Density vs Mass vs Volume: What's the Difference? Complete Guide

Quick Comparison Table

Property	Mass	Volume	Density
Definition	Amount of matter in an object	Space an object takes up	Mass per unit volume
Symbol	m	V	ρ or D
Common Units	grams (g), kilograms (kg), pounds (lb)	milliliters (mL), liters (L), cubic meters (m³)	g/mL, kg/m³, lb/ft³
How to Measure	Use a scale or balance	Measure dimensions or use water displacement	Calculate using formula D = M/V
Intensive Property?	No (depends on amount)	No (depends on size)	Yes (same for all samples)
Affected by Gravity?	No (constant everywhere)	No (constant everywhere)	No (constant everywhere)
Real-Life Example	A kilogram of lead is 1 kg anywhere	A liter of water always occupies the same space	All lead has density of 11.34 g/cm³

What is Mass?

Mass is the amount of matter that an object contains. It's one of the most fundamental properties in physics.

Key Characteristics of Mass:

Measured with: A scale or balance
Symbol: m
Common units: grams (g), kilograms (kg), milligrams (mg), pounds (lb)
Constant everywhere: Mass doesn't change based on location or gravity
Extensive property: Depends on the amount of matter (more matter = more mass)

Mass vs Weight

Students often confuse mass and weight. Here's the difference:

Mass is the amount of matter (constant everywhere)
Weight is the force of gravity pulling on that mass (changes with location)
Example: You weigh less on the Moon than on Earth, but your mass stays the same

Example: Mass of Common Objects

A pencil: ~5 grams
A textbook: ~1 kilogram
A person: ~70 kilograms
A car: ~1,500 kilograms

What is Volume?

Volume is the amount of space an object occupies. It measures how much three-dimensional space something takes up.

Key Characteristics of Volume:

Measured with: Graduated cylinders, rulers (for calculations), or displacement
Symbol: V
Common units: milliliters (mL), liters (L), cubic centimeters (cm³), cubic meters (m³)
Different for each object: Changes based on shape and size
Extensive property: Larger objects have larger volumes

Ways to Measure Volume

For regular shapes: Use geometric formulas
- Rectangular box: length × width × height
- Sphere: (4/3) × π × radius³
- Cylinder: π × radius² × height
For irregular shapes: Water displacement method
- Measure initial water level
- Submerge object
- Measure new water level
- Difference = object's volume
For liquids: Use graduated cylinders

Example: Volume of Common Objects

A drinking glass: ~250 mL
A milk carton: ~1 liter
A classroom: ~200 cubic meters
A sugar cube: ~1 cm³

What is Density?

Density combines mass and volume to describe how tightly packed matter is in a given space. It's calculated by dividing mass by volume.

Density = Mass ÷ Volume
D = M ÷ V

Key Characteristics of Density:

Symbol: ρ (rho) or D
Common units: g/mL, kg/m³, g/cm³, lb/ft³
Intensive property: Doesn't depend on amount (all gold samples have the same density)
Calculated property: Cannot be directly measured, must be calculated from mass and volume
Identifies substances: Each pure substance has a characteristic density

Why Density Matters

Identification: Different substances have different densities
Predicting behavior: Less dense objects float on more dense fluids
Material selection: Engineers choose materials based on density requirements
Quality control: Manufacturers verify product purity using density

Example: Density of Common Substances

Water: 1.0 g/mL (reference standard)
Aluminum: 2.7 g/cm³
Gold: 19.3 g/cm³
Cork: 0.24 g/cm³
Lead: 11.34 g/cm³

How Density, Mass, and Volume Relate

The Fundamental Relationship

The three properties are connected through a simple mathematical relationship:

D = M ÷ V (Density = Mass ÷ Volume)
M = D × V (Mass = Density × Volume)
V = M ÷ D (Volume = Mass ÷ Density)

What This Means

If mass increases (volume constant): Density increases
If volume increases (mass constant): Density decreases
If density is constant: Mass and volume are proportional

Real-World Analogy

Think of a sponge vs. a brick:

A sponge and a brick might have similar mass
But the brick occupies less volume (it's more tightly packed)
So the brick has higher density
That's why the brick sinks and the sponge floats

Real-World Examples

Example 1: Why Oil Floats on Water

Water density: 1.0 g/mL
Oil density: 0.92 g/mL
Result: Oil is less dense, so it floats on water

Example 2: Why Icebergs Float (Mostly Underwater)

Water density: 1.0 g/mL
Ice density: 0.92 g/mL
Result: Ice is less dense, so it floats, but only ~10% shows above water

Example 3: Same Mass, Different Volumes

1 kilogram of lead: Volume ≈ 88 cm³
1 kilogram of aluminum: Volume ≈ 370 cm³
Explanation: Lead is denser, so same mass takes up much less space

Example 4: Same Volume, Different Masses

1 liter of water: Mass = 1 kg
1 liter of mercury: Mass = 13.6 kg
Explanation: Mercury is much denser, so same volume has much more mass

The Density Triangle Method

A helpful way to remember the relationships between D, M, and V is the "density triangle":

How to Use the Triangle

To find Mass (M): Cover M, multiply D × V
To find Density (D): Cover D, divide M ÷ V
To find Volume (V): Cover V, divide M ÷ D

Examples Using the Triangle

Find M: D = 2.7 g/cm³, V = 10 cm³ → M = 2.7 × 10 = 27 g

Find D: M = 50 g, V = 10 mL → D = 50 ÷ 10 = 5 g/mL

Find V: M = 100 g, D = 10 g/mL → V = 100 ÷ 10 = 10 mL

Key Takeaways

Mass = Amount of matter (measured with a scale)
Volume = Space occupied (measured with graduated cylinders or calculations)
Density = Mass per unit volume (calculated from M ÷ V)
Relationship: D = M ÷ V (can be rearranged to find any variable)
Density identifies substances: Each pure material has its own characteristic density
Understanding all three is essential for chemistry, physics, and engineering applications

Material Density Reference