Density Calculator
Calculate the density of materials from mass and volume. Includes common material densities, specific gravity, and buoyancy determination.
Formula
Density (ρ) = Mass (m) ÷ Volume (V)
Density equals mass divided by volume. Common units are g/cm³ or kg/m³. Specific gravity is density relative to water.
Worked Examples
Example 1: Identify Unknown Metal
Problem:A metal cube measuring 2cm × 2cm × 2cm has a mass of 86.4 grams. What metal is it?
Solution:Volume = 2 × 2 × 2 = 8 cm³ Mass = 86.4 g Density = 86.4 ÷ 8 = 10.8 g/cm³ Density = 10,800 kg/m³ This is close to silver (10,490 kg/m³)
Result:10.8 g/cm³ - likely Silver
Example 2: Will It Float?
Problem:An object has mass 450g and volume 500 mL. Will it float in water?
Solution:Density = Mass ÷ Volume Density = 450g ÷ 500mL Density = 0.9 g/cm³ = 900 kg/m³ Water density = 1000 kg/m³ Since 900 < 1000, it floats!
Result:0.9 g/cm³ - Floats in water
Example 3: Calculate Object Mass
Problem:A gold bar measures 10cm × 5cm × 2cm. How much does it weigh?
Solution:Volume = 10 × 5 × 2 = 100 cm³ Gold density = 19.3 g/cm³ Mass = Density × Volume Mass = 19.3 × 100 = 1,930 g Mass = 1.93 kg ≈ 4.25 pounds
Result:1.93 kg (4.25 lb)
Frequently Asked Questions
How do I calculate density?
Density = Mass ÷ Volume. Measure the object's mass with a scale, determine volume by displacement or geometry, then divide. Common units are g/cm³ or kg/m³.
What is specific gravity?
Specific gravity (SG) is the ratio of a substance's density to water's density (1000 kg/m³). SG = Density ÷ 1000. If SG > 1, it sinks in water; if SG < 1, it floats.
Why does ice float on water?
Ice has lower density (917 kg/m³) than liquid water (1000 kg/m³). Water is unusual - it expands when freezing. Most substances are denser as solids than liquids.
How do I measure volume of irregular objects?
Use water displacement: submerge the object in water and measure the volume of water displaced. This is Archimedes' method. Make sure the object doesn't absorb water.
What affects density?
Temperature (heating usually decreases density), pressure (compressing increases density), and composition. Alloys and mixtures have densities between their components.
How do I convert between density units?
1 g/cm³ = 1000 kg/m³ = 62.428 lb/ft³. To convert g/cm³ to kg/m³, multiply by 1000. Water is 1 g/cm³ = 1000 kg/m³.
What's the densest common element?
Osmium (22,590 kg/m³) is the densest naturally occurring element, followed by iridium (22,560), platinum (21,450), and gold (19,300).
How is density used in engineering?
Density determines material selection, structural weight, buoyancy calculations, fluid dynamics, and shipping costs. It's crucial for aircraft, ships, and building design.
What is bulk density?
Bulk density includes air spaces between particles (for powders, grains). It's less than solid density. Flour's bulk density is ~500 kg/m³ vs wheat grain's ~1500 kg/m³.
How does altitude affect density?
Air density decreases with altitude due to lower pressure. At sea level, air is ~1.225 kg/m³; at 10,000m it's ~0.41 kg/m³. This affects aircraft performance.
Background & Theory
Density is mass per unit volume, a fundamental property that characterizes materials and determines their behavior in physical situations.
Formula:
ρ = m / V
Where:
- ρ (rho) = density
- m = mass
- V = volume
Common Units:
| Unit | Usage |
|---|---|
| kg/m³ | SI standard |
| g/cm³ | Common for solids |
| g/mL | Common for liquids |
| lb/ft³ | US engineering |
Conversion:
1 g/cm³ = 1000 kg/m³ = 62.428 lb/ft³
Specific Gravity:
SG = ρ_substance / ρ_water
Water at 4°C: SG = 1.000
Buoyancy:
Objects float if their density < fluid density
Objects sink if their density > fluid density
Factors Affecting Density:
- Temperature (usually inverse relationship)
- Pressure (direct relationship for gases)
- Composition/purity
- Phase (solid, liquid, gas)
Applications:
- Material identification
- Quality control
- Buoyancy calculations
- Fluid dynamics
- Geology and mineralogy