K-Factor Calculator (sheet metal neutral axis from a test bend)

Understanding the K-factor calculator — concept and principle

This calculator finds the sheet-metal K-factor from a test bend: you bend a strip of known flat length, measure the two outside flange lengths, and it works out where the neutral axis lies. It also returns the bend allowance, bend deduction, outside setback and Y-factor, which you can then use to lay out flat patterns for parts in the same material, thickness and tooling.

Metal stretches outside and squeezes inside; K says how far into the thickness the unstretched layer lies.

How it is calculated

Outside setback OSSB = tan(θ/2) × (R + T)

Bend allowance BA = flat length − (A − OSSB) − (B − OSSB)

K = (BA ÷ θ − R) ÷ T, with θ in radians

Bend deduction BD = 2 × OSSB − BA; neutral axis from the inside face = K × T; Y-factor = K × π/2

T is the thickness, R the inside bend radius, A and B the measured outside flange lengths, all in mm.

The principle

When sheet metal bends, the outside stretches and the inside compresses. Somewhere in between is a layer, the neutral axis, whose length does not change. The flat blank must be as long as the parts of the flanges plus the arc length of the neutral axis through the bend. That arc is θ(R + KT), so a measured test bend lets you solve for K. K always lies between 0 and 0.5, because the neutral axis moves towards the inside of the bend.

Worked example

Default inputs: T = 2 mm, R = 2 mm, 90°, A = B = 50 mm, flat length 96.4 mm.

OSSB = tan(45°) × (2 + 2) = 4 mm.
BA = 96.4 − (50 − 4) − (50 − 4) = 4.4 mm.
K = (4.4 ÷ 1.5708 − 2) ÷ 2 = (2.8011 − 2) ÷ 2 = 0.4006.
BD = 2 × 4 − 4.4 = 3.6 mm; neutral axis = 0.4006 × 2 = 0.801 mm from the inside face.
Y-factor = 0.4006 × π/2 = 0.6292; plausibility: within the physical range 0–0.5.

Each point is the calculator re-run with only “Flat blank length before bending (mm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Flat blank length before bending (mm)	K-factor
24.1	-22.6132
48.2	-14.942
72.3	-7.2707
96.4	0.4006
120	8.0718
145	15.7431
193	31.0856

How to read the result

Typical K-factors are often around 0.3 to 0.5, smaller for tight bends and larger for generous radii. Use the K-factor only for the same material, thickness, tooling and bending method, since all of these change it. A value outside 0–0.5 points to a measurement error.

Common mistakes

Measuring inside instead of outside flange lengths.
Entering the bend angle as the included angle instead of the angle bent through.
Measuring a strip that sprang back without re-measuring the actual angle.
Using one K-factor for every material and thickness.

Keep in mind: K-factors depend on material, grain direction, tooling and process. Confirm flat patterns with test parts before production.

Frequently asked questions

What is the neutral axis?

The layer inside the bend that neither stretches nor compresses.

What is the difference between bend allowance and bend deduction?

Bend allowance is the arc length added for the bend; bend deduction is what you subtract from the sum of the outside flange lengths.

What K-factor should I start with?

Start from your CAD or shop default and replace it with a measured value from a test bend.

What is the Y-factor?

An alternative form used by some CAD systems, equal to K × π/2.

Sources: Standard sheet-metal layout relations (OSSB = tan(θ/2)(R + T), BA = θ(R + KT), BD = 2·OSSB − BA)

Checked 9 Nov 2026. Sheet-metal layout relations (OSSB = tan(θ/2)(R + T), BA = θ(R + KT), BD = 2·OSSB − BA): standard formula.

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