Machining & Metalworking

BendMatrix

Precision Sheet Metal Bend Allowance, Bend Deduction & Flat Pattern Engine

Bend Parameters

in
in
Default rule of thumb: Inside Radius ≈ Material Thickness
deg (°)
The excluded angle the bend sweeps through, i.e. 180° minus the angle enclosed between the finished flanges. 90° for a right-angle flange; a 45° bend leaves flanges enclosing 135°.
ratio (t/T)
Neutral axis ratio: 0.33 (tight bend, radius near material thickness) to 0.50 (large radius / coining)
in
Measured to the outside apex (mould line), not the inside leg
in
Measured to the outside apex (mould line), not the inside leg

Interactive Cross-Section & Neutral Axis

Live Render
Sheet Metal Body Neutral Axis (K-Line) Flange Legs
Required Flat Pattern Length 4.885 in L₁ + L₂ − BD
Bend Allowance (BA) 0.125 in Arc along neutral axis
Bend Deduction (BD) 0.115 in (2 × OSSB) − BA
Outside Setback (OSSB) 0.120 in tan(θ/2) × (T + R)
Inside Setback (ISSB) 0.060 in tan(θ/2) × R
Neutral Axis Shift (t) 0.020 in K × T from inside edge

Understanding Sheet Metal Bend Calculations

When sheet metal is bent on a press brake, the material undergoes intense plastic deformation. The outer surface of the bend stretches under tension, while the inner surface compresses. Between these two opposing forces lies an imaginary boundary called the Neutral Axis — a layer where the material experiences zero stress and retains its original unbent length.

What is K-Factor?

The K-Factor represents the location of the neutral axis expressed as a ratio of neutral axis depth (t) to total material thickness (T):

K = t / T

Because metal compresses more readily than it stretches, the neutral axis shifts inward toward the inside bend radius. In practical shop operations, K-Factor typically ranges between 0.33 and 0.50 depending on material composition, bend angle, tooling, and forming method (Air Bending vs. Bottoming vs. Coining).

Bend Allowance vs. Bend Deduction

Fabricators use two distinct methods to convert 3D CAD dimensions into flat sheet metal cut patterns:

  • Bend Allowance (BA): The actual arc length along the neutral axis around the bend. Calculated as:
    BA = (π / 180) × θ × (R + K × T)
    Throughout this page θ is the excluded bend angle: the angle the flange turns through, which is 180° minus the angle enclosed between the finished flanges. The two are equal only at 90°, so a 45° bend is entered as 45 even though its flanges enclose 135°. Entering the enclosed angle instead makes the arc term far too long, the deduction far too large, and the blank too short to bend.
  • Bend Deduction (BD): The amount subtracted from the sum of the outside flange dimensions to arrive at the exact flat layout length:
    BD = (2 × OSSB) − BA

Step-by-Step Flat Pattern Formula Reference

Parameter Symbol Mathematical Formula Shop Application
Bend Allowance BA (π / 180) × θ × (R + K × T) Length of material needed to form the radius curvature
Outside Setback OSSB tan(θ / 2) × (T + R) Distance from apex of outer flange extensions to bend line
Bend Deduction BD (2 × OSSB) − BA Value subtracted from (Flange A + Flange B) for CNC shearing
Flat Pattern Length Lflat L₁ + L₂ − BD Total unbent length of raw metal stock required

Forming Method Guidelines

Air Bending

The punch contacts the metal at three points without pressing it into the bottom of the V-die. Material springback is highest. Typical K-factor: 0.33 – 0.50, set mainly by inside radius relative to thickness: 0.33 – 0.40 where R is up to T, 0.40 – 0.45 where R runs from T to 3T, and 0.50 above 3T. Air bending therefore spans the whole practical range, and K alone does not tell you which forming method produced a part.

Bottom Pressing (Bottoming)

The metal is pressed firmly against the V-die surfaces under higher tonnage. Springback is reduced. Typical K-factor: 0.42 – 0.45.

Coining

Extreme tonnage penetrates the neutral axis, eliminating springback entirely. Neutral axis shifts nearly to center. Typical K-factor: 0.48 – 0.50.

Frequently Asked Questions

Bend allowance is the length of material consumed in a bend, which determines the flat blank size. It depends on material thickness, bend radius, bend angle, and the K-factor — the position of the neutral axis within the thickness. This tool computes bend allowance, bend deduction, and flat length.

What is the K-factor and why does it vary?

K-factor is the ratio of the neutral axis position to material thickness. During bending the outside stretches and the inside compresses; the neutral axis shifts inward. It typically ranges from 0.33 to 0.5 depending on material, temper, bend radius relative to thickness, and forming method. Air bending, bottoming, and coining all give different values.

What K-factor should I start with?

0.44 is a reasonable default for mild steel air-bent with a generous radius, and 0.33 is common for tight bends where the radius approaches material thickness. These are starting points, not answers. Bend a test coupon in your actual material on your actual press and back-calculate the real K-factor.

What is the difference between bend allowance and bend deduction?

Bend allowance is the arc length added along the neutral axis. Bend deduction is the amount subtracted from the sum of the two flange lengths measured to the apex. They describe the same geometry from different directions — use whichever matches how your drawing dimensions the part.