SteelThe formula
The mass of a wire is its cross-section area times its length times the density of the steel. A round wire of diameter d has a cross-section area of π/4 × d². With d in metres and the density ρ in kg/m³, the mass of one metre of wire is π/4 × d² × ρ in kilograms. Multiply by 1000 to get the mass of one kilometre, which is also the mass of 1000 m.
With ρ = 7850 kg/m³ and d in millimetres, this works out to about 6.165 × d² kilograms per km.
The density used
The calculator uses 7850 kg/m³ (7.85 g/cm³), the value usually given for carbon steel. Steel density depends on the alloy and is usually quoted in a range of roughly 7750 to 8050 kg/m³, so the result is a theoretical mass.
What the result does not include
The result is the mass of the steel only. It does not include a zinc coating, packaging, or the effect of the diameter tolerance. Use it for planning and comparing, and treat the mass on the packing list as the final figure.
How to read the numbers
Mass grows with the square of the diameter: doubling the diameter makes the wire four times heavier per metre. The worked examples above use the same formula as the form, so the two always agree.
