Calculate specific gravity (relative density) and density in g/mL from pycnometer weights at 20 °C, 25 °C or any temperature, with an optional air buoyancy correction. Enter several sample weights to get each result and the mean.
Specific gravity vs density
| Specific gravity (relative density) | Density | |
|---|---|---|
| Definition | Mass of a volume of sample ÷ mass of the same volume of water, at a stated temperature | Mass per unit volume |
| Units | None (a ratio) | g/mL (or kg/m³) |
| Pharmacopoeia | USP <841> Specific Gravity (normally at 25 °C); Ph. Eur. 2.2.5 relative density d2020 | Ph. Eur. 2.2.5 density ρ20 |
The old version of this calculator labelled the ratio (W₂ − W₀) ÷ (W₁ − W₀) as “density”. That ratio is the specific gravity. To get density in g/mL, multiply it by the density of water at the test temperature, as this calculator now does.
Formulas (pycnometer method)
Specific gravity = (W₂ − W₀) ÷ (W₁ − W₀)
Density (g/mL) = specific gravity × ρwater
With air buoyancy correction: density = specific gravity × (ρwater − ρair) + ρair
W₀ = empty, dry pycnometer · W₁ = pycnometer filled with water · W₂ = pycnometer filled with sample · ρwater = 0.998203 g/mL at 20 °C and 0.997043 g/mL at 25 °C · ρair ≈ 0.0012 g/mL
Procedure
- Clean and dry the pycnometer, bring it to the test temperature and weigh it empty (W₀).
- Fill it with freshly boiled and cooled purified water at the test temperature (for example 25 °C), insert the stopper, wipe off the excess, and weigh (W₁).
- Empty, clean and dry the pycnometer. Fill it with the sample at the same temperature, and weigh (W₂).
- Calculate the specific gravity and, if required, the density. Repeat for replicate determinations.
Worked example
W₀ = 25.4321 g, W₁ = 50.3874 g, so the water mass is 24.9553 g. Three fills of an oral solution give W₂ = 55.6412, 55.6398 and 55.6425 g. Mean specific gravity = 1.2105. At 25 °C, density = 1.2105 × 0.997043 = 1.2069 g/mL, or 1.2067 g/mL with the air buoyancy correction.
Why density matters in pharma QC
- Identification and quality tests for liquids, such as glycerin, ethanol, syrups and oils, against monograph limits for specific gravity or relative density.
- Converting between weight and volume, for example a “per mL” label claim when a liquid is weighed, or filling by weight.
- Checking batch-to-batch consistency of solutions and suspensions.
Common mistakes
- Reporting the ratio as density in g/mL without multiplying by the density of water.
- Measuring water and sample at different temperatures.
- Air bubbles in the pycnometer, or liquid left on the outside.
- Using a pycnometer that is not completely dry before filling with the sample.
- Comparing a result at 25 °C with a monograph limit stated at 20 °C.
Frequently asked questions
Is specific gravity the same as density?
No. Specific gravity is a unitless ratio to water. Density has units (g/mL). At 4 °C water has a density of almost exactly 1 g/mL, so the two values are close, but at 20–25 °C they differ by about 0.2–0.3%.
What temperature should I use?
The one stated in the monograph: usually 25 °C for USP specific gravity and 20 °C for Ph. Eur. relative density and density.
Can I use this for a digital density meter?
A digital oscillating U-tube density meter reports density directly. Use this calculator for pycnometer measurements, or to convert a density to specific gravity by dividing by the density of water.
Related tools and guides
References
- USP General Chapter <841> Specific Gravity.
- Ph. Eur. 2.2.5 Relative density.