Density Calculator
Free Density Calculator for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations. Free math tool.
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\nMass = 86.4 g\n\nDensity = 86.4 ÷ 8 = 10.8 g/cm³\nDensity = 10,800 kg/m³\n\nThis 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\nDensity = 450g ÷ 500mL\nDensity = 0.9 g/cm³ = 900 kg/m³\n\nWater density = 1000 kg/m³\nSince 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\nGold density = 19.3 g/cm³\n\nMass = Density × Volume\nMass = 19.3 × 100 = 1,930 g\nMass = 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 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.
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.