Density Calculator
Density (kg/m³)
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Density (g/cm³)
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Floats in Water?
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How Density Works
Density is a fundamental physical property that measures how much mass is contained within a given volume of a substance. Defined by the formula rho = m/V, density is expressed in SI units of kilograms per cubic meter (kg/m3) or in CGS units of grams per cubic centimeter (g/cm3). According to the National Institute of Standards and Technology (NIST), density is one of the key physical constants used to identify and characterize materials in science, engineering, and industry.
Density determines whether objects float or sink in fluids, how structures bear loads, and how materials behave under pressure. Engineers use density to select construction materials, geologists use it to classify rocks and minerals, and chemists use it to verify the purity of substances. This calculator computes density from mass and volume, converts between kg/m3 and g/cm3, and tells you whether the material would float in water. For related calculations, try our Buoyancy Calculator or Volume Calculator.
The Density Formula and Its Rearrangements
The density formula can be rearranged to solve for any of the three variables:
Density: rho = m / V | Mass: m = rho x V | Volume: V = m / rho
- rho (density) — the ratio of mass to volume, measured in kg/m3 or g/cm3. Note: 1 g/cm3 = 1,000 kg/m3.
- m (mass) — the amount of matter in the object, measured in kilograms or grams.
- V (volume) — the space occupied by the object, measured in m3, cm3, or liters (1 L = 0.001 m3).
Worked example: A block of aluminum has a mass of 2.7 kg and a volume of 0.001 m3. Density = 2.7 / 0.001 = 2,700 kg/m3. This matches the known density of aluminum (2,700 kg/m3), confirming the material's identity.
Key Terms You Should Know
Specific gravity — the ratio of a substance's density to the density of water (1,000 kg/m3). A specific gravity of 2.7 means the substance is 2.7 times denser than water. Specific gravity is dimensionless and is commonly used in geology, brewing, and urine analysis.
Buoyancy — the upward force exerted on an object submerged in a fluid, equal to the weight of fluid displaced (Archimedes' principle). An object floats when its average density is less than the fluid's density. Ships float because their hull encloses air, making their average density less than water.
Bulk density — the mass of a granular or particulate material divided by its total volume, including void spaces between particles. Soil bulk density typically ranges from 1,100 to 1,600 kg/m3. Use our Soil Calculator for gardening applications.
Relative density — another term for specific gravity. Used extensively in the petroleum industry, where API gravity (a modified inverse specific gravity scale) classifies crude oil: light crude has API > 31.1, heavy crude has API < 22.3.
Density of Common Materials
The table below lists densities of frequently referenced materials at standard conditions (20C, 1 atm). Values are from the Engineering ToolBox and CRC Handbook of Chemistry and Physics. Pure water at 4C (its maximum density) serves as the baseline at exactly 1,000 kg/m3.
| Material | Density (kg/m3) | Density (g/cm3) | Floats in Water? |
|---|---|---|---|
| Air (sea level) | 1.2 | 0.0012 | N/A |
| Pine wood | 500 | 0.50 | Yes |
| Ice | 917 | 0.917 | Yes |
| Water (4C) | 1,000 | 1.000 | Baseline |
| Concrete | 2,400 | 2.40 | No |
| Aluminum | 2,700 | 2.70 | No |
| Iron / Steel | 7,874 | 7.87 | No |
| Copper | 8,960 | 8.96 | No |
| Lead | 11,340 | 11.34 | No |
| Gold | 19,300 | 19.30 | No |
Practical Examples
Example 1 — Identifying an unknown metal: A metallic sample has a mass of 445 g and displaces 50 cm3 of water. Density = 445 / 50 = 8.9 g/cm3. Checking the table, this matches copper (8.96 g/cm3), identifying the sample. This water displacement method, attributed to Archimedes, remains the standard technique for measuring irregular solids.
Example 2 — Estimating concrete weight: A concrete slab measures 3m x 4m x 0.15m = 1.8 m3. Using concrete density of 2,400 kg/m3: mass = 2,400 x 1.8 = 4,320 kg (about 9,524 lbs). This calculation is essential for structural engineering and crane capacity planning. Use our Concrete Calculator for project-specific estimates.
Example 3 — Checking gold purity: A gold ring has a mass of 15 g and displaces 0.82 cm3 of water. Density = 15 / 0.82 = 18.3 g/cm3. Pure gold is 19.3 g/cm3, so this ring is likely 18-karat gold (75% gold alloy), which has a density of approximately 15.5-18.5 g/cm3 depending on the alloy metals.
Tips for Working with Density
- Remember the water baseline: Water at 4C is exactly 1,000 kg/m3 (1 g/cm3). Anything less dense floats; anything more dense sinks. Ice (917 kg/m3) floats, which is why icebergs exist.
- Convert units carefully: To go from g/cm3 to kg/m3, multiply by 1,000. To go from kg/m3 to lb/ft3, multiply by 0.0624. Unit errors are the most common mistake in density calculations.
- Use water displacement for irregular objects: Submerge the object in a graduated cylinder and measure the volume of water displaced. This method works for any solid that does not dissolve in water.
- Account for temperature: Density changes with temperature. Water is densest at 4C. Metals expand when heated, reducing their density. For precise work, always note the temperature.
- Distinguish mass from weight: Density uses mass (kg), not weight (Newtons). On Earth, weight = mass x 9.81 m/s2. On the Moon, your weight changes but your mass and density remain the same.
Density in Science and Engineering
Density is a cornerstone measurement in materials science. The International Bureau of Weights and Measures (BIPM) defines the kilogram using a fixed value of Planck's constant, but density remains the practical way to verify material composition in industrial settings. In aerospace engineering, aluminum (2,700 kg/m3) is preferred over steel (7,874 kg/m3) for aircraft because its strength-to-density ratio is superior. According to NASA, the average density of Earth is 5,515 kg/m3, significantly higher than the surface rock density of about 2,700 kg/m3, indicating that Earth's core is composed of much denser iron and nickel.
Frequently Asked Questions
What is the density formula?
The density formula is rho = m / V, where rho is density, m is mass, and V is volume. The SI unit is kilograms per cubic meter (kg/m3), while the CGS unit is grams per cubic centimeter (g/cm3). To convert from g/cm3 to kg/m3, multiply by 1,000. This formula can be rearranged to find mass (m = rho x V) or volume (V = m / rho), making it versatile for various engineering and science problems.
What is the density of water?
Pure water reaches its maximum density of 999.97 kg/m3 (essentially 1,000 kg/m3 or 1.000 g/cm3) at 3.98 degrees Celsius. This value decreases as temperature rises or falls from that point — water at 20C has a density of about 998.2 kg/m3, and at 100C it drops to about 958.4 kg/m3. Seawater is denser at approximately 1,025 kg/m3 due to dissolved salts. The NIST Standard Reference Database provides precise water density values at various temperatures.
Why do some objects float and others sink?
An object floats when its average density is less than the density of the fluid it is placed in, according to Archimedes' principle. Wood (roughly 500-900 kg/m3) floats in water (1,000 kg/m3), while iron (7,874 kg/m3) sinks. Ships float despite being made of steel because their hull shape traps air, reducing the ship's average density below that of water. A steel ball sinks because its density is uniform at 7,874 kg/m3. Ice floats because it expands upon freezing, dropping its density to 917 kg/m3.
How do you measure the density of an irregular object?
Use the water displacement method: fill a graduated cylinder with a known volume of water, submerge the object completely, and read the new water level. The difference is the object's volume. Then weigh the object on a scale to find its mass. Density = mass / displaced volume. For example, a rock weighing 150 g that displaces 55 mL of water has a density of 150/55 = 2.73 g/cm3. This technique was reportedly discovered by Archimedes in ancient Syracuse when testing whether a crown was pure gold.
How does temperature affect density?
Temperature affects density because materials expand when heated and contract when cooled, changing the volume while mass stays constant. For most substances, density decreases as temperature rises. Water is unusual: it reaches maximum density at 3.98C and becomes less dense both above and below that temperature. This anomaly is why ice floats and lakes freeze from the top down, which is critical for aquatic life survival in winter. Metal density tables in engineering handbooks always specify the reference temperature, typically 20C.
What is the densest naturally occurring element?
Osmium is the densest naturally occurring element at 22,590 kg/m3 (22.59 g/cm3), slightly denser than iridium at 22,560 kg/m3. For comparison, gold is 19,300 kg/m3 and lead is 11,340 kg/m3. Among everyday materials, tungsten at 19,250 kg/m3 is one of the densest metals commonly used in industry. At the other extreme, aerogel — the lightest solid material — has a density as low as 1.2 kg/m3, barely denser than air. Use our Weight Converter to translate between mass units.