Need an answer now? Use the free online section modulus and moment of inertia calculator. No download needed, for round, square and rectangular tube and solid bar.
Section Modulus Calculator and Bending Formulas
Calculate area, moment of inertia and section modulus for the shapes you bend, with the tube bending formulas engineers use every day.
- Squares, rounds and half rounds
- Triangles, rectangles and trapezoids
- Hexagons, octagons and more
- Common tube bending formulas
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Why Section Modulus Matters in Tube Bending
Section modulus measures how strongly a cross-section resists bending. In tube bending, it helps estimate the bending moment, and so the machine capacity a part needs. Tube benders are usually rated by a maximum tube size and wall in mild steel. Comparing section modulus (and material yield strength) lets you check whether a different size, shape or alloy is within a machine's capacity.
Common Section Formulas
- Round tube: I = π(D⁴ − d⁴) ÷ 64, and S = π(D⁴ − d⁴) ÷ (32D), where D is the outside diameter and d the inside diameter
- Square tube: I = (B⁴ − b⁴) ÷ 12, and S = (B⁴ − b⁴) ÷ (6B), where B is the outside width and b the inside width
- Rectangular tube (bending about the height): I = (BH³ − bh³) ÷ 12, and S = (BH³ − bh³) ÷ (6H)
Everyday Tube Bending Formulas
- D of bend = centerline radius ÷ tube OD. A "2D" bend has a CLR twice the OD.
- Wall factor = tube OD ÷ wall thickness. Higher numbers mean thinner walls that need more tooling support.
- Arc length of a bend = π × CLR × bend angle ÷ 180. Add the arcs and straights for the developed length.
- Approximate outside wall after bending = t × 2R ÷ (2R + D), where t is the original wall, R the CLR and D the OD
D of bend and wall factor together decide what tooling a bend needs.
Frequently Asked Questions
What shapes does the section modulus calculator cover?
Squares, rounds and half rounds, triangles, rectangles and trapezoids, hexagons, octagons and more, plus common tube bending formulas.
What is D of bend?
The centerline radius divided by the tube OD. For example, a 1.5 in OD tube on a 3 in CLR is a 2D bend.
What is wall factor?
Tube OD divided by wall thickness. Along with D of bend, it tells you how difficult a bend is and whether you need a mandrel and wiper die.