Rocks come in a variety of shapes, sizes and compositions. Sedimentary, igneous and metamorphic rocks relate to each other as different stages in the rock cycle. Differentiating one type of rock from another sometimes depends on subtle differences in characteristics. Density, combined with observations and additional tests, helps identify and differentiate one rock from another. Since density measures the ratio of mass to volume, calculating density requires accurately measuring mass and volume.

Finding the density of a rock requires measuring the rock's mass in grams and volume in cubic centimeters. These values fit into the equation:

where D means density, m represents mass, and V represents volume. Insert the values and solve for density. In general, volume measurements use water displacement, taking advantage of the relationship that one milliliter of water occupies one cubic centimeter of space.

## Sample Selection

Rocks range from a collection of crystals of one mineral to mixtures of different minerals. The minerals may be all microscopic, all macroscopic or a mixture of microscopic and macroscopic crystals. The minerals may be distributed evenly through the entire rock or they may be arranged in layers or clusters. For accuracy, the tested sample must include all minerals of the rock. Also, the sample shouldn't have any weathered surfaces. The weathering process changes the original mineralogy, which also changes the density. So, to accurately measure the overall density, the rock sample selected must represent all of the minerals in the same ratio as the larger rock mass. In general, geologists select a hand specimen, a rock sample about the size of a fist or baseball. A very small rock sample might not represent the mineralogy of the entire rock mass while a very large sample challenges the ability to accurately measure mass or volume or both.

## Measuring Mass

The concepts of mass and weight confuse many people. Mass measures the amount of matter in an object while weight measures the pull of gravity on a mass. The confusion arises because on Earth the gravitational pull equals 1, so mass and weight only differ by tiny amounts, influenced by elevation and underlying massive rocks.

Measuring mass accurately requires a balance scale. Electronic scales, triple-beam balances or other balance scales measure mass. Basic weight scales like bathroom scales generally do not provide the accuracy necessary for finding mass. Each mass scale has specific directions, but the general technique sets the scale to balance at zero, places the rock on the pan, balances the scale, then directly reads the mass of the specimen. When measuring mass, record the units in grams.

## Measuring Volume

Volume, quite simply, measures the space an object occupies. Finding the volume of regular geometric shapes like spheres, cubes and boxes uses established formula. Rocks rarely come in geometric shapes, unfortunately. Finding volume therefore requires a special technique. Archimedes discovered water displacement, and finding volume using water displacement requires a little thought and a touch of dexterity. Also, remember that one cubic centimeter of water equals one milliliter of water.

Water displacement means that an object placed in water displaces a volume of water equal to the volume of the object. For example, an object with a volume of 5 cubic centimeters submerged in a container of water will displace 5 milliliters of water. If the container has measurements, an initial reading of 10 milliliters of water will change to 15 milliliters after the 5 cubic centimeter object is submerged in the water.

Finding volume through water displacement requires placing the rock sample in a container with measured volume markings, like a measuring cup. Before adding the rock, place enough water in the cup, so the rock will be completely submerged. Measure the volume of water. Add the rock, being sure no bubbles stick to the rock. Measure the resulting volume of water. Subtract the initial, water-only, volume from the final, water and rock, volume to find the volume of the rock. So, if the initial water volume is 30 milliliters and the final water plus rock volume is 45 milliliters, the volume of the rock alone is 45-30=15 milliliters, or 15 cubic centimeters. Of course, numbers in nature, like the rock, will likely not be even numbers.

If the rock won't fit a measuring cup, use a container large enough to submerge the rock. Place the container in a tray. Fill the container completely full of water. Carefully, without any waves or splashing, slide the rock into the water. All water spilled from the container must be captured in the underlying tray. Very carefully remove the container from the tray without accidently spilling any more water into the tray. Measure the intentionally spilled water in the tray to determine the volume of the rock. The amount of water displaced from the container by the rock and captured in the tray equals the volume of the rock.

#### Warnings

Some sedimentary rocks, like sandstone, disintegrate when submerged in water. An accepted method to stop this sample degradation uses thin layers of wax to protect the sample. Dip the sample several times in melted wax, letting the wax cool slightly between layers. Let the wax cool completely, then find the mass of the rock with the wax coating. Subtract the wax-encased mass from the rock-only mass to find the mass of the wax. Use the water displacement method to find the total volume. Use the density formula (density of paraffin wax ranges from 0.88 to 0.92) to find the volume of the wax. Subtract the volume of wax from the measured total volume to find the volume of the rock sample.

## Calculating Density

Calculating density from mass and volume requires a simple formula: density equals mass divided by volume. So, if the measured rock mass equals 984.2 grams and the measured volume equals 382.9 milliliters, using the formula gives the equation:

showing the density of the sample equals 2.57 grams per cubic centimeter.

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About the Author

Karen earned her Bachelor of Science in geology. She worked as a geologist for ten years before returning to school to earn her multiple subject teaching credential. Karen taught middle school science for over two decades, earning her Master of Arts in Science Education (emphasis in 5-12 geosciences) along the way. Karen now designs and teaches science and STEAM classes.