How to use specific gravity
Specific gravity is the weight of a liquid compared with the weight of the same volume of water. Water weighs 1 g per mL, so a liquid's specific gravity is numerically its grams per millilitre, and that's the whole use of it: it converts between a volume and a weight. Formulas are often written by weight while the ingredients are measured by volume, or the reverse, and specific gravity is the bridge.
weight (g) = volume (mL) × SG • volume (mL) = weight (g) ÷ SG • SG = weight (g) ÷ volume (mL)
Specific gravity has no unit, because it's a ratio of two weights. Treat it as g/mL in the arithmetic anyway; the units come out right.
Worked example 1: volume to weight
Glycerin has a specific gravity of 1.25. What does 120 mL weigh?
weight = 120 × 1.25 = 150 g
Worked example 2: weight to volume
Alcohol has a specific gravity of 0.81. What volume contains 100 g?
volume = 100 ÷ 0.81 = 123.46 → 123.5 mL
A liquid lighter than water takes up more than 100 mL per 100 g; a liquid heavier than water takes up less. That's the sanity check. Glycerin at 1.25 makes 100 g fit into 80 mL. Alcohol at 0.81 needs 123.5 mL for the same weight. If your answer moves in the wrong direction, you multiplied where you should have divided.
Worked example 3: finding the specific gravity
60 mL of a syrup weighs 78 g.
SG = 78 ÷ 60 = 1.3
A question may give this as a pycnometer or a graduated-cylinder measurement: the empty container weighs so much, the container plus liquid weighs so much more, and the volume is known. Subtract the container's weight before dividing.
Where it shows up inside other problems
A percent w/w formula that has to be made to a volume. A compounding order listing an ingredient in grams that the pharmacy stocks and measures as a liquid. A w/v strength of a liquid-in-liquid preparation. In each case the specific gravity step comes first, so that everything is in one kind of unit before the main calculation. When a question mentions specific gravity and you can't see why, look for the place where a weight and a volume are about to be compared.
Where students lose the points
- Direction. Volume × SG gives weight. Weight ÷ SG gives volume. Check against water: for SG below 1, the volume is the bigger number.
- Treating SG as a percent or a density in other units. It's grams per millilitre, no conversion needed.
- Applying it to a solid. Specific gravity is for liquids and semisolids measured by volume. Tablets and powders are weighed.
- Forgetting the container weight. When a weight is given "with the container", subtract the empty container first.