Calculate the length of wire, bar, pipe or flat stock from its weight, or the weight from its length, using material presets like steel and aluminum.

Total weight can be a mass (kg, lb) or a gravitational force (N, lbf); choose under Total-weight basis.

Result units

Weight to Length Formula

For uniform material, length L = mass m รท linear mass density ฮป, where ฮป = density ฯ ร— cross-sectional area A. If weight W is gravitational force in newtons instead, first use m = W/g. Choose the matching Total-weight basis in the calculator.

L = W / 9.81 / D / A
  • Where L is the material length (m)
  • W is the total weight (N) 
  • D is the density (kg/m3) 
  • A is the cross-sectional area (m2) 

For gravitational force W in N and the explicit assumption g = 9.81 m/sยฒ, L = W/(9.81 ร— ฯ ร— A). For mass in kg, use L = m/(ฯ ร— A) without dividing by gravity. Select Direct cross-sectional area and Custom density to reproduce the examples below.

Weight to Length Conversion Table (Steel, ฯ = 7850 kg/mยณ; A = 1.000 inยฒ; g = 9.81 m/sยฒ)
Weight (N) Length (m) Length (ft)
100.2010.660
250.5031.651
501.0063.302
751.5104.953
1002.0136.604
1503.0199.905
2004.02613.207
2505.03216.509
3006.03819.811
4008.05126.414
50010.06433.018
75015.09649.527
100020.12866.036
150030.19299.054
200040.255132.071
250050.319165.089
300060.383198.107
400080.511264.143
5000100.638330.179
10000201.277660.357
* Rounded to 3 decimals. Assumptions: steel (ฯ = 7850 kg/mยณ), cross-sectional area A = 1.000 inยฒ = 0.00064516 mยฒ, gravity g = 9.81 m/sยฒ. Formula: L = W / (ฯยทgยทA). Under these assumptions: ฯยทgยทA = 49.6828038600 N/m, so 1 N โ‰ˆ 0.02012769 m โ‰ˆ 0.06603572 ft. In the calculator choose Direct cross-sectional area 1 inยฒ, steel density 7850 kg/mยณ, force in N and g = 9.81 m/sยฒ.

How to Calculate Weight to Length?

The following two example problems outline the steps and information needed to calculate the Weight to Length.

Example Problem #1

  1. First, determine the total weight (N).
    • The total weight (N) is calculated to be 500.
  2. Next, determine the density (kg/m3).
    • The density (kg/m3) is measured to be 3.
  3. Next, determine the cross-sectional area (m2).
    • The cross-sectional area (m2) is found to be 5.
  4. Finally, calculate the Weight to Length using the formula above: 

L = W/9.81/D/A

The values provided above are inserted into the equation below and computed.

L = 500/(9.81 ร— 3 ร— 5) โ‰ˆ 3.397893 m. These are illustrative inputs; choose force in N, custom density 3 kg/mยณ and direct area 5 mยฒ.

Example Problem #2

The variables required for this problem are provided below:

total weight (N) = 600

density (kg/m3) = 4

cross-sectional area (m2) = 8

Choose Length, Direct cross-sectional area, Custom density 4 kg/mยณ, area 8 mยฒ, and Gravitational force 600 N with the article gravity assumption 9.81 m/sยฒ.

L = 600/(9.81 ร— 4 ร— 8) โ‰ˆ 1.911315 m.