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How It Works
The density equation ρ = m / V relates how much matter is packed into a given space. A high density means the substance is tightly packed; a low density means it is spread out. You can rearrange the same equation to find mass or volume when the other two values are known.
Common units are kg/m³ (SI), g/cm³ (CGS), and slugs/ft³ (imperial). Water's density at 4 °C is 1,000 kg/m³ (1 g/cm³), which serves as the reference for many comparisons.
Example Problem
A block of aluminum has a mass of 2,700 g and occupies 1,000 cm³. What is its density?
- Convert to SI: m = 2.7 kg, V = 0.001 m³
- ρ = 2.7 / 0.001 = 2,700 kg/m³
This matches the known density of aluminum, confirming the sample is pure.
Frequently Asked Questions
How do you calculate density from mass and volume?
Divide the mass by the volume: ρ = m / V. For example, a 500 g object that occupies 200 cm³ has a density of 500 / 200 = 2.5 g/cm³.
What is the density of water?
Pure water at 4 °C has a density of 1,000 kg/m³ (1 g/cm³). This value decreases slightly as temperature rises or falls from 4 °C.
Does an object float if its density is less than water?
Yes. An object floats in a fluid when it is less dense than that fluid. Wood (~600 kg/m³) floats on water, while iron (~7,870 kg/m³) sinks.
What is the difference between density and specific gravity?
Density has units (kg/m³), while specific gravity is a dimensionless ratio of a substance's density to the density of a reference (usually water). A specific gravity of 2.7 means the substance is 2.7 times denser than water.
Related Calculators
- Specific Gravity Calculator — compare a substance's density to a reference.
- Specific Volume Calculator — find volume per unit mass (the reciprocal of density).
- Fluid Pressure Calculator — calculate pressure in a fluid column using density and depth.
- Weight Equation Calculator — find gravitational force from mass.
- Density Converter — convert between kg/m³, g/cm³, lb/ft³, and other density units.
Reference: Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.