Physical Pharmacy

Density & Relative Density Bottle Calculator

Relative density (specific gravity) and density of a liquid from three weighings of a pycnometer.

Experiment

Sample name (optional)

Printed on the lab result card.

Weighings

All three with the same bottle and stopper, to the balance's full precision.

Mass of empty bottle (W₁)

Clean and dry, with stopper.

Mass of bottle + water (W₂)

Filled to the capillary.

Mass of bottle + sample (W₃)

Filled to the capillary.

Conditions

Water density is used for the sample's density; temperature and volume are optional.

Density of water

g/mL

1.000 unless your manual gives a value at the working temperature.

Temperature (optional)

°C

Enter 15–30 °C to see the density of water at that temperature.

Bottle volume (optional)

Nominal volume — used for a second, volume-based density.

Try a worked example

Laboratory calculation card

Enter the three weighings and the density of water.

Mass of water = W₂ − W₁

Mass of sample = W₃ − W₁

Relative density = (W₃ − W₁) / (W₂ − W₁)

Density of sample = Relative density × Density of water

The bottle holds the same volume of water and of sample, so the ratio of their masses equals the ratio of their densities. Multiplying by the density of water at the working temperature turns that ratio into the sample's density in g/mL. If a nominal bottle volume is entered, density is also calculated directly as mass / volume; it is only as good as the volume printed on the bottle.

Example (25 mL bottle): W₁ = 20.500 g, W₂ = 45.450 g, W₃ = 51.950 g gives 31.450 g / 24.950 g = 1.2605.

References

Stockton SJ. Stoklosa and Ansel's Pharmaceutical Calculations. 16th ed. Philadelphia: Wolters Kluwer; 2021.

Common questions

In pharmacy practice, yes — both mean the mass of a volume of the substance divided by the mass of an equal volume of water. Because grams divide by grams it has no unit, while density is in g/mL.

The capillary in the stopper defines the volume. Liquid that stops short, or that overflows and is left on the outside, changes the mass without changing the nominal volume and throws off the ratio.

Liquids expand as they warm, so the same bottle holds slightly less mass of a warmer liquid. Water itself changes from 0.99910 g/mL at 15 °C to 0.99565 g/mL at 30 °C. Pharmacopoeial relative densities are quoted at a stated temperature, commonly 20 °C or 25 °C.

The water-calibrated value (relative density × density of water). The volume printed on a bottle is nominal; weighing it full of water measures its true volume at the working temperature, so the volume-based density is useful only as a cross-check.

The sample is lighter than water — ethanol, many volatile oils and liquid paraffin fractions are examples. It is not an error, as long as W₃ is still heavier than the empty bottle.

About the density bottle

A relative density bottle (pycnometer, specific gravity bottle) holds exactly the same volume every time it is filled to its capillary. Weighing it empty, full of water and full of sample gives two masses of the same volume — and their ratio is the relative density.

Because it is mass divided by mass, relative density is dimensionless. It is also temperature-dependent: liquids expand on warming, so both the sample and the water should be at the same, recorded temperature.

Good technique

Fill until liquid rises through the stopper's capillary, so the volume is exact

Wipe the outside dry before weighing — a film of liquid adds mass

Tap out air bubbles; a trapped bubble displaces liquid

Let the filled bottle reach thermal equilibrium, e.g. in a water bath

Use the same bottle and stopper for all three weighings

Common errors

Handling the bottle with bare hands warms it and the liquid

Weighing a bottle that is not fully dry inside for W₁

Using the nominal volume instead of calibrating with water

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy