Welcome to the “Bending Formulas” section of our website. Below you will find a variety of rotary-draw tube bending related formulas and calculations to help you evaluate your tube bending application. Please reference the “Table of Factors” for each of the formulas listed.

Table of Factors and Terms For Bending Formulas

B = degree of bend
E = feathered edge thickness
Fb = bend difficulty factor
Fd = “D” of bend
Fw = wall factor
Kr = constant for rigidity
Ks = constant for minimum clamp length
Kz = constant for feathered edge
Lc = clamp length
Lp = pressure die length
Mb = mandrel ball diameter
Md = mandrel nose diameter
Mm = mandrel body diameter
Mr = mandrel nose radius
Pe = percentage of elongation at arc
Pt = percentage of wall-thinning
Pw = wall thickness after thinning
R = centerline radius
Ri = inside radius
Ro = outside radius
S = maximum set-up depth
T = tube outside diameter
Ti = tube inside diameter
W = wall thickness
Wi = thickness of inside lamination
Wo = thickness of outside lamination

Tube inside diameter:

Ti = T – ( W x 2 )

Inside radius:

Ri = R – ( T / 2 )
Outside radius:

Ro = R + ( T / 2 )

Wall factor:

Fw = T / W

D” of bend:

Fd = R / T

Bend difficulty rating (the higher the value, the more difficult the bend is to make; rule of thumb only):

Where “Kr” = a constant for material rigidity (assign the same value to “Kr” as you would to calculate pressure die length; a value of 2 is suitable for most applications; click here for more information) and “n1” through “n4” are values to adjust the weight of each factor in the equation (see below for our recommended weighting):

General formula: Fb = [ ( n1 x Kr ) + ( n2 x Fw ) + ( ( n3 x B ) / 180 ) ) ] / [ n4 x Fd ]

Formula with recommended weighting: Fb = [ 2Kr + .2Fw + ( B / 180 ) ] / [ Fd ]

Note: A bend difficulty rating (calculated with our recommended weighting) of 7 or less indicates a bend that is relatively simple to produce with the rotary-draw method. Factors in excess of 7 typically require either additional precision in set-up or close attention during production in order to hold the set-up parameters.

Wall-thinning of extrados at outside radius after bending (rule of thumb only):

Where “Pt” = percentage of wall-thinning and “Pw” = targeted thickness of wall after thinning out from bending:

Pt = ( Ro – R ) / Ro

Pw = W x ( 1 – Pt )

Percentage of elongation at arc of the bend (rule of thumb only):

Pe = ( Ro / R ) – 1

Mandrel nose diameter for single-wall tubing:

Md = T – ( W x 2.21 )

Mandrel nose diameter for double-wall tubing:

Where “Wo” = wall thickness of outside lamination and “Wi” = wall thickness of inside lamination:

Md = ( T – ( Wo x 2 ) ) – ( Wi x 2.21 )

Mandrel nose radius:

if Fw .006* then E = T x Kz else E = .006*

* Inches. For metric applications, substitute .15 millimeters.
Clamp length:

Where “Kr” = a constant for material rigidity (assign a value of 2 to “Kr” for most applications; click here for more information) and “Ks” = a constant limiting the minimum clamp length depending upon the surface of the cavity (assign to “Ks” the value of 2 for smooth cavities and 1 for serrated cavities; click here for more information):

if ( T x ( Kr x 2.5) ) – R