_0)}{(m_1-m_0)-(m_3-m_2)}\cdot \rho_W

I did a first test with a rest filament OWL, PETG Yellow and found a density of 1.32 g/cm³. I will start a list and measure all the filaments.

CompanyNameSourceRelative Density (g/cm³)
OWLPETG YellowAmazon1.32