The relative density formula is : divide the density of a material by the density of water. Because both are in kg/m³, the units cancel and relative density is a plain number. Iron, at 7870 kg/m³, has a relative density of 7.87, meaning it is 7.87 times as dense as water.
US books usually call the same ratio specific gravity. The reference is water at 4 °C, where its density is 1000 kg/m³. For gases, air is sometimes used as the reference instead, so read the question. Relative density is the quickest way to predict sinking and floating, and it sits next to the density formula on the fluids formula sheet.
Quick facts
Formula
By weighing
SI unit
None: it is a ratio of two densitiesDimensional formula
[M⁰ L⁰ T⁰]Other name
specific gravityShortcut
RD has the same number as the density in g/cm³
The relative density formula, term by term
| Symbol | Meaning | Unit |
|---|---|---|
| RD | Relative density of the material | none |
| Density of the material being tested | kg/m³ | |
| Density of water at 4 °C | 1000 kg/m³ |
Since both densities are mass per volume, you can also compare masses of equal volumes: RD equals the mass of any volume of the substance divided by the mass of the same volume of water. That version needs no density calculation at all, only two weighings of equal volumes.
Values below 1 float in water, values above 1 sink. Cork is about 0.24, ice 0.917, sea water 1.025, aluminium 2.70 and mercury 13.6.
Formula for relative density by weighing in water
A solid that sinks can be weighed in air and then fully under water. The difference is the buoyant force, which equals the weight of water with the same volume as the solid. So
This comes straight from Archimedes' principle; see the buoyant force formula for the force itself. Class 9 practicals use a spring balance and a beaker for exactly this measurement.
Solved examples
Example 1: from a density
Copper has a density of 8960 kg/m³. Find its relative density.
No unit is written: the kg/m³ cancel.
Example 2: by weighing
A rock weighs 30 N in air and 20 N when fully under water. Find its relative density and its density.
Loss of weight = 30 − 20 = 10 N, so .
Density: .
Example 3: finding a mass using RD
Mercury has a relative density of 13.6. What is the mass of 50 cm³ of mercury?
Density = 13.6 × 1000 = 13 600 kg/m³, which is 13.6 g/cm³.
Why relative density has no unit or dimensions
Both the top and the bottom of the ratio have dimensions [M L⁻³], so
A dimensionless number is the same in every unit system, which is why tables can quote one value for SI and CGS users alike. The dimensional formula of relative density page lists other dimensionless quantities such as strain and refractive index.
Common mistakes
- Writing a unit after RD. An answer such as 3.0 kg/m³ for relative density loses the mark.
- Dividing by the weight in water instead of the loss of weight. The bottom of the fraction is W_air − W_water.
- Using 1 as the water density in SI. Water is 1000 kg/m³, or 1 g/cm³; match the units of the top.
- Confusing it with density. Density carries kg/m³; relative density compares it with water.
Frequently asked questions
What is the formula for relative density?
RD = density of the substance / density of water at 4 °C. For a sinking solid you can also use RD = weight in air / loss of weight in water.
What is the SI unit of relative density?
Relative density has no unit because it is a ratio of two densities. In bracket form that is [M⁰ L⁰ T⁰].
Is relative density the same as specific gravity?
Yes. Both compare a substance's density with that of water. Indian books prefer relative density, US books specific gravity.
What is the relative density of water?
Exactly 1, since water is compared with itself. Liquids with RD less than 1, such as kerosene, float on water.
How is relative density used to tell if an object floats?
If the RD of a solid is less than the RD of the liquid, it floats. Ice (0.917) floats on water (1.00) but sinks in alcohol, which has an RD near 0.79.