All formulas for relative density

The most fundamental formula for relative density is the ratio of the density of the substance to the density of the reference substance.

$$\text{RD} = \frac{\rho_{\text{substance}}}{\rho_{\text{reference}}}$$

Where:

• $\rho_{\text{substance}}$ is the density of the substance
• $\rho_{\text{reference}}$ is the density of the reference substance (e.g., water)

Since density ($\rho$) is mass ($m$) divided by volume ($V$), if we consider equal volumes of the substance and the reference material, the formula can be expressed in terms of mass:

$$\text{RD} = \frac{m_{\text{substance}}}{m_{\text{reference}}}$$

Where:

• $m_{\text{substance}}$ is the mass of a certain volume of the substance
• $m_{\text{reference}}$ is the mass of an equal volume of the reference substance

Similarly, since weight ($W$) is mass ($m$) times the acceleration due to gravity ($g$), if we consider equal volumes, the formula can be expressed in terms of weight:

$$\text{RD} = \frac{W_{\text{substance}}}{W_{\text{reference}}}$$

Where:

• $W_{\text{substance}}$ is the weight of a certain volume of the substance
• $W_{\text{reference}}$ is the weight of an equal volume of the reference substance

When a substance is weighed in air and then weighed while fully immersed in a fluid (like water), the apparent loss of weight is equal to the weight of the fluid displaced.

$$\text{RD} = \frac{\text{Weight of substance in air}}{\text{Apparent loss of weight in water}}$$ $$\text{RD} = \frac{W_{\text{air}}}{W_{\text{air}} - W_{\text{water}}}$$

Where:

• $W_{\text{air}}$ is the weight of the substance in air
• $W_{\text{water}}$ is the weight of the substance when fully immersed in water

These formulas allow for the calculation of relative density based on different measurable properties.