Unit conversion

Convert 1 kg/m³ into lb/ft³ using dimensional analysis

1 kg/m³ = 0.06242796 lb/ft³. Density is [M L⁻³], so only the powers of mass, length and time decide the factor.

Mass×2.2046231 kg = 2.204623 lb

Length³×0.028316851 m = 3.28084 ft

1 kg/m³ 0.06242796 lb/ft³

Working

Step by step

The dimension of densityDensity has the dimensions [M L⁻³]. Only the powers of M, L and T matter for the conversion.
The conversion ruleA quantity with dimensions [M^a L^b T^c] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂] [L₁/L₂]⁻³.
The size of each base unitM: 1 kilogram (kg) is 2.204623 pound (lb). L: 1 metre (m) is 3.28084 foot (ft).
Put the numbers inn₂ = 1 [1 kg / 1 lb] [1 m / 1 ft]⁻³
Work out each bracket[M₁/M₂] = 2.204623; [L₁/L₂]⁻³ = 3.28084⁻³ = 0.02831685
Multiplyn₂ = 1 × 2.204623 × 0.02831685 = 0.06242796
The answer1 kg/m³ = 0.06242796 lb/ft³

Questions

How do you convert kg/m³ to lb/ft³?

Density is [M L⁻³]. Multiply by the ratio of each base unit raised to its power in the dimension. That gives 1 kg/m³ = 0.06242796 lb/ft³.

What is 1 kg/m³ in lb/ft³?

1 kg/m³ = 0.06242796 lb/ft³.