⚛️ Physics Education6 min readReviewed: August 2026

The Density Formula Explained: V = m ÷ ρ and Algebraic Rearrangements

Derivation, 3-way triangular relationships, dimensional analysis, and step-by-step worked examples.

The density equation is one of the most fundamental formulas in classical physics and applied engineering. It governs the physical interplay between how much space an object occupies (volume) and how much matter it contains (mass).

The Three Permutations of the Density Triangle

V = m ÷ ρ | m = V × ρ | ρ = m ÷ V

V = Volume(Litres (L), mL, m³, or gal)

m = Mass(Kilograms (kg), g, or lbs)

ρ (rho) = Density(kg/L, g/cm³, or kg/m³)

Interactive Formula Playground

Drag the sliders to see how mass and density affect volume in real-time.

1.00=1÷1.00

V (L) =m (kg) ÷ρ (kg/L)

Mass (m) 1.0 kg

0.1 kg50 kg

Density (ρ)1.00 kg/L

0.10 kg/L3.00 kg/L

1.0 kg of substance with density 1.00 kg/L occupies 1.00 litres.

1. The Density Triangle & Algebraic Rearrangements

By placing Mass (m) at the apex of a triangle with Density (ρ) and Volume (V) at the base, you can visually solve for any missing variable:

• To find Volume (V): Cover V → V = m ÷ ρ (Mass divided by Density)

• To find Mass (m): Cover m → m = V × ρ (Volume multiplied by Density)

• To find Density (ρ): Cover ρ → ρ = m ÷ V (Mass divided by Volume)

2. Worked Examples with Common Fluids

Example 1 (Solve Volume): How many litres are in 25 kg of sulfuric acid (ρ = 1.84 kg/L)?

V = 25 kg ÷ 1.84 kg/L = 13.587 Litres.

Example 2 (Solve Mass): How much does a 200-litre drum of motor oil weigh (ρ = 0.88 kg/L)?

m = 200 L × 0.88 kg/L = 176.000 kg.

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Frequently Asked Questions

Common questions about this physics topic.

Why must units match before using the density formula?+

If mass is in kilograms and density is in g/cm³, direct division will give an incorrect answer off by a factor of 1,000. Always ensure mass is in kg when density is in kg/L to obtain volume in litres.

What is the Greek letter for density?+

The standard physics symbol for density is the lowercase Greek letter rho (ρ), though the Latin letter "d" or "D" is occasionally used in introductory textbooks.