To calculate density, divide the mass of an object by its volume using the formula D = M ÷ V, where D is density, M is mass, and V is volume. For example, if an object has a mass of 50 grams and a volume of 10 milliliters, its density is 5 g/mL.
Understanding the Density Formula
Density measures how tightly packed matter is in a given space. It's one of the most fundamental concepts in physics and chemistry, and calculating it is straightforward once you understand the formula.
The Basic Formula
ρ (or D) = m ÷ V
Where:
ρ (rho) or D = Density
m = Mass (in grams, kilograms, pounds, etc.)
V = Volume (in mL, L, cm³, m³, etc.)
Alternative Formulas
The density formula can be rearranged to solve for different variables:
For Mass: m = ρ × V
For Volume: V = m ÷ ρ
Common Density Units
Density can be expressed in different units depending on the context:
g/mL (grams per milliliter) - most common in labs
g/cm³ (grams per cubic centimeter) - equivalent to g/mL
kg/m³ (kilograms per cubic meter) - SI unit
lb/ft³ (pounds per cubic foot) - common in engineering
Step-by-Step Guide to Calculate Density
Follow these five simple steps to calculate the density of any object:
Step 1: Measure or Identify the Mass
First, you need to know the mass of the object. You can either:
Measure it directly using a balance scale or digital scale
Look it up if the mass is already known
Calculate it if you know density and volume
Tip: Make sure your scale is calibrated and zeroed before measuring. Record the mass with its units (grams, kilograms, etc.).
Example: A piece of aluminum weighs 27 grams
Step 2: Measure or Calculate the Volume
Next, determine the volume of the object. There are several methods:
For regular shapes: Use geometric formulas (length × width × height for rectangles)
For irregular shapes: Use water displacement method
If known: Use the given volume
Water Displacement Method:
Fill a graduated cylinder with water to a known level
Carefully place the object in the water
Note the new water level
Volume = New level - Initial level
Example: The aluminum piece has a volume of 10 cm³
Step 3: Ensure Units Are Compatible
Check that your mass and volume units are compatible. Common combinations:
Mass in grams + Volume in mL → Density in g/mL
Mass in grams + Volume in cm³ → Density in g/cm³
Mass in kilograms + Volume in m³ → Density in kg/m³
Tip: If units don't match, convert before calculating. For example, if mass is in kg and volume in mL, convert kg to grams first.
Step 4: Divide Mass by Volume
Now apply the formula: D = M ÷ V
Simply divide the mass by the volume to get density.
Example: D = 27 g ÷ 10 cm³ = 2.7 g/cm³
Step 5: Include Units and Check Your Answer
Always include units in your final answer. The units tell you how the density is expressed.
Check your work by:
Comparing to known densities (water = 1 g/mL, aluminum ≈ 2.7 g/cm³)
Working backwards: multiply density × volume to get mass
Final Answer: The aluminum piece has a density of 2.7 g/cm³
Worked Examples: Calculate Density
Example 1: Finding Density of a Metal Cube
Problem: A solid iron cube has a mass of 78.8 grams and each side measures 2 centimeters. What is its density in g/cm³?
Solution:
Identify mass: m = 78.8 g
Calculate volume: V = 2 cm × 2 cm × 2 cm = 8 cm³
Apply formula: D = m ÷ V
Calculate: D = 78.8 g ÷ 8 cm³ = 9.85 g/cm³
Answer: The iron cube has a density of 9.85 g/cm³ (This is close to iron's actual density of 7.87 g/cm³, so we're in the right ballpark!)
Example 2: Calculating Density of a Liquid
Problem: You have 500 mL of cooking oil that weighs 460 grams. What is the density of the oil?
Solution:
Mass: m = 460 g
Volume: V = 500 mL
Formula: D = m ÷ V
Calculate: D = 460 g ÷ 500 mL = 0.92 g/mL
Answer: The oil has a density of 0.92 g/mL (Oil is less dense than water, which is why it floats!)
Example 3: Converting Units While Calculating
Problem: A piece of gold has a mass of 0.193 kilograms and a volume of 10 cm³. Calculate its density in g/cm³.
Solution:
Convert mass: 0.193 kg × 1000 = 193 grams
Volume: V = 10 cm³
Formula: D = m ÷ V
Calculate: D = 193 g ÷ 10 cm³ = 19.3 g/cm³
Answer: Gold has a density of 19.3 g/cm³ (Gold is very dense, which is why it's so valuable!)
Example 4: Density of Gas at Standard Temperature
Problem: At STP (standard temperature and pressure), 2.8 grams of CO₂ gas occupies 1.4 liters. Calculate its density in g/L.
Solution:
Mass: m = 2.8 g
Volume: V = 1.4 L
Formula: D = m ÷ V
Calculate: D = 2.8 g ÷ 1.4 L = 2.0 g/L
Answer: CO₂ has a density of 2.0 g/L
Example 5: Using Water Displacement
Problem: A stone is placed in a graduated cylinder. The water level rises from 50 mL to 75 mL. The stone weighs 100 grams. Calculate its density.
Solution:
Mass: m = 100 g
Volume: V = 75 mL - 50 mL = 25 mL
Formula: D = m ÷ V
Calculate: D = 100 g ÷ 25 mL = 4.0 g/mL
Answer: The stone has a density of 4.0 g/mL
Common Mistakes to Avoid
Mistake 1: Forgetting to Convert Units
Problem: Using grams for mass and cm³ for volume, then expecting the answer in kg/m³
Solution: Keep units consistent throughout. If using g and cm³, your answer will be in g/cm³
Mistake 2: Confusing Mass and Weight
Problem: Using weight (which depends on gravity) instead of mass
Solution: Always use mass. On Earth, weight and mass are numerically similar, but density uses mass
Mistake 3: Incorrect Volume Calculation
Problem: Measuring only part of the object's volume (especially for irregularly shaped objects)
Solution: Use water displacement for irregular shapes to ensure you capture the entire volume
Mistake 4: Rounding Too Early
Problem: Rounding intermediate values, which compounds errors
Solution: Keep full precision during calculations and round only at the end
Mistake 5: Forgetting Units in Final Answer
Problem: Writing just "2.7" without specifying g/cm³
Solution: Always include units! "2.7 g/cm³" is complete; "2.7" is incomplete
Practice Problems
Easy Problems
Problem 1: A block of wood has a mass of 50 grams and a volume of 100 cm³. Calculate its density.
Use Calculator or solve by hand, then check below
Answer: 0.5 g/cm³
Problem 2: Mercury has a density of 13.6 g/cm³. If you have 27.2 grams of mercury, what is its volume?
(Hint: Use V = m ÷ D)
Answer: 2 cm³
Medium Problems
Problem 3: A liquid sample has a mass of 250 grams and occupies 0.25 liters. Calculate its density in g/mL.
Answer: 1.0 g/mL
Problem 4: A rectangular aluminum block measures 10 cm × 5 cm × 2 cm and weighs 270 grams. What is its density?
(Hint: Calculate volume first as length × width × height)
Answer: 2.7 g/cm³
Challenge Problems
Problem 5: Two identical-looking spheres have the same volume (100 cm³), but one has a mass of 270g and the other has a mass of 270 kg. Calculate the density of each and identify which is likely made of aluminum and which is made of lead.
Answers: 2.7 g/cm³ (aluminum) and 2700 g/cm³ or 2.7 kg/cm³ (lead)
Frequently Asked Questions
What's the difference between density and weight?
Density measures how much mass is packed into a unit volume (g/mL), while weight is the force exerted by gravity on an object's mass (measured in pounds or newtons). Density is an intrinsic property that doesn't change with location, while weight changes with gravity.
Why is water's density 1 g/mL?
Water's density of 1 g/mL is defined by convention as the reference standard at 4°C. Scientists chose water because it's abundant, stable, and convenient. Other substances' densities are compared to water's density.
Does temperature affect density calculations?
Yes! Most substances become less dense when heated because particles move faster and spread out. This is why hot air rises and ice floats. Always measure at the same temperature for consistent results.
Can I use the calculator instead of calculating by hand?
Absolutely! Our density calculator is perfect for quick calculations and verification. However, understanding the manual process helps you grasp the concept better.
What if my calculated density doesn't match the known value?
Check your measurements and calculations. Common issues include: incorrect unit conversions, imprecise mass or volume measurements, or temperature differences. Even small errors compound in the calculation.