Here is the whole set of everyday press brake bending formulas on one page, with what each symbol means and when you use it. Keep it by the machine. For the longer explanations, each one links to its own guide. Symbols used throughout: T is material thickness, R is inside radius, A is bend angle in degrees, K is the K-factor, and V is the V-die opening.
|
What |
Formula |
Notes |
|---|---|---|
|
K-factor |
K = t / T |
t is the distance from the inside face to the neutral axis. Typically 0.3 to 0.5. Detail. |
|
Bend allowance (BA) |
BA = (π / 180) × A × (R + K × T) |
Added to the inside (tangent) legs. The neutral-axis arc length. |
|
Outside setback (OSSB) |
OSSB = (R + T) × tan(A / 2) |
Tangent point out to the apex. |
|
Bend deduction (BD) |
BD = 2 × OSSB − BA |
Subtracted from the outside (apex) legs. BA vs BD. |
|
Flat length |
Flat = A + B + BA, or A + B − BD |
Same answer, measured from tangent or from apex. |
Every formula below uses these symbols. Units are millimetres and degrees unless stated.
|
Symbol |
What it means |
Unit / typical value |
|---|---|---|
|
T |
Material thickness (capital T). The thickness of the sheet before bending. |
mm. Example: 2 mm |
|
t |
Distance from the inside face of the sheet to the neutral axis (lowercase t). The neutral axis is the line inside the metal that neither stretches nor compresses when it bends. You only need t to work out K. |
mm. Always less than T |
|
R |
Inside bend radius. Measured on the inner face of the bend, not the centreline. |
mm. Example: 2.5 mm |
|
A |
Bend angle: how many degrees the flange turns from flat. Flat sheet is 0°, a right-angle corner is 90°. If your drawing gives the included angle between the two flanges, use A = 180° − included angle. |
degrees. Example: 90° |
|
K |
K-factor. The neutral axis position as a fraction of thickness: K = t ÷ T. See the K-factor guide. |
No unit. Typically 0.3 to 0.5 |
|
V |
V-die opening. The width of the groove in the bottom die. |
mm. Example: 16 mm |
|
BA |
Bend allowance. The length of the bend measured along the neutral axis. Added to the flat length when you work from the tangent points. |
mm |
|
BD |
Bend deduction. The amount you subtract from the sum of the outside lengths to get the flat length. |
mm |
|
OSSB |
Outside setback. The distance from where the bend starts (the tangent point) to the outside apex, the imaginary sharp corner. |
mm |
|
L1, L2 |
Flange lengths of the finished part. Outside lengths run to the apex, tangent lengths run to the start of the bend. |
mm |
|
F, L |
F is the approximate press force in tons. L is the length of the bend in metres. |
tons, metres |
These are shop rules, not exact physics, so treat them as a starting point and confirm against your machine and material.
A normal flat-pattern job runs in order. Settle your K-factor from a test bend, compute the bend allowance or bend deduction, build the flat length, then check your V-die with the rule of 8 and your tonnage against the chart before you load material. Springback is the one thing no formula nails exactly, so bend a sample and let the CNC correct the angle. For the why behind each number, start with K-factor and bend allowance vs bend deduction.
All five examples use the same part so you can follow the numbers from one step to the next: 2 mm mild steel, one 90° bend, 2.5 mm inside radius, and outside flange lengths of 50 mm and 80 mm. Round only at the end, then check the result against your CAD flat pattern.
Formula: K = t / T
Where: t is the distance from the inside face to the neutral axis, and T is the sheet thickness.
Example: The neutral axis sits 0.8 mm from the inside face of a 2 mm sheet, so K = 0.8 / 2 = 0.40. In the shop you rarely measure t directly. You take K from a test bend or from a chart for your material and radius, and the examples below use K = 0.40.
Formula: BA = (π / 180) × A × (R + K × T)
Where: A is the bend angle in degrees, R is the inside radius, K is the K-factor and T is the thickness.
Example: A = 90°, R = 2.5 mm, K = 0.40, T = 2 mm. K × T = 0.8, then R + K × T = 3.3. (π / 180) × 90 = 1.5708. BA = 1.5708 × 3.3 = 5.18 mm. That is the length of the bend along the neutral axis.
Formula: OSSB = (R + T) × tan(A / 2)
Where: R is the inside radius, T is the thickness and A is the bend angle in degrees.
Example: OSSB = (2.5 + 2) × tan(45°) = 4.5 × 1 = 4.50 mm. The bend starts 4.50 mm back from the outside corner.
Formula: BD = 2 × OSSB − BA
Where: OSSB is the outside setback from step 3 and BA is the bend allowance from step 2.
Example: BD = 2 × 4.50 − 5.18 = 3.82 mm. This is what you subtract from the outside lengths.
Formula: Flat = L1 + L2 + BA (tangent lengths), or Flat = L1 + L2 − BD (outside lengths)
Where: L1 and L2 are the two flange lengths, BA is the bend allowance and BD is the bend deduction.
Example, outside lengths: L1 = 50 mm and L2 = 80 mm run to the outside corner. Flat = 50 + 80 − 3.82 = 126.18 mm.
Example, tangent lengths: Take OSSB off each leg: L1 = 50 − 4.50 = 45.5 mm and L2 = 80 − 4.50 = 75.5 mm. Flat = 45.5 + 75.5 + 5.18 = 126.18 mm.
Both routes give 126.18 mm. That is the blank length to cut.
BA = (π / 180) × A × (R + K × T), where A is the bend angle in degrees, R is the inside radius, K is the K-factor and T is the thickness. It is the arc length of the bend along the neutral axis, and you add it to the tangent flange lengths to get the flat.
As a rule of thumb, air bending mild steel over a standard die needs about 7 to 8 tons per metre for every 1 mm of thickness, with a V-die around eight times the thickness. Stronger material and coining need much more. For a real job, use the tonnage chart for your machine and die, since the die opening and material strength change the number.