Bending Guide
How to Calculate Bend Allowance
The formula behind every flat pattern calculation, a worked example, and how it feeds into cutting the right size blank.
Bend allowance is the number that tells you how much material a bend actually consumes. Skip it, or estimate it badly, and a flat pattern comes out the wrong length — the part ends up oversized, undersized, or just doesn't sit right after folding. The good news: it comes from four inputs you'll already have on hand for any bend — thickness, inside radius, bend angle, and K-factor.
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The bend allowance formula
Bend allowance (BA) is the arc length of the neutral axis — the layer inside the material that neither stretches nor compresses — as it passes through the bend:
Where:
- Angle — the bend angle in degrees (90° for a standard right-angle fold).
- R — the inside bend radius, in the same units as thickness.
- K — the K-factor, the position of the neutral axis as a fraction of thickness from the inside surface. See K-factor explained.
- T — material thickness.
The π / 180 term simply converts the angle from degrees to radians so the arc-length maths works out correctly.
Worked example
Take a 90° bend in 2mm material, with a 2mm inside radius and a K-factor of 0.44 (a common general-purpose default):
Step by step
- BA = (π / 180) × 90 × (2 + 0.44 × 2)
- BA = 1.5708 × (2 + 0.88)
- BA = 1.5708 × 2.88
- BA ≈ 4.52mm
That 4.52mm is the length of neutral-axis material consumed by this one bend. On its own it's rarely the number you need for cutting — for that you convert it into a bend deduction and subtract it from your flange lengths. See bend allowance vs bend deduction for that next step, or how to calculate the full flat pattern length.
Why K-factor and radius matter so much
Both R and K sit inside the same bracket, so they trade off directly: a tighter radius or a lower K-factor both shrink the bend allowance, meaning less material gets "used up" by the bend and more of the flat blank survives as usable flange. Get either one wrong and the error compounds across every bend in the part — which is exactly why measuring your own K-factor from a test bend (rather than trusting a generic default) pays off on repeat jobs.
Common mistakes
- Using a generic K-factor for a precision part. 0.44 is a reasonable starting point, but your actual tooling, material and bend radius all shift the real value.
- Mixing inside and outside radius. The formula uses the inside bend radius — using an outside radius by mistake throws the result off.
- Forgetting to convert angle to radians. If you're calculating by hand rather than with a tool, missing the
π / 180conversion gives a wildly wrong number. - Applying one bend allowance to a multi-bend part. Each bend needs its own BA calculated from its own angle and radius, then summed.
Frequently asked questions
What is bend allowance in sheet metal?
It's the arc length of the neutral axis through a bend — the length of material the bend itself consumes. It's the building block for working out how much flat material a folded part needs.
What's the bend allowance formula?
BA = (π/180) × Angle × (R + K × T), where Angle is the bend angle in degrees, R is inside bend radius, K is K-factor, and T is material thickness.
Is bend allowance the same as bend deduction?
No — bend allowance is the developed length of the bend itself. Bend deduction is what gets subtracted from the sum of the outside flange dimensions to reach the correct flat length. They're related but calculated from different reference points.
Do I need bend allowance for every bend in a part?
Yes — a part with multiple bends needs a bend allowance, and resulting bend deduction, calculated for each bend individually, then summed for the total flat pattern length.