Calculate the warping constant Cw of an I-section from flange and web dimensions, or from Iy and flange spacing, plus the torsional constant J.

Equal flanges and a centered web, modeled as rectangular plates without fillets or holes.

Optional settings

Warping Constant Formula

For a doubly symmetric I-section, the calculator uses the approximate geometric relationship below. Geometry mode uses equal rectangular flanges and a centered web, without fillets or holes. It is not a member strength or stability check.

Cw ≈ Iy × h₀² ÷ 4; reverse spacing h₀ ≈ √(4 × Cw ÷ Iy).

Variables:

  • Cw is the warping constant (mm6)
  • Iy is the weak-axis second moment of area (mm⁴ or in⁴)
  • h₀ is the distance between flange centroids (mm or in)
  • Cw has dimensions of length⁶; all entered units must be converted consistently

Multiply weak-axis Iy by flange-centroid spacing squared and divide by four. Geometry mode computes h₀ = d − tf and Iy = [2tf × b³ + (d − 2tf) × tw³] ÷ 12. It also reports thin-plate J ≈ [2b × tf³ + (d − 2tf) × tw³] ÷ 3; this approximation becomes less reliable for thick plates.

What is a Warping Constant?

The warping constant is a geometric section property used in restrained-warping torsion analysis. Its units are length⁶. Elastic modulus E combines with Cw in the warping rigidity E × Cw; E is not part of the geometric Cw calculation. Saint-Venant torsion uses the separate torsional constant J. Use verified section properties and appropriate analysis for structural design.

How to Calculate Warping Constant?

The following steps outline how to calculate the Warping Constant.

  1. First, choose geometry, known Iy and spacing, or reverse spacing mode.
  2. For geometry, enter flange width b, total depth d, equal flange thickness tf, and web thickness tw. Require d greater than 2tf and tw smaller than b.
  3. For known-property mode, enter weak-axis Iy and flange-centroid spacing h₀; for reverse mode, enter Cw and Iy.
  4. Use Cw ≈ Iy × h₀² ÷ 4, or h₀ ≈ √(4 × Cw ÷ Iy) for reverse spacing.
  5. Select Calculate. Cw is reported in mm⁶ or in⁶, and spacing in mm or in. Unit changes convert the entered quantity.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Weak-axis Iy = 100,000,000 mm⁴

Flange-centroid spacing h₀ = 300 mm

Approximate Cw = 100,000,000 × 300² ÷ 4 = 2.25 × 10¹² mm⁶. Reverse-solving these same Cw and Iy values gives h₀ = 300 mm. The 90%/110% spacing sensitivity holds Iy fixed; it is not a complete redesign.