Density Calculator
Calculate density, mass, or volume using the density formula ρ = m/V. Includes material database.
Density Calculator
Calculate:
Quick Select Material:
Density Formula:
ρ = m / V
Density = Mass / Volume
Density
2.0000 g/cm³
Density in Different Units:
Water Behavior
Sinks in water
Buoyancy force: -0.4905 N
Similar Materials:
Common Material Densities
Metals
Liquids
Other Materials
Understanding Density
What is Density?
Density is how much mass is packed into a given volume. Higher density means more mass per unit volume. It's an intensive property - it doesn't depend on the amount of material.
Specific Gravity
Specific gravity is the ratio of a substance's density to water's density. Values less than 1 float in water, greater than 1 sink.
What is Density?
Density is the mass per unit volume of a substance. It's an intensive property, meaning it doesn't depend on the amount of material—a small piece of gold has the same density as a large gold bar.
| Property | Description | Key Point |
|---|---|---|
| Definition | Mass per unit volume | ρ = m/V |
| SI Unit | Kilogram per cubic meter | kg/m³ |
| Common Unit | Gram per cubic centimeter | g/cm³ |
| Nature | Intensive property | Same for any sample size |
Key relationship: 1 g/cm³ = 1,000 kg/m³ = 1 kg/L. Water's density of exactly 1 g/cm³ at 4°C is not coincidental—the gram was originally defined this way.
Density Formula
Where:
- ρ= Density (kg/m³ or g/cm³)
- m= Mass (kg or g)
- V= Volume (m³ or cm³)
Density of Common Materials
Material densities span several orders of magnitude:
| Material | Density (g/cm³) | Density (kg/m³) |
|---|---|---|
| Air (sea level, 20°C) | 0.0012 | 1.2 |
| Styrofoam | 0.05 | 50 |
| Cork | 0.24 | 240 |
| Balsa wood | 0.16 | 160 |
| Oak wood | 0.75 | 750 |
| Ice | 0.92 | 920 |
| Water (4°C) | 1.00 | 1,000 |
| Seawater | 1.03 | 1,030 |
| Aluminum | 2.70 | 2,700 |
| Steel | 7.85 | 7,850 |
| Copper | 8.96 | 8,960 |
| Lead | 11.34 | 11,340 |
| Gold | 19.30 | 19,300 |
| Platinum | 21.45 | 21,450 |
| Osmium (densest element) | 22.59 | 22,590 |
Floating and Sinking
Whether an object floats or sinks depends on its density relative to the surrounding fluid:
| Condition | Result | Example |
|---|---|---|
| ρ_object < ρ_fluid | Floats | Wood in water, helium balloon |
| ρ_object = ρ_fluid | Neutral buoyancy | Submarine, fish with swim bladder |
| ρ_object > ρ_fluid | Sinks | Stone in water, air bubble rising |
| Object | Density (g/cm³) | In Water |
|---|---|---|
| Ice | 0.92 | Floats (92% submerged) |
| Human body | 0.95-1.05 | Borderline (depends on fat/muscle) |
| Egg (fresh) | 1.03 | Sinks slowly |
| Egg (old) | ~0.95 | Floats (gas buildup) |
Archimedes' Principle: An object floats when it displaces water weighing equal to its own weight.
Fraction Submerged
Where:
- ρ_object= Density of floating object
- ρ_fluid= Density of fluid
Specific Gravity
Specific gravity (relative density) is the ratio of a substance's density to a reference (usually water):
| Concept | Formula | Note |
|---|---|---|
| Specific gravity | SG = ρ_substance / ρ_water | Dimensionless number |
| For water reference | SG = ρ (in g/cm³) | Since ρ_water = 1 g/cm³ |
| API gravity (petroleum) | API = 141.5/SG - 131.5 | Higher API = lighter oil |
| Substance | Specific Gravity | Application |
|---|---|---|
| Gasoline | 0.72-0.78 | Fuel industry |
| Diesel fuel | 0.82-0.95 | Fuel industry |
| Milk | 1.028-1.035 | Dairy quality testing |
| Battery acid | 1.26-1.28 | Fully charged battery |
| Honey | 1.36-1.45 | Food industry |
| Antifreeze solution | 1.05-1.10 | Automotive testing |
Advantage: Specific gravity is independent of units—SG = 2.7 means 2.7 times denser than water regardless of whether you measure in g/cm³ or kg/m³.
Temperature Effects on Density
Temperature significantly affects density, especially for gases:
| Material | Temperature Effect | Magnitude |
|---|---|---|
| Gases | Inversely proportional to T | Large effect (ρ ∝ 1/T) |
| Liquids | Decreases with T (usually) | Moderate effect |
| Solids | Decreases with T | Small effect |
| Water (anomaly!) | Max density at 4°C | Unusual behavior |
| Water Temperature | Density (g/cm³) | Volume Change |
|---|---|---|
| 0°C (ice) | 0.9167 | +9% from 4°C |
| 0°C (liquid) | 0.9998 | -0.02% from 4°C |
| 4°C (maximum) | 1.0000 | Reference |
| 20°C | 0.9982 | +0.18% |
| 100°C | 0.9584 | +4.3% |
Water's anomaly: Water is densest at 4°C, which is why lakes freeze from the top down, allowing aquatic life to survive below.
Ideal Gas Density
Where:
- P= Pressure (Pa)
- M= Molar mass (kg/mol)
- R= Gas constant (8.314 J/mol·K)
- T= Temperature (K)
Measuring Density
Several methods exist for measuring density:
| Method | Principle | Best For |
|---|---|---|
| Mass and volume | ρ = m/V directly | Regular-shaped solids |
| Water displacement | Archimedes' principle | Irregular solids |
| Hydrometer | Buoyancy depth | Liquids |
| Pycnometer | Known volume vessel | Precise liquid/powder measurement |
| Digital densimeter | Oscillating tube | High-precision liquids |
Archimedes' method: Weigh object in air (m_air), then submerged in water (m_water). Density = m_air × ρ_water / (m_air - m_water).
Practical Applications
Density measurements have many practical applications:
| Application | Density Relevance | Example |
|---|---|---|
| Ship design | Hull must displace enough water | Steel ships float despite dense metal |
| Hot air balloons | Heated air is less dense | Buoyancy lifts the balloon |
| Battery testing | Acid SG indicates charge | SG 1.265 = fully charged |
| Gemstone testing | Density identifies gems | Diamond: 3.52 g/cm³ |
| Medical diagnostics | Bone density scans | Osteoporosis detection |
| Quality control | Consistent material properties | Concrete, metals, plastics |
Worked Examples
Calculate Object Density
Problem:
A metal block has mass 540 g and dimensions 4 cm × 3 cm × 5 cm. What is its density and what metal might it be?
Solution Steps:
- 1Calculate volume: V = 4 × 3 × 5 = 60 cm³
- 2Apply density formula: ρ = m/V
- 3Substitute: ρ = 540 / 60 = 9.0 g/cm³
- 4Compare to known metals: Copper is 8.96 g/cm³
- 5Conclusion: Likely copper
Result:
Density = 9.0 g/cm³ (likely copper)
Will It Float?
Problem:
A wooden sphere has mass 400 g and volume 500 cm³. Will it float in water, and how much will be submerged?
Solution Steps:
- 1Calculate density: ρ = 400/500 = 0.8 g/cm³
- 2Compare to water: 0.8 < 1.0, so it floats
- 3Fraction submerged = ρ_wood / ρ_water = 0.8/1.0 = 0.8
- 480% of the sphere is underwater
Result:
Floats with 80% submerged (20% above water)
Find Mass from Density
Problem:
A gold bar measures 25 cm × 5 cm × 2 cm. Gold density is 19.3 g/cm³. What is its mass?
Solution Steps:
- 1Calculate volume: V = 25 × 5 × 2 = 250 cm³
- 2Rearrange formula: m = ρ × V
- 3Substitute: m = 19.3 × 250 = 4,825 g
- 4Convert: 4,825 g = 4.825 kg ≈ 10.6 lbs
Result:
Mass = 4.825 kg (about 10.6 lbs)
Tips & Best Practices
- ✓1 g/cm³ = 1,000 kg/m³ = 1 kg/L: Easy conversions for water-based reference
- ✓Objects float when their density is less than the surrounding fluid
- ✓Fraction submerged equals the density ratio (object/fluid) for floating objects
- ✓Specific gravity is dimensionless—it's the same number regardless of units
- ✓Temperature affects density: most materials expand when heated (exception: water below 4°C)
- ✓Use water displacement to measure the volume of irregular objects
- ✓Average density of a hollow object includes the air space
Frequently Asked Questions
Sources & References
Last updated: 2026-01-22