Density calculator

1. What density is

Density is how much mass is packed into each unit of volume. A rock's density does not depend on its size: a pebble and a boulder of the same granite have the same density. That is what makes it useful for telling materials apart.

density ρ = mass m ÷ volume V

Geologists usually quote it in grams per cubic centimetre (g/cm³). Water is almost exactly 1 g/cm³, so the number also tells you how many times heavier the rock is than the same volume of water; this ratio is called the specific gravity. In SI units, 1 g/cm³ is 1,000 kg/m³.

2. Measuring volume with water: Archimedes' principle

Weighing a rock is easy; measuring the volume of a lumpy shape is not. Water solves this. A body held under water pushes aside its own volume of water, and the water pushes back up on it with a force equal to the weight of the water pushed aside. This is Archimedes' principle, and the upward force is called buoyancy.

So the rock's volume equals the mass of the water it displaces divided by the density of water. There are two kitchen-friendly ways to measure that mass, and the calculator handles both.

1. Jug on the scales. Stand a jug of water on the scales and press zero. Lower the rock in on a thread until it hangs completely under water, touching neither the sides nor the bottom. The scales now read more, because the water is pushing up on the rock and, by Newton's third law, the rock pushes down on the water just as hard. The increase in grams is the mass of water displaced.
2. Hanging under the scales. Hang the rock from a hook under the scales (or from a spring balance) and weigh it in air. Then raise a container of water around it until it is fully covered and weigh it again. It now seems lighter. The loss of weight is the mass of water displaced.

V = m_water ÷ ρ_water   so   ρ_rock = m_air × ρ_water ÷ m_water

3. A worked example

A dark stone weighs 120 g. Lowered on a thread into a zeroed jug of water at 20 °C, it raises the reading to 35 g.

V = 35 g ÷ 0.9982 g/cm³ = 35.06 cm³    ρ = 120 g ÷ 35.06 cm³ = 3.42 g/cm³

That sits in the range of the H chondrites, the most metal-rich of the ordinary chondrites, and is clearly above most surface rocks. It does not prove the stone is a meteorite, but it is a good reason to look closer.

Using the hanging method, the same stone would weigh 120 g in air and 85 g in water. The loss, 35 g, is the same displaced water, so the answer is identical.

4. How precise is your answer?

Every reading on a scale is uncertain by up to half its last digit. Kitchen scales that show whole grams could be out by half a gram on each reading. That matters most for the displaced water, which is always the smaller number. The calculator combines the relative errors in the usual way for a quotient:

δρ/ρ = √[(δm_air/m_air)² + (δm_water/m_water)²]

In the hanging method the water mass comes from subtracting two readings, so its uncertainty is √2 times one reading's. For a 120 g stone on whole-gram scales the result is good to about ±0.05 g/cm³. For a 10 g stone it is only good to about ±0.6, enough to blur an ordinary chondrite into a basalt or a stony-iron. Use the most precise scales you can, and the biggest piece you have.

5. Why meteorites are dense

Most rocks at Earth's surface are made of light silicate minerals such as quartz (2.65 g/cm³) and feldspar (about 2.6), so they come out at about 2.6 to 2.8. Ordinary chondrites contain the same kinds of silicates as Earth's deep mantle, olivine and pyroxene (3.2 to 3.6), together with grains of iron-nickel metal (about 7.9) and iron sulphide (about 4.6). The mixture gives about 3.2 to 3.6. Stony-irons are roughly half metal and come out at about 4 to 5, and irons, almost pure metal, at 7.3 to 7.9.

Not every meteorite is heavy. Carbonaceous chondrites such as Murchison and Tagish Lake are full of clay-like minerals that hold water, and many are porous. Some are lighter than ordinary rock: the Orgueil meteorite has a density of only about 1.6.

6. Bulk density, grain density and porosity

This method measures bulk density: the mass divided by the whole volume, including any tiny cracks and pores. Scientists also measure grain density, the density of the solid material alone, using gas that seeps into the pores. The gap between them gives the porosity:

porosity = 1 − bulk density ÷ grain density

Ordinary chondrite falls typically have porosities of a few per cent to about 10%; some carbonaceous chondrites have 20 to 35%. The porosity of meteorites helps scientists work out how loosely packed their parent asteroids are.

7. Getting it right

• Use fine thread or fishing line; its own volume is too small to matter.
• Make sure the rock is completely covered and not touching the jug. Tap off any air bubbles clinging to it, because each bubble adds volume and makes the rock seem lighter for its size.
• Read the scales quickly. Porous rocks soak up water, which changes the reading as you watch.
• Weathered meteorites read low, because their metal turns to rust, which is less dense and takes up more space.
• The air also buoys the rock slightly when you weigh it in air, but by only about 0.04%, far less than the scale's error, so the calculator ignores it.
• Keep the dunking short and let the rock dry thoroughly at room temperature afterwards: water speeds up rusting. Museums avoid wetting confirmed meteorites at all, so ask before testing one you already know is a meteorite.

8. What density can and cannot tell you

Density is one of the best quick tests because it is hard to fake: slag, magnetite and hematite are the only common look-alikes that are heavier than ordinary rock, and each has its own give-away. But density ranges overlap. A result of 3.3 fits an ordinary chondrite, a Martian meteorite and some Earth rocks from the deep crust. Use it alongside the magnet test, a look for fusion crust and metal grains, and the streak test.