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Air Bending Force Calculator (V-Die)

Estimate of the maximum V-die air bending force, to help select a press and tooling.

Equation and coefficients

F = k · UTS · L · t² / W, with F in N when UTS is in MPa and L, t and W are in mm.

F is the maximum bending force, UTS the ultimate tensile strength, L the bend length, t the thickness and W the V-die opening.

The coefficient k depends on the ratio of die opening to thickness. Values published by Misumi:

The calculator interpolates linearly between these points. Other sources use a fixed value near 1.42 for conventional air bending, so results with fixed coefficients are shown too.

Check against a textbook example

Groover, Example 20.2: sheet 3.2 mm thick and 44.5 mm wide, TS = 450 MPa, die opening D = 25 mm, V-bending. The book obtains 10,909 N with K_bf = 1.33. With those inputs and a manual k = 1.33, this calculator gives 10.9 kN. In automatic mode (W/t = 7.8) it uses k = 1.341 and gives 11.0 kN, 0.8% higher. ASM Handbook, vol. 14B, p. 309: plate 6.35 mm thick and 305 mm long, 30 tsi (≈ 414 MPa), die opening 8t (50.8 mm), k = 1.33. The book gives approximately 130 kN (15 tonf). With those inputs the calculator gives 133.2 kN (14.97 US tonf) in SI units and 133.1 kN in imperial units (60 ksi, 0.25 in, 12 in, 2 in). At W = 8t the automatic mode uses k = 1.330.

Scope and limits

• V-die air bending only. Bottoming and coining need different forces and manufacturer data.
• This is an estimate of the maximum air bending force. The force varies during the stroke and rises sharply if the bend reaches the bottom of the die. Springback, angle, radii and friction are not modeled explicitly.
• The W = 8 × t rule is a reference for mild steel; other materials and thicknesses often use other openings.
• The result depends on punch and die radii, lubrication and real variation in material properties. Leave a safety margin when choosing the press.
• The calculator adds no margin unless you enter one. Harsle, a press brake manufacturer, recommends 20% to 25% on its calculator page; confirm the value with your tooling manufacturer.

Sources

Textbooks and handbooks (primary sources)

• Groover, M. P., Fundamentals of Modern Manufacturing: Materials, Processes, and Systems, 3rd ed., John Wiley & Sons, 2007. Chapter 20, Eq. (20.8) and Example 20.2 (pp. 450–451). F = K_bf·TS·w·t²/D, with K_bf = 1.33 for V-bending (0.33 for edge bending), based on simple beam theory.
• ASM Handbook, Volume 14B: Metalworking: Sheet Forming, S. L. Semiatin (ed.), ASM International, 2006. Article “Press-Brake Forming”, pp. 307–318: Eq. 1 (p. 308) and sample calculation (p. 309). L = l·t²·k·S/s (tonf, in., tsi), with k from 1.2 (die opening 16t) to 1.33 (8t), for 90° V-bends without bottoming. DOI 10.1361/asmhba0005177.
• Tschaetsch, H., Metal Forming Practise: Processes – Machines – Tools, Springer, 2006 (translated by A. Koth from the 8th German ed., Vieweg, 2005). Chapter 16, Section 16.7.1 (p. 199): F_b = 1.2·b·s²·R_m/d_w. ISBN 978-3-540-33216-9.

Secondary sources

• Misumi Tech Central, “Press forming force (3): Bending force” (coefficient C1 by die opening; uses tensile strength)
• Jeelix, “Understanding Bending Force in Press Tools” (F = 1.42·Rm·L·t²/(1000·V) in kN, with worked example)
• ADH Machine Tool, “What Is The Rule Of 8 On A Press Brake?” (V = 8 × T for mild steel)

The secondary sources are from manufacturing and training. The value k = 1.33 at W ≈ 8 × t agrees with Groover and the ASM Handbook; Tschaetsch uses a single value of 1.2.

Last reviewed: November 2026.