Enter the weight and length into the calculator to determine the weight to length ratio. This calculator helps to evaluate the ratio of weight per unit length for various materials or objects.
Weight to Length Ratio Formula
The weight to length ratio is the linear weight of an object, equal to its weight divided by its length.
R = W / L
- R = weight-to-length ratio (kg/m, lb/ft, g/cm, lb/in)
- W = total weight
- L = total length
To get length from a known ratio and weight, rearrange to L = W / R. To get weight from a known ratio and length, use W = R × L.
For round wire or rod, the ratio comes from material density and cross-section area:
R = ρ × (π × D² / 4)
- ρ = material density (kg/m³)
- D = wire diameter (m)
- π × D² / 4 = cross-sectional area
The three calculator modes match these formulas. Ratio divides weight by length. Convert solves for the missing weight or length when you already know the ratio. Round wire computes the ratio directly from diameter and density without needing a sample weight.
Typical Values and Unit Conversions
Common linear weights for reference. Use these to sanity-check your result.
| Item | Approx. ratio (kg/m) | Approx. ratio (lb/ft) |
|---|---|---|
| 12 AWG copper wire | 0.029 | 0.020 |
| 1/2 in steel rebar (#4) | 1.00 | 0.668 |
| 1 in steel round bar | 3.98 | 2.67 |
| 2×4 lumber (dry softwood) | 1.7 | 1.15 |
| PEX 1/2 in tubing | 0.07 | 0.047 |
| Standard steel chain (1/4 in) | 0.55 | 0.37 |
Unit conversion factors used by the calculator:
| From | To | Multiply by |
|---|---|---|
| kg/m | lb/ft | 0.6720 |
| lb/ft | kg/m | 1.4882 |
| kg/m | g/cm | 10.000 |
| kg/m | lb/in | 0.0560 |
Example Problems
Example 1. A 10 m steel cable weighs 50 kg. The ratio is 50 / 10 = 5 kg/m. If you have a 200 kg spool of the same cable, the length is 200 / 5 = 40 m.
Example 2. Find the linear weight of a 3 mm copper wire. Density of copper is 8960 kg/m³. The cross-section area is π × (0.003)² / 4 = 7.069 × 10⁻⁶ m². The ratio is 8960 × 7.069 × 10⁻⁶ = 0.0633 kg/m, or about 0.0426 lb/ft.
FAQ
Is weight-to-length ratio the same as linear density? Yes. Linear density, mass per unit length, and weight-to-length ratio refer to the same value when gravity is constant. In everyday units, kg/m and lb/ft are used interchangeably for both.
Why does the round wire mode ask for density? A measured weight already accounts for the material. With diameter alone, you need density to know how much mass that volume holds. Steel and aluminum of the same diameter have very different ratios.
Does the ratio change with length? No. The ratio is constant for uniform material. A 1 m and a 100 m piece of the same wire share the same kg/m value.
Can I use this for rope, cable, or chain? Yes, as long as the product is uniform along its length. Use the Ratio mode with a known sample weight and length, or check the manufacturer’s spec sheet for the listed linear weight.
