How to Calculate Density (Solids, Liquids and Irregular Objects)

Density is mass divided by volume: ρ = m ÷ V. A block with a mass of 250 grams and a volume of 100 cubic centimeters has a density of 250 ÷ 100 = 2.5 g/cm³. To find it for any object, measure its mass on a scale, measure or calculate its volume, and divide.

Density is a property of the material, not the object. A gold ring and a gold bar have the same density, about 19.3 g/cm³, which is why density can identify what something is made of.

The density formula

The Greek letter ρ (rho) is the standard symbol. Rearranging gives the other two forms:

The SI unit is kilograms per cubic meter (kg/m³). In labs, grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL) are more convenient; they are numerically identical because 1 mL = 1 cm³.

Three ways to measure density

1. Regular solids: calculate the volume

For a box-shaped block, cylinder or sphere, measure its dimensions and use a volume formula; see how to calculate volume.

2. Irregular solids: water displacement

For a rock, key or piece of jewelry, measure the volume by how much water it pushes aside. This is the method traditionally credited to Archimedes.

1. Weigh the object.
2. Partly fill a graduated cylinder with water and record the level.
3. Gently lower the object in until fully submerged, without splashing.
4. Record the new level. The rise is the object’s volume.

This works only if the object sinks and does not absorb water. For floating objects, push them under with a thin wire and account for the wire’s small volume.

3. Liquids: weigh a measured volume

Weigh an empty graduated cylinder, add a known volume of liquid, and weigh again.

The density calculator solves for density, mass or volume from the other two, in any units.

Densities of common materials

Values are approximate, at about 20°C and normal atmospheric pressure unless noted.

Ice is less dense than liquid water, which is unusual among substances and is why ice floats and lakes freeze from the top down.

Converting density units

Water at room temperature is about 62.3 lb/ft³ or 8.33 lb/gal, so a 55-gallon drum of water weighs roughly 458 pounds before counting the drum. The density converter handles any pair of units.

Using density to find mass or volume

Rearranging the formula is often more useful than the formula itself.

Contractors use the first calculation constantly: knowing the weight of a load of concrete, gravel or soil tells you whether a truck or trailer can carry it. For mass and weight conversions, the weight and mass converter helps.

Specific gravity

Specific gravity (relative density) is a material’s density divided by the density of water. Because it is a ratio, it has no units, and in g/cm³ it is numerically almost the same as density. Aluminum has a specific gravity of about 2.70. Brewers, battery technicians and gemologists use it routinely.

Density, floating and buoyancy

An object floats if its average density is less than the fluid it is in. A fluid pushes up with a force equal to the weight of the fluid displaced, so a floating object sinks until it has displaced its own weight. Ice at 0.917 g/cm³ floats with about 92% of its volume below the surface of fresh water, since 0.917 ÷ 0.998 ≈ 0.92. The buoyancy calculator works through these forces.

Getting an accurate result

Small reading errors matter more than people expect. Graduated cylinders are usually read to the nearest 0.5 or 1 mL, so a 1 mL error on the 62 mL rock example shifts the density by about 1.6%, from 2.71 to as low as 2.67 or as high as 2.75 g/cm³. To reduce the error:

• Use the smallest cylinder the object fits in, since narrower cylinders have finer graduations.
• Read the bottom of the meniscus at eye level.
• Tare the scale with the container on it so you weigh only the object or liquid.
• Keep units consistent: grams with cubic centimeters, or kilograms with cubic meters. Mixing grams and cubic meters produces answers a million times off.
• Report sensible precision. With a 168 g mass and a 62.0 mL volume, three significant figures (2.71 g/cm³) is appropriate; see significant figures rules.

Things that change density

• Temperature. Most materials expand when heated, so their density drops. Water is densest near 4°C.
• Pressure. Gases compress easily; air at the bottom of a scuba tank is far denser than air at the surface. Liquids and solids barely change.
• Composition and porosity. Wood, soil and concrete vary with moisture and air content, so published values are averages.

Density also links to pressure in fluids: the pressure at depth h in a liquid is ρgh, which is why the pressure calculator appears alongside density in so many problems. For moles and concentration, the chemistry counterpart, see how to calculate molarity.